Dispute Resolution Institutions
and Strategic Militarization¤
Adam Meirowitzy
Massimo Morelliz
Kristopher W. Ramsayx
Francesco Squintani{
First draft, November 2014 — This draft: April, 2016.
Abstract
Engagement in a costly and destructive war can be understood as the ‘punishment’
for entering into an international dispute. Institutions that reduce the chance that
disputes lead to wars make this punishment less severe. This may incentivize hawkish
foreign policy choices and militarization, and potentially o¤set the acts of peacebrokering institutions. We provide a simple model in which international support
for unmediated peace talks, while e¤ective in improving the chance of peace for a
given distribution of military strength, ultimately leads to the emergence of more
disputes and to higher incidence of con‡ict outbreak. Happily, we …nd that not all
con‡ict resolution institutions su¤er from these, apparently paradoxical, but actually
quite intuitive drawbacks. We identify a form of third-party mediation inspired by
the celebrated work by Myerson, and show that it can e¤ectively broker peace in
disputes once they emerge and also avoid perverse militarization incentives.
¤
We thank audiences at the Institute for Advanced Studies in Princeton, the Con‡ict Conference at
Northwestern University, and Institutions and Political Economy Conference in Alghero, Italy, and at political economy seminars at University of Utah Business School, Stanford University, Princeton University,
University of Rochester, University of Warwick, London School of Economics, as well as John Duggan,
Steve Callander, Debraj Ray, Ronny Razin and Tomas Sjöström for their valuable comments, and Mike
Rubin for very valuable assistance.
y
Princeton University, Department of Politics.
z
Bocconi University, IGIER, and NBER.
x
Princeton University, Department of Politics.
{
Warwick University, Department of Economics.
1
1
Introduction
The assessment of which institutions e¤ectively resolve disputes that might otherwise lead
to military con‡ict is of fundamental importance and has been addressed in several investigations.1 These studies take the emergence of a dispute as the starting point of the
analysis, and ask questions of the sort: given a dispute, how will di¤erent institutions such
as mediated or un-mediated peace talks likely in‡uence the outcome? This paper broadens
the scope of analysis. Instead of taking disputes as given, we ask: how are disputes likely to
emerge, given the players’ expectations about the con‡ict resolution institutions adopted
by the international community? Intuitively, a bloody, costly and wasteful con‡ict can be
understood as the eventual ‘punishment’ for militarizing and entering a dispute in the …rst
place. Hence, institutions that minimize the chances that crises lead to con‡ict may breed
perverse militarization incentives, and lead to the emergence of more disputes. Evaluating this possibility is an important part of forming an assessment of the overall value of
con‡ict-resolution institutions.2
The payo¤ of our theoretical model is that it clari…es these nuanced considerations.
We show that the analysis of the connection between dispute resolution institutions and
militarization incentives may signi…cantly challenge established views. Speci…cally, we …nd
that un-mediated peace talks, while e¤ective in reducing the chance that an emergent
dispute turns into open warfare, may provide perverse incentives for militarization and
precipitate the emergence of disputes. This negative e¤ect can be so strong, that the
1
Much recent theoretical work analyzes the e¤ectiveness of peace talks and third-party mediation as
con‡ict resolution institutions (e.g., Bester and Wärneryd 2006, Fey and Ramsay 2010, Hörner, Morelli,
and Squintani 2015, Kydd 2003). Others considers how various forms of direct diplomacy can in‡uence the
probability of con‡ict (e.g., Baliga and Sjöström 2004, Ramsay 2011, Sartori 2002, Smith 1998). Bercovich
and Jackson (2001) and Wall and Lynn (1993) review the vast empirical literature on the e¤ectiveness of
mediation as a con‡ict resolution institution.
2
The possibility that well-meaning third party intervention may lead to perverse incentives for the
emergence of disputes is a concrete concern for academics and practitioners. For example, Kuperman
(2008) presents evidence that expectations of humanitarian military intervention have emboldened weaker
groups to trigger con‡ict against dominant entities (see also De Waal, 2012). Kydd and Straus (2010)
provide a theoretical model of this issue. Unlike us, they do not consider mediation and do not endogenize
militarization choices in their analysis.
1
resulting total probability of warfare becomes higher than it would be in a world in which
un-mediated peace talks are not supported by the international community.
The reasoning behind this unexpected result is actually quite simple. Take as the
starting point of the analysis a …xed dispute that has already emerged. The players’
militarization decisions are sunk, and signi…cant resources are devoted to guarding their
secrecy. Hence, the players are uncertain about each other’s strength.3 This uncertainty
leads to wars: strong players who do not know their opponents’ strength are willing to take
their chances and …ght.4 Informative communication in un-mediated peace talks reduces
the uncertainty, and hence decreases the chance that the dispute evolves into open warfare.5
Let us now consider the whole strategic interaction, and analyze how the expectation
that a future dispute will be dealt with un-mediated peace talks shape the incentives
for militarization. Un-mediated peace talks reduce the expected downside of arming and
entering into the dispute, as they reduce the chance of an eventual destructive con‡ict.
By reducing uncertainty, un-mediated peace talks also increase the expected bene…t of
militarization, as they make the opponent more willing to acquiesce to the player’s demands,
knowing that the latter is highly militarized. In sum, potential players have a greater
incentive to militarize and enter disputes, so that more disputes emerge. Although each
dispute is less likely to evolve into open warfare, the increased emergence of disputes turns
out to lead to more wars, in our model.
3
This is hardly disputable, given the extent to which States engage in espionage and counter-espionage,
as well as manipulating beliefs about their actual military strength. Among some famous episodes of
manipulations, Soviets ‡ew jets with fake missiles in parades, and Serbians put cardboard tanks in their
towns during NATO-led air strikes. Likewise, the prospect of the Star Wars program sponsored by the
Reagan administration were grossly exaggerated.
4
Militarization cannot lead to deterrence if it is a hidden action, as there cannot ever be an equilibrium
in which players militarize and war does not take place, in any reasonable model of con‡ict. In anticipation
that war will not take place, each player would deviate at the militarization stage and secretly choose
to devote the resources earmarked to militarization to welfare enhancing means (see the discussion in
Meirowitz and Sartori, 2008, and Jackson and Morelli, 2009). Indeed, it is intuitive that observability of
militarization is crucial for deterrence. In the words of Dr. Strangelove: “Of course, the whole point of a
Doomsday Machine is lost, if you *keep it a secret*!”
5
This result was …rst proved formally by Baliga and Sjöström (2004). As we explain later in details,
our analysis of un-mediated peace talks signi…cantly advances their …ndings. We identify reasons di¤erent
from the ones they singled out, for which communication reduce the chance of con‡ict in emerged disputes.
2
Given this apparently paradoxical insight, it is natural to ask whether all con‡ict resolution institutions su¤er from these same drawbacks. Happily, we …nd that this is not the
case. We identify a type of third-party intermediation inspired by the celebrated work by
Roger Myerson (1979, 1982) and hence called ‘Myerson mediation’ here, that improves the
chances of peace-brokering in emerged disputes more e¤ectively than un-mediated peace
talks, and also makes the players less willing to militarize. Importantly, this is despite the
fact that the mediator’s mandate cannot realistically include the objective of preventing
militarization and dispute emergence, because the players’ militarization decisions are sunk
when the mediator is called in to deal with the ongoing dispute.
Myerson mediation is conducted by third parties who do not have access to privileged
information, nor to the military or …nancial capability to enforce peaceful settlements.
Hence, the mediator’s role is only to facilitate negotiations by managing the ‡ow of information among the players. In practice, this is achieved mainly by setting the agenda and
modes of communication of the peace talks. In the taxonomy of Fisher (1995), Myerson
mediation is a form of ‘pure mediation’, whereas it is closer to ‘procedural mediation’ in
the terminology by Bercovich (1997). A review of the literature …nds compelling evidence
that this form of mediation is often employed.6
We conclude the analysis with a deep and general result. Myerson mediation strategies,
while designed to only give the highest chance of peace in emerged disputes, also provide the
best possible incentives against dispute emergence, within the class of institutions that do
not give intermediaries access to privileged information, nor to a budget to make transfers
6
Scholars in international relations have identi…ed two main types of mediation: communication facilitation mediation, and procedural mediation. The latter is descriptively the closest to this paper’s model,
because players pre-commit to let the mediator set the procedure for the dispute resolution process. In
practice, this seriously impedes their capability to negotiate, or renegotiate an agreement outside the mediation process. Procedural mediation is widely adopted as it is perceived to be the most e¤ective form of
mediation. Since World War I, over 30 territorial disputes have been brought to an international adjudication body (Huth and Allee 2006) which took the form of procedural mediation. Among all other cases
in which mediation was involved (roughly …fty percent of cases according to Wilkenfeld et al. 2005), many
can be coded as procedural mediation. Also, 427 disputes have been brought up for ‘arbitration’ within
the World Trade Organization between 1995 and 2011 (WTO database). This form of arbitration shares
similarities with procedural mediation, because the enforcement is based on the actions of individual WTO
member States.
3
to players. In other terms, the narrow mandate of Myerson mediators does not entail any
welfare loss.
The reasoning behind this result is more complex than the intuition behind the drawbacks of un-mediated peace talks. The …rst step in our argument is the application of the
‘revelation principle’ by Roger Myerson (1982). In our context, this general result implies
that an optimal way to organize the third-party intermediation we consider here is as follows. First, the players report their information independently to the mediator. Second, the
mediator submits a settlement proposal to the players for their independent approval. The
revelation principle tells us there is an equilibrium that maximizes the chance of peace,
in which the settlement proposal strategies by the mediator are chosen so as to ensure
that players will reveal all their private information to the mediator, in anticipation of the
settlements that the mediator will propose.
In practice, the mediator sets the agenda to “collect and judiciously communicate select
con…dential material” (Rai¤a, 1982, 108–109). The role for mediation that we identify is
performed by holding private and separate caucuses with the players. This practice of
‘shuttle diplomacy’ has become popular since Henry Kissinger’s e¤orts in the Middle East
in the early 1970s and the Camp David negotiations mediated by Jimmy Carter. The
mediator conveys information back and forth between parties, providing suggestions for
moving the con‡ict toward resolution (see, for example, Kydd, 2003). As is standard in
applied theory, the revelation principle allows us to conveniently summarize the outcomes
of the equilibrium play in these more complex caucuses.
The second step of our evaluation of Myerson mediation consists in the precise characterization of the optimal settlement proposal strategies. We …nd that a stronger, more
militarized player must receive more favorable terms of settlement on average, than a weaker
one. Otherwise, the stronger player will never accept the proposed settlements, preferring
instead to wage war in the expectation that its eventual payo¤ will be larger. As a consequence, the mediator faces the task of choosing settlements that make sure that weak
4
players do not pretend to be stronger, when reporting their information in the …rst stage
of the intermediation. Thus, the mediator proposal strategies are chosen to minimize the
expected reward for a weak player to pretend that it is strong, when, in fact, it did not militarize. As an unintended consequence, they also minimize the incentives for a weak player
to militarize and become strong. Hence, the mediators we consider here not only improve
the chance that disputes are resolved peacefully relative to un-mediated peace talks. They
also keep in check the potential players incentives to engage in disputes and to militarize.7
2
Literature Review
This paper pushes for a reformulation of the study of con‡ict and institutional design and
draws a …ner distinction between di¤erent ways of fostering peace for a given dispute; some
are also bene…cial at reducing militarization while others may generate o¤setting negative
incentives.
Our results are related to the study of contests and appropriation (see Gar…nkel and
Skaperdas, 1996, for a survey). In such a conceptualization, strategic militarization is
treated as an arms race to prepare for a sure con‡ict where the military capacities of
each country in‡uence the war-payo¤s through a contest function. Instead, in our model
militarization increases the expected payo¤ of …ghting in a dispute. The goal is expected
utility maximization in a game in which war is not a foregone conclusion. Players may
either reach a settlement or …ght, and the militarization choice has strategic e¤ects on both
settlements, the odds of …ghting and the payo¤s from …ghting.
There is also a recent body of formal theory on endogenous militarization in the shadow
of negotiation and war …ghting. Meirowitz and Sartori (2008) connect militarization with
negotiation but provide only results on the impossibility of avoiding con‡ict. They do not
study optimal mechanisms or make comparisons across di¤erent institutions. Jackson and
7
As we explain in the conclusion, these results may also be useful for the study of optimal taxation with
mechanism design.
5
Morelli (2009) consider militarization and war, but States observe each other’s investment
decisions prior to negotiations, and thus there is no incomplete information in their analysis. Akcay, Meirowitz and Ramsay (2012) study investment that in‡uences the value of
agreement for one player, and disagreement for the other, prior to the play of a mechanism.
The investments are over a private value component, whereas here the investment by either
player in‡uences the payo¤s of both players.
Our study of Myerson mediation falls within the large literature of mechanism design
that dates back at least to Hurwicz (1960). But unlike mechanisms used in economics
applications, the mediators studied here do not have the power to enforce their settlement
decisions. The key distinguishing feature of international disputes is that the players involved are sovereign entities, and hence there is no legitimate or recognized third party to
which they can credibly delegate decision and enforcement power (see e.g. Waltz, 1959).
For this reason, mechanism design models of international relations should dispense with
the assumption that the mediator can enforce her decisions, and focus on self-enforcing
mechanisms instead.8
In a more distantly connected literature, militarization is assumed to be observable, and
is viewed as a deterrent or a signal. Gar…nkel (1990) focuses on a simple repeated armament
setting that illustrates this role, and Powell (1993) provides an example of the conditions
under which endogenous observable armament can lead to e¤ective deterrence. Similarly,
Fearon (1997) argues that observed military expenditures can be a form of costly signaling.
Collier and Ho-er (2006) consider the signaling and deterrent e¤ects of armament as
competing mechanisms explaining levels of post-con‡ict military expenditures in countries
that have recently experienced a civil war. Chassang and Padró (2010) show that while
weapons have deterrence e¤ects under complete information in a repeated game, when
adding strategic uncertainty it is no longer true that there is a monotonic relationship
8
Among the few papers studying self-enforcing mechanisms in contexts di¤erent from international
relations, see Matthews and Postlewaite (1989), Banks and Calvert (1992), Cramton and Palfrey (1995),
Forges (1999), Skreta (2006), Compte and Jehiel (2009), and Goltsman, Hörner, Pavlov and Squintani
(2009).
6
between the size of an arsenal and the degree of deterrence in equilibrium. For very di¤erent
reasons, also in our model the e¤ects of endogenous militarization incentives on peace are
non-monotonic. Taken together with the point made in footnote 4, this work highlights the
importance of whether militarization is observable or not, for the study of deterrence. It is
then natural to ask whether mechanisms that improve observability (such as espionage or
military inspections) would lead to more or less militarization, deterrence, or con‡ict. We
leave these questions for future research.
3
Un-mediated Peace Talks and Militarization
In this section we develop the baseline model of militarization and negotiation and augment
it to allow for un-mediated communication, so as to show that un-mediated peace talks may
breed perverse incentives for militarization. Un-mediated peace talks help resolve disputes
by allowing for settlements that would not otherwise be possible when the players are strong.
But the expectation that war is less likely if a dispute emerges leads to an increased incentive
for the players to militarize. As a result, we show that for some model parameters, unmediated peace talks can increase the overall war probability when militarization decisions
are taken into account.
The Baseline Model of Militarization and Negotiation The analysis starts with the
description of a model of militarization and negotiation, without mediated or un-mediated
peace talks. Ideally, this model represents a world in which there is no support for these
initiatives by the international community. The model introduced is deliberately minimal
so that its augmentation to include communication and mediation can lead to results that
can be described simply.
Two players,  and  dispute a prize or pie normalized to unit size. If no peaceful
settlement is reached, the players …ght. Con‡ict is treated as a lottery that shrinks the
7
expected value of the pie to   19 The odds of winning a war depend on the players’
sunk arming decisions. Each player’s arming level can be either high,  or low,  and
this arming level is private information. When the two players’ arming level is the same,
each wins the war with probability 12. When a strong, highly militarized, player …ghts
against a weaker player, its probability of winning is   12 and hence its expected payo¤
is  whereas the weaker player’s payo¤ is (1 ¡ )10 Note that whether player  is strong
or weak in‡uences player ’s payo¤ from …ghting, hence we are in a context of private
information of interdependent value.
In the initial militarization stage,  and  each decide whether to remain militarily weak
or to arm and become strong, at a cost   0. We characterize a mixed arming strategy by
 2 [0 1], the probability of arming and becoming strong.11 The militarization decisions
are treated as hidden actions, so neither player observes the choice of the other nation. Of
course, in equilibrium the players hold correct conjectures of the equilibrium strategy —and
thus they know the probability that their opponent has armed. For expositional purposes,
we assume that military strength is entirely private information. Our results hold also if
the players have some information on each other’s military, as long as there is also some
residual private information. For simplicity, given the symmetry of the game, we focus the
analysis on equilibria that are symmetric in the militarization strategies 
After militarization decisions are sunk, players attempt to negotiate a peaceful agreement and avoid a destructive war. Several game forms may be adopted, but none would
succeed in avoiding militarization or con‡ict. Because militarization is a hidden action,
the emergence of militarized disputes and the development of some of these disputes in
9
Con‡ict destruction need not only consist of physical war damages, but may also include foregone gains
from trade, and increased military ‡ow costs.
10
We assume that   12 otherwise the dispute can be trivially resolved by agreeing to split the pie
in half.
11
The consideration of mixed strategies should not be taken as literally claiming that players are indi¤erent and randomize when making their choices. As is known since Harsanyi (1973), mixed strategy
equilibria can be explained as the limit of pure strategy equilibria of a game in which players are not
precisely sure about the payo¤s of opponents. Further, an alternative interpretation of this simple model
is that  is the level of investment in uncertain military technologies that lead to high military strength
with probability  and low strength otherwise, and that such technologies bear the linear cost 
8
open warfare is unavoidable.12 In the interest of tractability, and to make the exposition
concrete, we represent negotiations as a Nash demand game (see Nash, 1953, and Matthews
and Postlewaite, 1989, for the private information case considered here). Players simultaneously make demands  and  both in [0 1], analogously to giving their diplomats a set
of instructions to “. . . bring back at least a share  of the pie.” If one player’s demands are
su¢ciently generous to accommodate the minimal demands of the other, i.e., if the sum of
the demands is less than 1, then each player receives a split of the pie equal to its demand
plus half the surplus. If the demands  and  are incompatible, meaning they sum to
more than the whole prize, then no split is feasible and the outcome is war. Besides its
simplicity, the Nash demand game is often seen as a reasonable starting point to model
international negotiations.13
The adoption of the Nash demand game as a speci…c game form to represent negotiations
is not restrictive for these paper’s results. First, because the main result of this section is
a possibility result (that un-mediated peace talks may worsen militarization incentives in
international negotiations), any reasonable game form can be adopted as benchmark model
of negotiations while still preserving the power of the result. Furthermore, the results of
this section are robust to changes of the game that represent negotiations. For example,
they hold if adopting the variations of the Nash demand game described in footnote 13, and
with many more others, including a ‘smoothed’ Nash demand game, in which incompatible
demands lead to a peaceful settlement with probability decreasing in the demands’ distance.
And it can be shown that also modi…cations of the negotiation game that move further
away from the Nash demand game would still preserve these section’s results.
12
There cannot exist any game of militarization and negotiation in which arming is a hidden action,
and in which players arm with positive probability but do not …ght in equilibrium (peace by deterrence).
Very simply, if players anticipate that they will not …ght, they will secretly deviate from this hypothesized
equilibrium and choose not to arm. Likewise there cannot exist an equilibrium in which players do not
ever militarize, as each one of them will have the unilateral incentive to secretly militarize and subjugate
the opponent.
13
Wittman (2009) and Ramsay (2011) use the Nash demand game in their studies of con‡ict. Baliga
and Sjöström (2015) adopt a slightly more elaborated version of Nash demand game as a workhorse model
of con‡ict. Jarque et al. (2003) develop a repeated version of the Nash demand game.
9
Second, the adoption of the Nash demand game as a negotiation model is without loss of
generality for the results of the next section, that mediation does not worsen militarization
incentives in international negotiations. Indeed, these results hold with any baseline model
of negotiations that, just like the Nash demand game, does not constrain the e¤ectiveness
of mediation once arming decisions are sunk. Modelling negotiations with constraining
game forms seems di¢cult to justify in this context, as one would like to derive results that
are as general and ‘game-free’ as possible. So, representing negotiations as a Nash demand
game is without loss of generality for our results on mediation.
The next part of this section calculates the optimal equilibrium of the Nash demand
game. It is important for our purposes that the Nash demand game has ‘con‡ict equilibria’
in which the players coordinate on war with probability one, because their demands are
incompatible.14 This equilibrium outcome represents instances in which con‡icts erupt
because of failure to coordinate on a peaceful dispute resolution. The historical record
is replete with such instances.15 Even a ‘rationalistic’ theory of war should not exclude
the possibility of coordination failure as a cause of con‡ict (see the discussion in Fey and
Ramsay, 2007, and Jackson and Morelli, 2011, for example).
To make the exposition of results more parsimonious, we introduce the parameter
 ´ ( ¡ 12)(12 ¡ 2) which subsumes the two parameters  and  The numerator of
 is the gain from waging war against a weak player instead of accepting the equal split, and
the denominator is the loss from waging war against a strong player rather than accepting
the equal split; so  representing the ratio of bene…ts over cost of war for a strong player.
For simplicity, we henceforth assume that  ¸ 1 or equivalently that ( + 12) ¢  ¸ 1 i.e.,
14
Indeed, any demand strictly larger than 1 ¡ (1 ¡ ) leads to war with probability one, because it is so
excessive that even a weak player who knows that the opponent is stronger would prefer to …ght than to
acquiesce to this demand.
15
Failure of coordination on a peaceful solution of disputes can take place for a number of reasons. For
example, con‡icts may erupt because of successful derailment by fringe extremists (e.g., the assassination
of Yitzak Rabin in 1995 contributed to the failure of the Oslo peace process, and WWI started because
of the assassination of Archduke Franz Ferdinand of Austria in 1914). Further, miscalculation of strength
by overcon…dent or biased leaders may hinder coordination on peaceful con‡ict resolution. Likewise,
miscalculation of negotiation tactics by delegates may lead to the failure of peace brokering initiatives.
10
that war is not too destructive and the strong player’s military advantage is signi…cant. But
our …nal and deep result (Theorem 1) also holds for   1 as explained in the Appendix.
Our welfare analysis is based on three measures: the equilibrium militarization probability
of a country,  the probability of peaceful con‡ict resolution, de…ned as  and the total
utilitarian ex-ante welfare,  ´ (1 ¡  ) +  ¡ 2
Solution of the Baseline Model As a consequence of the existence of con‡ict equilibria
in the Nash demand game, our game of militarization and negotiation has a grim ‘armand-…ght’ equilibrium in which both players arm with probability  = 1, in the expectation
that they will later …ght. The collective interest is to devise institutions that minimize
the chance that disputes emerge and led to open warfare, i.e., that players mis-coordinate
on this grim equilibrium. Unfortunately, as already pointed out, it is impossible to fully
avoid militarization and warfare. We begin our analysis on the e¤ectiveness of di¤erent
institutions by solving our model of militarization and negotiation without mediated or
un-mediated peace talks, presented above.
First, suppose that militarization decisions are sunk; i.e., let us solve the Nash demand
game holding the militarization probability  …xed. As a function of  Proposition 1 reports
the equilibrium of this game that maximizes the peace probability  It demonstrates that
even a negotiation game as simple as the Nash demand game improves upon the ‘state-ofnature’ in which disputes always lead to war.
Proposition 1 As a function of the arming probability  the Nash demand game equilibrium that maximizes the peace probability  is as follows. For  ¸  ( + 1)  the players
always achieve peace, by playing  =  = 12 For  ( + 1)   ¸  ( + 2)  peace
is achieved unless both players are strong; strong players demand  2 [ 1 ¡ (1 ¡ ) ]
and weak players demand  = 1 ¡   For    ( + 2)  peace is achieved only if both
players are weak, weak players demand  = 12 whereas strong players trigger war by
demanding   12
11
The arguments leading to this result may be summarized as follows. When  is su¢ciently large,  ¸  ( + 1)  each player  anticipates that the opponent is likely strong,
and prefers not to trigger a …ght. Both players demand a fair share  = 12 and peace is
achieved. Conversely, when    ( + 1)  strong players are not afraid to make prevaricating demands   12 When, in addition,  ¸  ( + 2)  the risk of facing a strong
player is still su¢ciently high that weak players want to avoid war and make demands compatible with the strong players’ demands (i.e.,  = 1 ¡  ) So, war occurs only in strong
player pairs. Instead, when  is su¢ciently small,    ( + 2)  weak players prefer to
make demands that trigger war with strong players, and peace is achieved only by weak
player pairs.
Having calculated the optimal equilibrium of the Nash demand game for any given militarization probability  we now move one step back and solve for the optimal equilibrium
of the whole game, which includes also the militarization stage. For any given value of
the cost of arming  Proposition 2 calculates the equilibrium of our militarization and
negotiation game that maximizes the players’ welfare  For expositional reason, we here
report only the case in which the militarization cost  is neither too small, nor too large.
Speci…cally, we work under the parameter restriction that  ¸  ´ (1 ¡ ) 2 ¢  ( + 1)
and  ·  ´ (1 ¡ ) 2 ¢ ( + 1)  ( + 2) 16
£
¤
Proposition 2 When the cost of arming  2    the equilibrium of the militarization
and negotiation game that maximizes the players’ welfare  is such that each player mil-
itarizes with probability  () =  ¡ 2(1 ¡ ) 2 [ ( + 2)   ( + 1)] strong players
demand  =  weak players demand  = 1 ¡  and war erupts only if both players
are strong.
This result is proved in two steps. First, we show when the arming cost  lies between
 and  there is an equilibrium of the militarization and negotiation game in which players
16
The full characterization of equilibrium for the complementary military cost range is available upon
request.
12
arm with probability  () =  ¡ 2(1 ¡ ) and then strong players demand  =  in the
Nash demand game, weak players demand  = 1 ¡  and war erupts only if both players
are strong. Intuitively, when the militarization cost  is neither too small,  ¸  nor too
large,  ·  players are willing to randomize their arming decision  with ‘intermediate’
values that lie between  ( + 2) and  ( + 1)  At the negotiation stage, the strategies
of this equilibrium are consistent with the equilibria selected by Proposition 1. Hence, this
equilibrium maximizes the peace probability  at the negotiation stage.17
The second step is based on showing that there cannot exist any other equilibrium with a
smaller militarization probability  This result is implied by the fact that, for  ( + 2) ·
   ( + 1)  the equilibrium of Proposition 2 yields the highest possible payo¤s to weak
players, the lowest payo¤s to strong players, and the lowest ex-ante incentives to militarize.
At the negotiation stage, strong players demand  =  in the Nash demand game, weak
players demand  = 1 ¡  and war erupts only if both players are strong. There cannot
exist any equilibrium with lower strong players’ payo¤s, as these players can secure exactly
this payo¤ by …ghting. Conversely, there cannot be any equilibrium of the Nash demand
game with higher weak players’ payo¤s. This is because the equilibrium of Proposition 2
minimizes the probability that weak players get involved in …ghts, and awards them the
highest possible share of the pie, 1 ¡  that avoids con‡ict with strong players.
Because the equilibrium of Proposition 2 minimizes the arming probability  at the
militarization stage, and maximizes the chance of peace in the ensuing negotiation stage, it
immediately follows that it maximizes welfare  in the whole game of militarization and
negotiation.
Un-Mediated Peace Talks The previous section has described the game of militarization and negotiation. We now augment this game by adding an extra intermediate stage.
17
Note also that the arming
strategy  () =  ¡ 2(1 ¡ ) decreases in  and is such that
¡ ¢
 () =  ( + 1) and   =  ( + 2): The equilibrium probability () spans the entire range
[ ( + 2)   ( + 1)] for which the optimal equilibrium of the Nash demand game is such that war
erupts only if both players are strong.
13
We assume that after the militarization stage, but before the negotiation game is played,
direct bilateral peace talks take place. Talks are modeled as a meeting in which the players
share information and attempt to …nd a (self-enforcing) agreement to coordinate their future play. In the meeting, both players  =   simultaneously send unveri…able messages
 2 f g to each other, so as to represent their arming level  or 18 Then, the meeting
continues with the players trying to …nd an agreement. Any equilibrium has the following
form: with some probability, the meeting is ‘successful,’ and the players agree on a peaceful
resolution. With complementary probability, the meeting fails and leads to con‡ict escalation. In any equilibrium in which information is meaningfully revealed, the probability
that the meeting results in a peaceful resolution depends on the players’ arming levels, as
we detail below in Proposition 3.
In more formal terms, we allow players to make use of a joint randomization device,
whose realization is observed by both players. So, players can possibly coordinate on
di¤erent equilibria of the negotiation game, as a function of both their messages and the
realization of the public randomization device.19 It is important that we can exploit the
equilibrium multiplicity of the Nash demand game to model the possibility of the failure
of the players’ attempts to coordinate on a peaceful outcome. This is not only a realistic
assumption. (One needs only to browse history books and contemporary press to appreciate
that, often, peace talks fail despite everyone’s best intentions; see, e.g. footnote 15). It
is also the only reason why un-mediated peace talks succeed in improving the chance of
peaceful resolution of disputes after arming decisions are sunk. Indeed, it can be proved
that absent this possibility of coordination on di¤erent equilibria, the players would never
reveal any information in the peace talks (and hence peace talks would not be organized
in the …rst place). As anticipated in footnote 5, this insight is novel, and complements the
18
For simplicity, we assume that only one round of unmediated communication takes place.
The same communication model is used by Krishna and Morgan (2004) and Aumann and Hart (2003) in
di¤erent contexts. The latter also prove that joint randomization can also be reconstructed as simultaneous
cheap talk. Hence, by allowing for public randomization devices we are ensuring that the logic of our result
holds for a large class of models of communication (albeit in a reduced form representation).
19
14
…ndings of Baliga and Sjöström (2004) whose model of un-mediated peace talks does not
include the possibility that a meeting acts as a public randomization device to select across
di¤erent continuation equilibria.
These insights are formalized in Proposition 3. It shows that, for any …xed probability of
militarization  un-mediated peace talks strictly improve the probability of peace (except
for the trivial case in which  ¸ ( + 1) where peace can be achieved even by the Nash
demand game). For expositional reasons, we focus our attention on equilibria with pure
communication strategies.
Proposition 3 For any given militarization strategy  the optimal equilibrium of the negotiation game with un-mediated peace talks is characterized by two parameters,   and
  and has the following form. Each player truthfully reveals its arming level during peace
talks. Then, strong player pairs ( ) coordinate on the peaceful demands  = 12
 = 12 with probability   and …ght with probability 1 ¡  ; asymmetric pairs ( ) coordinate on the peaceful demands ( 1 ¡ ) with probability   and …ght with probability
1 ¡  ; the case for ( ) is symmetric; and weak player pairs ( ) achieve peace with
probability one, making demands  = 12  = 12. Speci…cally, when   ( + 2)
 = 0 and  2 (0 1) ; whereas when ( + 2) ·   ( + 1)  = 1 and  2 (0 1) ;
…nally, when  ¸ ( + 1)  = 1 and  = 1 For any given militarization probability 
un-mediated peace talks improve the peace chance  and they improve it strictly whenever
  ( + 1)
The equilibrium in Proposition 3 is best illustrated by comparing it to the optimal
equilibrium of the negotiation game without communication, reported in Proposition 1. In
both cases, the players play a separating equilibrium (except for the trivial case in which
 ¸ ( + 1) in which peace is always achieved); i.e., the players reveal their arming
levels by means of their equilibrium choices. But in the Nash demand game without peace
talks, this information is revealed only after demands are made, whereas with un-mediated
communication, the information is shared before the demands are made. Intuitively, sharing
15
information before demands are made allows the players to use this information more
e¢ciently in the negotiation game, thereby improving the chance that the players coordinate
on a peaceful outcome. Speci…cally, when (+2) ·   (+1) the optimal equilibrium
of the Nash demand game without peace talks is such that war takes place with probability
one among strong players. The introduction of un-mediated peace talks in the Nash demand
game makes it possible for strong players to coordinate on a peaceful outcome resolution
with positive probability. Similarly, when   ( + 2) the addition of un-mediated
peace talks to the Nash demand game improves the chance of peace in asymmetric pairs
composed of a strong and a weak player.
We now turn to consider the implications of un-mediated peace in the whole game of
militarization and negotiation. We …nd that, paradoxically, un-mediated peace talks may
not improve the chance of peace and the players’ welfare. The result is very stark. Whenever un-mediated peace talks increase the chance of peace in the negotiations of emerged
disputes, i.e., after the arming decision are sunk, they also breed perverse incentives for
militarization. This e¤ect is so severe that un-mediated peace talks lead to reducing ex-ante
players’ welfare  when considering the whole model of militarization and negotiation.20
£
¤
Proposition 4 For any militarization cost  2    every equilibrium of the negotiation
game with un-mediated peace talks that increases the peace probability in emerged disputes
(i.e., after arming decision are sunk) leads to a strict increase of equilibrium militarization
probability  and a strict decrease of ex-ante welfare  in the associated equilibrium of the
whole game of militarization and negotiation.
The intuition for this seemingly perverse result is simple: in some sense, un-mediated
20
Of course, there are also uninformative, babbling, equilibria that induce the same outcomes as in the
game without un-mediated peace talks (cf. Proposition 2). We focus on informative equilibria that improve
the chance of peace in the negotiation game with sunk arming decisions for two reasons. First, equilibrium
selection is appropriate, because ours is only a possibility result (we argue that unmediated peace talks
can induce perverse militarization incentives). Second, focusing on informative peace talks is justi…ed by
simple ‘forward-induction’ arguments. There are signi…cant political and …nancial costs to organize peace
talks. It does not seem plausible that belligerent parties would go through all this trouble to meet and
only babble.
16
peace talks are victims of their own success. We know from Proposition 2 that, for  2
£
¤
   the equilibrium of the militarization and negotiation game is such that the arming
strategy  lies between ( + 2) and ( + 1) player pairs …ght only if both are strong,
and weak players obtain the best possible deal that guarantees peace to them. (They
obtain 12 when facing a weak player, and 1 ¡  when facing a strong one.) As we
already argued when commenting Proposition 2, it is plainly impossible for weak players
to achieve a higher payo¤ in equilibrium. Hence, un-mediated peace talks improve the
peace probability in emerged disputes when ( + 2) ·   ( + 1) only by reducing
the probability that pairs of strong players …ght; indeed,  = 1 and  2 (0 1) in this
case. Thus, un-mediated peace talks increase the expected payo¤ of becoming strong, and
lead players to arm with higher probability, in equilibrium. More disputes emerge, and
while un-mediated peace talks reduce the probability that each one of them erupts in open
con‡ict, it may be the case that the overall level of con‡ict is higher than in a world where
the international community does not provide support for un-mediated peace talks. That
this is the case is the …nal strong result derived in the proof Proposition 4, with direct
calculations on the welfare function 
4
Mediation
We have shown that bilateral un-mediated peace talks, exactly because they can reduce
the risk of con‡ict in ongoing disputes, may lead to more militarization, more emergence of
disputes, and ultimately to a higher level of con‡ict. We now show that there exist forms of
third-party intermediation that improve the e¤ectiveness of peace talks over un-mediated
communication, and do not breed perverse incentives for militarization.
Optimal Mediation, Given Militarization The speci…c form of intermediation we
consider is inspired by the celebrated work of Roger Myerson (1979, 1982): we call it
‘Myerson mediation’, or ‘mediation’ for brevity. A Myerson mediator is a neutral or “honest
17
broker” mediator who does not favor either of the players.21 The mediator has a mandate
to set the agenda, or procedure, of the peace talks so as to minimize the probability of
war when the international dispute militarization and negotiations, after the militarization
stage. That is, we consider a mediator who has a ‘narrow mandate’ to only resolve the
disputes that she is called to mediate. Her mandate cannot realistically include also shaping
the beliefs and incentives of potential future players, who base militarization choices also
on expectations on how mediators will deal with eventual disputes. So, a mediator in our
model takes the symmetric equilibrium militarization probability  as given, and tries to
minimize the chance that the dispute she is mediating erupts in con‡ict.
We begin our analysis by applying a celebrated result, the ‘revelation principle’ by
Myerson (1982) to our negotiation game, in which the arming probability  is taken as
given. This general result implies in this context that an optimal way for the mediator to
set the mediation agenda is as follows. First, players report their information independently
to the mediator. Second, the mediator submits a settlement proposal to the players. After
these proposals are made, the players bargain according to the Nash demand game, as
in the benchmark model of the previous section.22 Further, there is an equilibrium that
maximizes the chance of peace, in which the mediator’s proposal strategies lead the players
to reveal all their private information to the mediator, in anticipation of the proposals that
she will make, and in which the players are willing to adhere to the mediator’s proposals.
This intermediation procedure is often adopted by third-party negotiators in the form
of ‘shuttle diplomacy’, as we discussed in the introduction. Disputants do not report
information directly to each other, but through the intermediation of a mediator whose
actions are inspired by a principle of con…dentiality. As we explain later in more detail,
players have better incentives to disclose their type con…dentially to the mediator than they
21
Examples of such mediators might be Nobel Peace Prize winners like Martti Ahtisaari and Jimmy
Carter, or Nongovernmental Organizations like the International Crisis Group.
22
Alternatively, we could assume that the proposals are submitted for independent approval to the two
players, and are implemented if both the players approve them, as in Hörner, Morelli and Squintani (2015).
As we prove in the Appendix, our results are exactly the same with these two game forms.
18
have when communicating directly. As a result, the mediator improves the chance of peace
for any given arming probability  upon un-mediated peace talks.
Proposition 5 describes the optimal mediation strategies, given the militarization probability  In order to minimize the chance that an ongoing dispute turns into war, the
mediator must be capable to commit to her proposal strategies. To be e¤ective, the mediator must be able to quit the peace talks with some probability when one or both players
claim to be strong, leading to escalation of con‡ict and war, instead of seeking a peaceful agreement in all contingencies. Such commitments make information disclosure by the
contestants possible, as they provide a ‘punishment’ for weak players exaggerating their
strength. In fact, they are necessary for mediation to improve the chances of peaceful
con‡ict resolution of disputes. On the basis of all the evidence available, it seems realistic
to allow for the possibility that mediators can commit to quit talks if some contingencies
arise.2324 Relatedly, our model rules out the possibility of negotiation outside the mediation process. Realistically, players are not likely to go back to the negotiation table in the
attempt to broker a deal without the help of the mediator, once the mediation process has
failed.25
Proposition 5 For any given militarization strategy  the optimal equilibrium of the negotiation game with a Myerson mediator can be characterized by three parameters,    
 , and described as follows. Each player truthfully reveals its arms level to the mediator.
The strong player pairs ( ) coordinate on the peaceful demands (12 12) with probabil23
The online appendix of Hörner, Morelli and Squintani (2015) provide empirical evidence that mediators
as well as players recognize the value of a mediator’s commitment to quit. They also show that if mediators
cannot commit to quit, and seek a peaceful agreement in all contingencies, then they are entirely ine¤ective
at brokering peace in the disputes they are called to settle.
24
We have also interviewed a real-life experienced mediator, Mr. Gianluca Esposito, former Principal
Administrator at the Council of Europe, who participated in a number of international mediations including the ones associated with the Bosnian war. He con…rmed that mediators understand very much the
importance of being able to credibly set the rules of the mediation process, and credibly threaten to quit
if players persist with excessive demands (i.e., in the context of our paper, both report to be militarily
strong). The views expressed by Gianluca Esposito do not necessarily re‡ect the views of the Council of
Europe.
25
There are many reasons for this. For example, audience costs are recognized to provide an important
channel that makes war threats credible in case of failed negotiations (e.g., Tomz, 2007).
19
ity   and …ght with probability 1 ¡  ; asymmetric pairs ( ) coordinate on the peaceful
demands ( 1 ¡ ) with probability   on the demands (12 12) with probability 
and …ght with probability 1 ¡  ¡  —the case for ( ) is symmetric; and weak player
pairs ( ) achieve peace with demands (12 12) with probability one. Speci…cally, when
 · ( +2),  =  = 0 and  2 (0 1); when ( +2) ·   ( +1),  + = 1
 2 (0 1) and  2 (0 1) ; and …nally, when  ¸ ( + 1)  = 1 and  = 1 Whenever ( + 2) ·   ( + 1) mediation strictly improves the peace chance relative to
any equilibrium of the un-mediated peace talks game. For all values of  mediation yields
at least as large a chance of peace as un-mediated peace talks.
The above characterization of optimal mediation strategies is based on the following
insights. To begin, note that a strong, militarized player must receive more favorable terms
of settlement on average than a weak one. Otherwise, the strong player would reject the
settlement, in the expectation that the war payo¤ will be larger. But favorable settlements
to self-reported strong players provide an incentive for weak players to pretend to be strong,
when reporting its information to the mediator. Settlement strategies must be chosen so
as to avoid that weak players lie.
When ( + 2) ·   ( + 1) mediation strictly improves the peace chance relative
to all equilibria of the un-mediated peace talks, given any …xed arming probability  as it
makes a weak player more willing to reveal its type to the mediator, than if communicating
directly with its opponent. If revealing its arming level to a strong opponent, the weak
player will surely need to accept a low payo¤, 1 ¡  to secure peace. If instead communicating through a mediator, the weak player is proposed 12 of the pie with probability
  and the lower payo¤ 1 ¡  only with probability  = 1 ¡   To ensure that the
strong player is willing to accept these mediator’s proposal, the proposal strategy cannot let
the strong player infer its opponent’s type precisely. Speci…cally, when receiving proposal
(12 12), the strong player does not know if the opponent is strong or weak. The randomization value  is chosen so as to make the strong player exactly indi¤erent between
20
accepting the proposal (12 12) and …ghting. As a result, this optimal mediation strategy minimizes the di¤erence between strong and weak players’ expected payo¤s, among all
mediation strategies that make the players’ truthfully reveal their types, and accept the
mediator settlement proposals.
We will next see how these optimal mediation strategies also leads to optimal incentives
for militarization.
Mediation and Militarization We now build on Proposition 5 to solve for the militarization equilibrium probability  given that the ensuing dispute is solved via Myerson
mediation. The following result characterizes the equilibrium militarization and negotiation strategies. Importantly, it shows that mediation does not su¤er from the drawbacks
presented by un-mediated bilateral peace talks. Not only can such a mediator improve the
peace chance given militarization strategies  she can also improve welfare in the whole
game, which includes the militarization decisions.
Proposition 6 Consider a game of militarization and negotiation with a Myerson mediator who adopts the optimal mediation strategy described in Proposition 5. For any milita£
¤
rization cost  2    the unique equilibrium militarization strategy is:
() = (1 + )
2 ¡ (1 ¡ )

2(2 + ) ¡ (1 + )2 (1 ¡ )
(1)
which strictly decreases in  and is such that () = ( + 1)[ + ( + 1)2 ] and () =
( + 2) Myerson mediators strictly improves the chance of peace  and the welfare 
with respect to any equilibrium of the benchmark game of militarization and negotiation
with un-mediated peace talks, or without communication.
This result …nds that the optimal strategies of mediators, who are only given a mandate
to minimize the chance that con‡ict erupts in the dispute that they mediate, do not breed
perverse incentives for dispute emergence and militarization. Indeed, they strictly improves
21
peace chance and welfare relative to all equilibria of the game of militarization and con‡ict,
with un-mediated peace talks, or without communication.
Refreshingly, the reason for this powerful result is intuitive. We have seen in Proposition
4 that un-mediated peace talks provide an incentive for militarization because, by improving
the chance of peace in the negotiation game, they raise the payo¤ of strong players. Instead,
optimal mediation strategies increase the probability of peace in strong player pairs without
increasing strong players’ payo¤s relative to the baseline game of militarization and con‡ict
without (mediated or un-mediated) communication. This is because the strong players’
payo¤s under optimal mediation exactly equal their payo¤s when …ghting, as reported
when explaining Proposition 5. These payo¤s exactly coincide with the strong players’
payo¤s of the optimal equilibrium of the baseline militarization and negotiation game of
Proposition 2.
The key relevance of Proposition 6 lies in the comparison with Proposition 4. The latter shows that, the adoption of un-mediated peace talks to settle con‡icts may incentivize
arming, and thus ultimately even raise the risk of war. Instead, Proposition 6 shows that
Myerson mediation improves the chances of peaceful dispute resolution without creating
negative militarization distortions. So, while the exact nature of the negotiation or mediation protocol will likely have e¤ects on exact settlements, probability of war and chance
of peace, we predict that militarization strategies may di¤er across international disputes,
conditional on observed dispute settlement techniques. Indeed, this is what is found in
some data sets. For example, looking at the data from Svensson’s (2007) study on the
e¤ects of direct negotiations and mediation on agreements in all intrastate armed con‡icts
between 1989 and 2003, one …nds that if you compare the size of government armies in
crises with just bilateral negotiations to those with a mediator, the …rst category averages
273,901 troops, whereas when a mediator is used the average army size is only 124,277. A
simple t-test rejects the hypothesis of no di¤erence in these case at better than a .001 level.
22
The Institutional Optimality of Mediation The previous sub-section proved that
mediation not only improves the chance that disputes that emerge are resolved peacefully
more e¤ectively than un-mediated peace talks, but also that it keeps in check the potential
players incentives to engage in disputes and militarize. We now show an even stronger
and deeper result. Myerson mediation achieves the same welfare as a hypothetical optimal
third party intervention mechanism in which the third party has the broader mandate to
commit to ‘punish’ players for militarizing and entering a dispute in the …rst place.26 That
is, a hypothetical mediator with the mandate to consider total welfare and minimize the
militarization incentives that lead to dispute emergence can do no better than the Myerson
mediator with a ‘narrow’ and more realistic mandate to only foster the peaceful resolution
of the dispute that she is called to settle.
Theorem 1 Myerson mediation achieves the same welfare as a hypothetical optimal institution that recommends militarization strategies, collects players arming level reports, and
makes settlement proposals, with the objective to maximize players’ welfare 
The signi…cance of this result lies in the …nding that, although Myerson mediators may
not take into account the incentives they create for strategic militarization, they are an
optimal institution among all budget-balanced institutions with no direct access to players
information, for the aim of both arms reduction and peace chance maximization in the
game of militarization and negotiation.
The proof of Theorem 1 is involved, but the reasoning behind this result is intuitive.
As we explained in the discussion after Proposition 5, the optimal mediation strategies
minimize the di¤erence between strong and weak players’ expected payo¤s, among all
mediation strategies that make the players’ truthfully reveal their types, and accept the
26
Such an optimal hypothetical institution is not likely available in the real world, and serves only as
benchmark to assess how much is lost by the narrow mediator’s mandate. We maintain the assumption
that the optimal institution does not have access to privileged information beyond what it gathers from
communication with the players, and that it is budget balanced. That is, the optimal institution cannot
bribe or punish the players to force them to settle their dispute. The mandate of this hypothetical mediator
is de…ned precisely in the appendix.
23
mediator settlement proposals. This is because they are designed to minimize the expected
reward for a weak player to pretend that it is strong, when, in fact, it did not militarize. As
an unintended consequence, they also minimize the incentives for a weak player to militarize
and become strong. Hence, mediators not only maximize the chance that the disputes they
are called to settle are resolved peacefully. They also keep in check the players’ incentives
to militarize and make disputes emerge.
A more formal intuition can be grasped by noting that, given any dispute resolution
institution, the equilibrium mixed strategy  of the arming strategy is given by
=
 ( ) ¡ ( )

( ) ¡  ( ) +  ( ) ¡ ( )
(2)
where (   ) is player ’s expected payo¤ in the dispute when the players’ arming levels
are  and   Hence, the equilibrium militarization strategy  increases in  ( ) ¡
 ( ) the gain for being strong instead of weak, when facing a weak opponent. Similarly,
 decreases in  ( ) ¡ ( ) the loss for being strong instead of weak, when facing
a strong opponent.
Recall from Proposition 5 that, under optimal mediation, (i) weak players pairs never
…ght, (ii) the settlement ( 1 ¡ ) is chosen so as to keep the payo¤ of strong players
meeting weak opponents as low as possible, and (iii) strong players pairs are more likely
to …ght than any other pairs of players. Hence, the mediator minimizes the incentives
of a weak player to pretend that it is strong. As an unintended consequence, it also
minimizes the incentives for a weak player to militarize and become strong. That is,
mediation minimizes ( ) ¡  ( ) and maximizes  ( ) ¡  ( ) among all
budget-balanced institutions. Hence, it keeps the upstream incentives to arm in check, and
minimizes strategic militarization  in equilibrium. As result, a mediator induces the same
militarization incentives as the hypothetical institution whose mandate includes deterring
militarization which took place before the eruption of the dispute.
24
Because, by construction, the mediator’s strategy in Proposition 5 maximizes the chance
of peace given any militarization strategy , the fact that it also minimizes the equilibrium
militarization probability implies that it maximizes the overall players’ welfare, among all
budget-balanced institutions.
5
Conclusion
This paper pushes scholars of con‡ict to broaden their …eld of vision in thinking about
institutions. How nations negotiate can a¤ect more than whether the crises that emerge
are resolved peacefully; con‡ict resolution institutions can have pronounced a¤ects on the
types of crises that are likely to emerge by shaping militarization incentives. Because
engagement in a costly and destructive war can be seen as the ‘punishment’ for entering a
dispute, institutions that reduce the chances that a dispute lead to open con‡ict may make
more disputes emerge and incentivize militarization.
We show that consideration of militarization incentives is important when assessing the
overall e¤ectiveness of con‡ict resolution institutions. Our analysis …nds that the support
for un-mediated peace talks, while e¤ective in improving the chance of peace for a given
distribution of military strength, ultimately may lead to the emergence of more disputes and
to higher con‡ict outbreak. Happily, we …nd that not all con‡ict resolution institutions
su¤er from these, apparently paradoxical, but actually quite intuitive drawbacks. We
identify a form of third-party intervention inspired by the celebrated work by Myerson,
and show that it can broker peace in emerged disputes e¤ectively and also avoid perverse
militarization incentives.
Beyond broadening the focus of theoretical work on con‡ict resolution institutions to
consider the e¤ects we describe above, this paper contributes to our understanding of
communication and negotiations in international relations. A series of paper going back
to at least Kydd (2003) focus on the question of whether mediation can improve on direct
25
communication. At the heart of this debate is whether there is value in a mediator with
no independent private information and no ability to create external incentives. In the
case of private values the answer is no (Fey and Ramsay, 2010), but in the context of
interdependent values the answer is yes (Hörner, Morelli and Squintani, 2015).
In this paper we have focused on how the e¤ectiveness of mediated and un-mediated
communication can di¤er as the former does not breed perverse militarization incentives,
whereas the latter does. The di¤erence hinges on the con…dentiality of communication
through a mediator. Because of the mediator’s con…dentiality, players have better incentives to disclose their information than when communicating directly. By adopting a
non-fully revealing recommendation strategy, the mediator can optimally shape the equilibrium beliefs players assign to their opponent being strong at the time that they must
accept or reject an o¤er. In settings with interdependent values this belief is important as
it in‡uences what a strong player will accept. But in settings with private values the type
of the other nation is not payo¤ relevant and thus the ability to in‡uence this belief buys
a mediator nothing.
To be sure, mediators improve upon direct communication only if they are able to
commit to quit negotiations in which players report that they are highly militarized (and
as argued earlier, this supposition seems realistic on the basis of existing evidence). This
capability, while seemingly counterproductive, is necessary both to minimize the chance
that ongoing disputes erupt in open warfare, and to provide optimal incentives for arming
and dispute deterrence. Hence, one take away of this paper is a better understanding of
what makes a mediator e¤ective —the con…dentiality of communication, the commitment
capability, and when such attributes can have the most value —when the uncertainty is
about common value components.
We conclude by relating our …ndings with the study of optimal taxation with mechanism
design, a large literature that dates back at least to the celebrated work by Diamond and
Mirrlees (1971). The issue of tax evasion is of course a main concern of policy-makers. Tax
26
auditing is an imperfect system to tackle tax evasion, and one may want to complement it
with direct mechanisms that discourage income under-reporting, especially by high income
earners. And at the same time, a classical concern of the optimal taxation literature is that
the tax system does not reduce the incentives to work and increase income for low income
persons. Our results may be related to these matters. We have found that the optimal
mediation mechanism simultaneously discourages weak players from (falsely) reporting that
they are strong, and minimizes the incentive that they militarize and become strong in the
…rst place. This suggests that classical results on the construction of taxation schemes that
do not upset income generation incentives may also provide insights on how to incentivize
truthful income reporting.
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30
Appendix
Proof of Proposition 1. First, note that for 2 + (1 ¡ )  · 12 or  ¸  ( + 1) 
both weak and strong players can achieve peace by coordinating on the claims  =  =
12 When    ( + 1)  it is impossible that strong player pairs achieve peace. But it
is possible to achieve peace for all other pairs of players in equilibrium, as long as strong
and weak players’ demands are compatible, i.e.,  +  = 1 Also, a strong player must
prefer to demand  rather than triggering war against a weak player by making a higher
demand (if meeting a strong player, the demands will result in war anyway). Hence, we
need that  ¸ . Further, a weak player must prefer to demand  rather than triggering
war with a strong player, but collecting a higher share of the pie with a weak player, by
making the demand 1 ¡  . This requirement translates into the following inequality:
(1 ¡ ) 2 +  ¸ (1 ¡ ) (1 ¡  ) +  (1 ¡ )  Bringing together these two conditions,
we obtain the condition that  ¸  ( + 2)  When this condition fails, it is impossible to
achieve peace for asymmetric pairs composed of a strong and a weak player. As a result,
only weak players pairs achieve peace, by demanding  = 12
Proof of Proposition 2. The proof proceeds in two parts.
In the …rst part, we suppose that the Nash demand game is played according to the
equilibrium selection of Proposition 1 with  =  for  ( + 2) ·    ( + 1) 
As a function of the equilibrium militarization strategy  the expected payo¤ of arming
and becoming strong is:
8
>
< (1 ¡ ) + 2 ¡ 
 (; ) =
>
: 12 ¡ 
if    ( + 1)
if  ¸  ( + 1) 
(3)
whereas the expected payo¤ of not arming is:
8
>
>
(1 ¡ )2 + (1 ¡ )
>
>
<
 (; ) =
(1 ¡ )2 + (1 ¡ )
>
>
>
>
: 12
if    ( + 2)
if  ( + 2) ·    ( + 1)
(4)
if  ¸  ( + 1) 
The equilibrium arming probability  is given by the indi¤erence equation
 (; ) =  (; )
31
(5)
It is immediate that this equation cannot hold for any  ¸  ( + 1)  because  ¸
  0 implies (; )   (; ) For    ( + 1)  the function (; ) is linear in
 with negative slope ¡ ( ¡ 12)  The function  (; ) is piecewise linear in  with a
discontinuity point at  =  ( + 2) such that lim"(+2)  (; )  lim#(+2)  (; )
The function  (; ) has negative slope ¡ (12 ¡ (1 ¡ )) for    ( + 2)  and negative
slope ¡ ( ¡ 12) on  ( + 2) ·    ( + 1)  Because  (; ) =  ¡   12 =
 (; ) for  = 0 and the slope of  (; ) is less negative than the slope of (; ) for
   ( + 2)  the indi¤erence equation (5) cannot have a solution    ( + 2) 
Because the slope of  (; ) is more negative than the slope of  (; ) for  ( + 2) ·
   ( + 1)  there can exist at most a single value of  such that equation (5) holds,
and this equilibrium militarization strategy  lies in [ ( + 2)   ( + 1)) Solving the
resulting equation (1 ¡ ) + 2 ¡  = (1 ¡ )2 + (1 ¡ ) yields the solution () =  ¡
2(1¡) This function decreases in  and is such that () =  ( + 2) and lim# () =
 ( + 1) 
We have concluded that, if the Nash demand game is played according to the equilibrium
selection of Proposition 1 with  =  for  ( + 2) ·    ( + 1)  then for any
 2 ( ] the militarization and negotiation game has an equilibrium in which players arm
with probability  () =  ¡ 2(1 ¡ ) 2 [ ( + 2)   ( + 1)) strong players demand
 =  weak players demand  = 1 ¡  and war erupts only if both players are strong,
as stated in the proposition proved here. This equilibrium exists also for  =  because also
for  =  ( + 1)  the Nash demand game has an equilibrium in which peace is achieved
unless both players are strong, strong players demand  =  and weak players demand
 = 1 ¡ 
The second part of the proof shows that the equilibrium just described maximizes the
players’ welfare  in the militarization and negotiation game.
Consider any other equilibrium of the whole militarization and negotiation game, hence
allowing for any equilibrium of the Nash demand game, beyond the equilibrium selected in
Proposition 1.
Suppose that  ·  ( + 1)  In this case, strong players …ght each other in any equilibrium of the Nash demand game, and obtain the payo¤ of 2 A strong player’s payo¤
against a weak player cannot be lower than  in any equilibrium of the Nash demand
game, because the strong player can guarantee at least that payo¤ by …ghting. Hence,
for any  ·  ( + 1)  the equilibrium expected payo¤ ^ (; ) of arming and becoming
strong cannot be lower than the payo¤  (; ) reported in expression (3) determined by
the Nash demand game equilibrium selection of Proposition 1.
^
Conversely, we now show that the equilibrium expected payo¤ (;
) if remaining
weak cannot be higher than the payo¤  (; ) of expression (4), which is also determined
by the equilibrium of Proposition 1. For every  ·  ( + 1)  in fact, the equilibrium of
32
Proposition 1 minimizes the probability that weak players …ght, and gives them the highest
possible share of the pie  = 1 ¡  that secures peace when meeting a strong opponent,
in the case that  ( + 2) ·    ( + 1) 
Because (; ) · ^ (; ) and (; ) ¸ ^ (; ) for every  ·  ( + 1)  there cannot exist any value ^ strictly smaller than the value  that solves the indi¤erence equation
^
(5), and such that the indi¤erence condition ^ (; ^) = (;
^) holds. We have concluded
that the equilibrium derived in the …rst part of the proof minimizes the militarization
probability  among all equilibria of the militarization and negotiation game.
For  in the relevant range [ ( + 2)   ( + 1)) this equilibrium’s strategies at the
Nash demand stage conform with the equilibrium of Proposition 1. Hence this equilibrium
also minimizes the probability of con‡ict, given the militarization strategy  As a result, it
also maximizes players’ welfare  among all equilibria of the militarization and negotiation
game.
Proof of Proposition 3. We …rst reformulate the un-mediated communication problem
by substituting the Nash demand game, with the following, simpler, model. Given messages
 = (   )  and the outcome of the public randomization device, nature selects a split
proposal  and the players simultaneously choose whether to agree to the pie division
( 1 ¡ ) or not.
Every outcome of this simpler communication model is also an equilibrium of the Nash
demand game with peace talks. Suppose, in fact, that the players agree to the split division
( 1 ¡ ) in this simpler communication model. Then, they can achieve the outcome
( 1 ¡ ) in the Nash demand game, by making demands  =  and  = 1 ¡ 
Every separating equilibrium of the Nash demand game with peace talks is also an equilibrium of the simpler communication model. In a separating equilibrium, each player’s
strength is common knowledge in the Nash demand stage of the game. Hence, in equilibrium, the players know each other’s demands. If a player  demands  his opponent’s ’s
best response is either to demand 1 ¡  and secure peace, or to trigger war with a higher
demand. Player ’s choice of whether to trigger war or make the demand 1 ¡  follows
exactly the same calculation that  would make in the simpler model in which  only needs
to either agree to the split ( 1 ¡ ) or not. We have shown that every separating equilibrium of our Nash demand game with un-mediated cheap talk is also an equilibrium of the
simpler communication model introduced above.
The pure-strategy equilibria of this communication model can either be pooling or
separating. Of course, the former coincide with the equilibria of the Nash demand game
without peace talks. Hence, the optimal equilibria of the Nash demand game with unmediated cheap talk can be determined simply by comparing the equilibria described in
Proposition 1, with the optimal separating equilibria of the simpler game introduced in
33
this proof. These equilibria are fully characterized by Lemma 1 of Hörner, Morelli, and
Squintani (2015), henceforth shortened as HMS, and they are reported in the statement
of Proposition 3. They induce a higher peace chance than the equilibria described in
Proposition 1, because it is the case that   0 when ( + 2) ·  · ( + 1) and
that   0 when   ( + 2)
For future reference, the precise values of the optimal probabilities  and  are as
1¡
follows: For   (+2) then ¹ = 0 and ¹ = (1+)(1¡)¡2
; for (+2) ·  · (+1)


then ¹ = 1 and ¹ = 1 ¡ (+2) ; for  ¸ +1 , ¹ = 1 and ¹ = 1
£
¤
Proof of Proposition 4. We know from Proposition 2 that, for  2    the equilibrium of the militarization and negotiation game is such that the arming strategy  lies
between ( + 2) and ( + 1) that strong players demand  =  in the Nash demand
game, and weak players demand  = 1 ¡  Further, players …ght only if both are strong.
Weak players’ payo¤s are 12 when facing a weak player, and 1 ¡  when facing a strong
one. Because strong players’ payo¤s for …ghting is  it is impossible for weak players
to achieve a higher payo¤ than this in any equilibrium of the Nash demand game. So,
un-mediated peace talks can only improve the payo¤ of strong players in the Nash demand
game. Speci…cally by Proposition 3, they reduce the probability that pairs of strong players

…ght each other from one to 1 ¡   where 0   · ¹ = 1 ¡ (+2)
 So, un-mediated
peace talks increase the payo¤ for arming to
 (; ) = (1 ¡ ) + [2(1 ¡  ) +  2]  ¡ 
and cannot increase the payo¤  (; ) for remaining weak. Again, the equilibrium militarization strategy  solves the indi¤erence condition  (; ) = (; ) so that:
 = min
½
¾
 ¡ 2(1 ¡ )
 1 
1 ¡ 
(6)
which is proved to strictly increase in   recalling from Proposition 2 that  ¡2(1¡) ¸
£
¤
( + 2)  0 when  2   
To conclude that this is the optimal militarization strategy when negotiations are conducted with un-mediated peace talks, we need to show that there cannot exist an equilibrium of the militarization and negotiation game with arming strategy   ( + 2)
By Proposition 3, peace talks can only reduce the con‡ict probability in asymmetric
dyads to 1 ¡  where   0 when   ( +2) Hence, they yield weak players’ payo¤s
^
(;
) = (1 ¡ )2 +  [(1 ¡ )(1 ¡  ) +  (1 ¡ )]  (1 ¡ )2 + (1 ¡ )
34
without changing strong players’ payo¤s  (; ) We know from the proof of Proposition
£
¤
2 that, for  2    the unique value of  such that  (; ) = (1 ¡ )2 + (1 ¡ ) is
such that  2 [( + 2) ( + 1)] A fortiori, there cannot exist a value of   ( + 2)
such that  (; ) = ^ (; )
We are only left to inspect the e¤ect of un-mediated peace talks on the players’ welfare
 Because con‡ict erupts only in strong players pairs, and only with probability 1 ¡  
the welfare takes the simple form:
 = 1 ¡  2 (1 ¡  )(1 ¡ ) ¡ 2
(7)
The direct e¤ect of  is positive, as the con‡ict probability  2 (1 ¡  ) is reduced, for …xed
 But the indirect e¤ect of  through increased militarization  is negative. Substituting
expression (6) into (7), one obtains:
½
¾
(1 ¡ )
 = max 1 ¡
[ ¡ 2(1 ¡ )]  0 
1 ¡ 
which strictly decreases in  
Proof of Proposition 5. The proof of this result consists of showing that the optimal
equilibrium strategies of a Myerson mediator in our Nash demand game coincide with the
optimal mediation strategies in the following simpler game. First, each player  sends a
message  to the mediator. Then, the mediator recommends a split of the pie ( 1 ¡ )
as a function of the received messages (   )  The split is implemented if and only if
both players accept, and con‡ict erupts if at least one player rejects it.
Because this simple game is a direct revelation game, the revelation principle by Myerson
(1982) implies that every equilibrium of our Nash demand game with a mediator is also an
equilibrium of this simpler game.
To prove the converse, consider any equilibrium of the simple game introduced above.
Take any message pair (   )  suppose that the mediator recommends the split of the
pie ( 1 ¡ )  and the players accept it. Then, for the same message pair (   )  the
mediator of our model can recommend that the players demand precisely  =  and
 = 1 ¡  in the Nash demand game, and the players will be willing to implement these
recommendations, thus also averting war. If instead, the mediator recommends the split
of the pie ( 1 ¡ )  and one or both players reject it in the equilibrium of the simple
direct revelation game, then the mediator of our model can recommend that the players
make excessive demands (e.g.,  =  = 1) and coordinate the players on the con‡ict
equilibrium of the Nash demand game.
35
We have concluded that the optimal strategies of a mediator in our Nash demand game
coincide with the optimal strategies of a mediator in the simpler revelation game introduced
above. These strategies are characterized in Lemma 4 of HMS, and they are reported in
the statement of Proposition 5. The precise values of the probabilities     and 
1¡


are as follows: For  · ( + 2),  =  = 0  = (+1)(1¡)¡2
; for +2
·   +1
,
2¡(1¡)
2¡(1¡)

 = 1 ¡    = 1¡
  = 1 (+1)(1¡)¡
; for  ¸ +1
,  = 1 and  = 1
 (+1)(1¡)¡
Direct comparison of these values with the values of  and  of Proposition 3 shows
that (i) for ( +2) ·   ( + 1) mediation strictly improves the peace chance relative
to the optimal equilibrium (and hence to any equilibrium) of the Nash demand game with
un-mediated peace talks; and that (ii) for all other values of  mediation yields the same
peace chance as un-mediated peace talks.
Proof of Proposition 6. Consider the game of militarization and negotiation, in which
the negotiations are conducted by a mediator. Because of Proposition 5, each player’s
expected equilibrium payo¤s for militarizing and for remaining weak are, respectively:
 (; ) =  [ (1 ¡ ) +  2 + (1 ¡  ¡  )(1 ¡ )] + (1 ¡ )2;
(8)
 (; ) =  [ 2 + (1 ¡  )2] + (1 ¡ ) [  +  2 + (1 ¡  ¡  )] ¡ (9)
In the optimal equilibrium, the values of    and  depend on whether   ( + 2)
or ( + 2) ·  · ( + 1) —for the same arguments as in the proof of Proposition 2,
£
¤
there cannot exist an equilibrium with   ( + 1) when  2  2   
We consider the case in which   ( + 2) …rst. Substituting the values of   
and  reported in the proof of Proposition 5 into the expressions (8) and (9), and changing
variables, we obtain:
·
¸

(1 ¡ )
(1 ¡ ) ¡ 2
1¡
 (; ) =
[1 ¡ (1 ¡ )] +
[ ¡ ( + 1)(1 ¡ )] +
;
2 ( + 1)(1 ¡ ) ¡ 2
( + 1)(1 ¡ ) ¡ 2
2

1¡
 (; ) =
+
[(1 ¡ ) + 1]
2
2
Solving the indi¤erence condition  (; ) =  ( ) we obtain the value of militarization cost  which makes the players indi¤erent between arming and remaining weak, as a
function of the mixed strategy  and the model’s parameters:
1
(1 + ) ¡ (1 ¡ )
() = (1 ¡ ) ( + 1)

2
2 ¡ ( + 1)(1 ¡ )
36
(10)
Di¤erentiating () with respect to  we obtain:
 ()
1
3 ¡ (1 ¡ ) + 1
= ¡ (1 ¡ ) ( + 1) (1 ¡ )

2
(3 ¡  +  ¡ 1)2
/ ¡3 ¡ 1 + (1 ¡ )
The expression is positive for   ( ¡ 1)( + 3) and negative for   ( ¡ 1)( + 3)
on the range  2 [0 ( + 2)] ; further,  () = (1 ¡ ) 2 at  = 0 and  () =  at
 = ( + 2) We have thus concluded that there does not exist any equilibrium such that
 · 2 for  · 
Turning to the case ( + 2) ·   ( + 1) the expressions (8) and (9) take the
forms:
·µ
¶
¸
1 2 ¡ (1 ¡ )
1 2 ¡ (1 ¡ ) 1
1
(; ) =  1 ¡
(1 ¡ ) +
+ (1 ¡ )
 ( + 1)(1 ¡ ) ¡ 
 ( + 1)(1 ¡ ) ¡  2
2
·
µ
¶ ¸
1 ¡  2 ¡ (1 ¡ ) 1
1 ¡  2 ¡ (1 ¡ )

 (; ) = 
+ 1¡
 ( + 1)(1 ¡ ) ¡  2
 ( + 1)(1 ¡ ) ¡  2
·µ
¶
¸
1 2 ¡ (1 ¡ )
1 2 ¡ (1 ¡ ) 1
+(1 ¡ ) 1 ¡
 +
¡ 
 ( + 1)(1 ¡ ) ¡ 
 ( + 1)(1 ¡ ) ¡  2
Solving the indi¤erence condition (; ) =  (; )  we obtain the expression (1). This
function strictly decreases in  as () / ¡2(1 ¡ )( + 1) and takes the values
£
¤
() = ( + 1)( + ( + 1)2 ) and () = ( + 2) at the extreme of the interval   
£
¤
Because  ( + 1)  ( + 1)( + ( + 1)2 ) we conclude that for  2    there is
a unique equilibrium of the game of militarization and negotiation with optimal Myerson
mediation. The equilibrium militarization strategy  takes the expression (1).
Theorem 1 states that optimal Myerson mediation strategies achieve the same welfare as
a hypothetical institution that chooses militarization strategies, collects players arming level
reports, and makes settlement proposals with the objective to maximize players’ welfare 
Because this is game a revelation mechanism, it follows that optimal Myerson mediation
strategies weakly improves welfare  relative to all equilibria of the game of militarization
and negotiation with or without un-mediated peace talks. Plainly, a possible mediator’s
strategy is not to mediate at all (thereby replicating all equilibria of the baseline game
of militarization and negotiation). And as a consequence of the revelation principle by
Myerson (1982), the mediator can also reproduce all equilibria of the game of militarization
and negotiation with un-mediated peace talks.
£
¤
We want to prove that, for  2    the welfare improvement of Myerson mediators is
strict. By Proposition 4, we only need to compare the unique equilibrium of the game with
37
optimal Myerson mediation, with the equilibrium of Proposition 2. That these equilibria
do not yield the same welfare follows from the fact that   0 —i.e., strong player
pairs do not …ght with probability one, in the relevant equilibrium militarization range
( + 2) ·  · ( + 1)( + ( + 1)2 )  ( + 1)
Proof of Theorem 1. To prove this result, we …rst show a useful Lemma that compares equilibrium welfare of the militarization and negotiation game, when negotiations
are optimally mediated by a mediator (see Proposition 5), with equilibrium welfare when
negotiations are optimally settled by a Myerson arbitrator. Such an arbitrator acts analogously to our mediator, with one key di¤erence. Once both players have individually agreed
that the dispute will be settled by the arbitrator, the international community provides the
arbitrator with the means to enforce her recommendations. This is stark contrast with
mediators, who cannot enforce their recommendations.
Arguments identical to the ones of the proof of Proposition 5 show that, for any given
arming probability  the optimal Myerson arbitrator strategies (      ) coincide with
the solution of the arbitration program calculated in Lemma 1 of HMS: for  · ( + 2),
1¡
 = (1¡)+1
  = 1  = (+1)(1¡)¡2
  = 0; for ( + 2)   · ( + 1)  =
2
1 1¡4+3+2¡4+ 2 ¡2¡ 2 ¡ 2 +3+ 2

2
1¡2+(1¡)
2¡(1¡)
 = 1  = 1  = 1¡
 Noticeably,
 1¡2+(1¡)
this is the solution for all  (including   1)
Somewhat surprisingly, Lemma A below shows that equilibrium welfare of the militarization and negotiation game with optimal Myerson mediation and arbitration strategies is
the same. This result is of independent interest, and it reinforces the main …nding of Proposition 1 of HMS (the main result of that paper), that mediation and arbitration are equally
e¤ective in maximizing the probability of peace, taking the militarization probability  as
given.
Lemma A. The equilibrium welfare in the game of militarization and negotiation with
optimal Myerson mediation is the same as the equilibrium welfare in the militarization and
negotiation game in which negotiations are settled optimally by a Myerson arbitrator.
Proof of Lemma A. The equilibrium militarization strategy  when negotiations are
settled by a Myerson arbitrator is given by the indi¤erence condition:
 (; ) = (1 ¡ ) ((1 ¡  ) +  ) +  ((1 ¡  )2 +  2)
(11)
= (1 ¡ ) ((1 ¡  )2 +  2) +  ((1 ¡  )(1 ¡ ) +  (1 ¡ )) ¡  = (; )
Substituting the arbitration solution (     ) in this indi¤erence condition, we obtain
the expression (10) for  · ( + 2) and the expression (1) for ( + 2) ·  · ( + 1)
38
which correspond to the inverse of the equilibrium arming strategy in the militarization
and negotiation game with optimal Myerson mediation (for any  including   1)
We have concluded that the equilibrium militarization strategies in the game with a
mediator and with an arbitrator are the same. Because Proposition 1 of HMS proves that
mediation and arbitration are equally e¤ective in maximizing the probability of peace,
for any militarization probability  we conclude that also the equilibrium welfare of the
militarization and negotiation game with a mediator and with an arbitrator is the same.¥
As a consequence of the above Lemma, we can prove the Theorem simply by showing
that the optimal equilibrium welfare of the militarization and negotiation game with a
Myerson arbitrator achieves the same welfare as our hypothetical institution that includes
militarization deterrence in its objectives.
In fact, we prove a stronger result. We show that the arbitration solution achieves the
same welfare as an even more powerful hypothetical institution that not only aims to keep
militarization in check, but is also capable of enforcing its recommendations.
Letting weak and strong players’ interim expected payo¤s be, respectively,
 = ( (1 ¡ ) +  2 + (1 ¡  ¡  )(1 ¡ )) + (1 ¡ )2
 = ( 2 + (1 ¡  )2) + (1 ¡ )(  +  2 + (1 ¡  ¡  ))
this hypothetical institution chooses      and  so as to solve the program
min
  
(1 ¡ )2 (1 ¡  +  ) +2 (1 ¡ ) (1 ¡  +   ¡ )+ 2 (1 ¡  +   ¡ 2)
(12)
subject to the ex-ante obedience constraints:
 (1 ¡ ) [ ¡  ¡  ] = 0 [ ¡  ¡  ] ¸ 0 (1 ¡ ) [ ¡  ¡  ] · 0
to the interim individual rationality (for strong and weak players, respectively),
 ¸ (1 ¡ )  + 2
 ¸ (1 ¡ ) 2 +  (1 ¡ ) 
and to the interim incentive compatibility constraints (for strong and weak players, respec-
39
tively),
 ¸ (1 ¡ ) ((1 ¡  ) +  2) +  ((1 ¡  )2 +  (1 ¡ )) 
 ¸ (1 ¡ ) ((1 ¡  )2 +  ) +  ((1 ¡  )(1 ¡ ) +  2) 
In order to prove that the Myerson arbitration solution achieves the same welfare as
this hypothetical institution, we proceed in two steps.
The …rst step consists in showing that the solution (       ) of the minimization
of the con‡ict probability (given ):
 = (1 ¡ )2 (1 ¡  ) + 2 (1 ¡ ) (1 ¡  ) +  2 (1 ¡  )
(13)
subject to the interim individual rationality constraint of strong players
 = (1 ¡ ) (  + (1 ¡  ) ) +  ( 2 + (1 ¡  ) 2) ¸ (1 ¡ )  + 2
(14)
to the interim incentive compatibility constraint of weak players
(1 ¡ ) ((1 ¡  )2 +  2) +  ((1 ¡  )(1 ¡ ) +  (1 ¡ )) ¸
(1 ¡ ) ((1 ¡  )2 +  ) +  ((1 ¡  )(1 ¡ ) +  2) 
(15)
and to the ex-ante indi¤erence constraint
 (1 ¡ ) [ ¡  ¡  ] = 0
(16)
coincides with the solution (       ) of the minimization of the militarization probability  under the same constraints (13-16).
An immediate consequence of this result is that this solution (       ) is also
the solution of the maximization of welfare  under the constraints (13-16).
To prove this result. We …rst solve  in the indi¤erence constraint (16), and substitute
it in the constraints (14) and (15), respectively. Rearranging, these two constraints now
40
take the forms, respectively
¤
1
1£
 = (1 ¡ ) ¡  (1 ¡ ) (2 ¡ 1) + (1 ¡ ) (1 ¡ )2  + 2(1 ¡ ) + 2  ¸ 0
2
2
1
 =
 (2 ¡ 1) [1 ¡ (1 ¡ )  ¡  ] ¡  ¸ 0
2
Note now that the con‡ict probability  decreases in   that  is independent of  
and that  increases in   Because setting  = 1 makes  as small as possible without
violating the constraints  ¸ 0 and  ¸ 0 it has to be part of the solution (       )
of the con‡ict probability  minimization program above. Substituting  = 1 in  and
 we thus obtain the simpler expressions:
 = 2 (1 ¡ ) (1 ¡  ) +  2 (1 ¡  ) 
¤
1
1£
 = (1 ¡ ) ¡  (1 ¡ ) (2 ¡ 1) + (1 ¡ ) (1 ¡ )2 + 2(1 ¡ ) + 2  
2
2
Now, we observe that  decreases in  and   and that  = ¡ when  = 1 and
 = 1 Because  decreases in both  and   this concludes that the constraint  ¸ 0
must bind.
We now solve for  in the constraint  = 0 and substitute it into the expressions for
 and  We obtain
 =  2  + 1 (   ) 
1
 = ¡  2 (1 ¡ )  + 2 (   ) 
2
where the explicit formulas of 1 and 2 are inessential. Because  increases in  and
 decreases in   this concludes that the constraint either  = 0 must bind, or  = 0
Solving  in the constraint  = 0, and substituting the solution in the objective
function  we obtain:
2 ( ¡ ) (1 ¡ ) + 1 ¡ 
=

1¡
This function increases in  for  ·  ¡ 12 = (1 ¡ ) 2 (For   (1 ¡ ) 2 the
problem becomes trivial as militarization is so expensive that there is an equilibrium of the
equilibrium of the militarization and negotiation game in which militarization does not take
place,  = 0 and peace obtains.) Hence, the minimization of  under the constraints that
 = 0  = 0 0 ·  · 1 0 ·  · 1 and 0 ·  · 1 is equivalent to the minimization of
 subject to the constraints that  = 0  = 0 0 ·  · 1 0 ·  · 1 and 0 ·  · 1
41
The second step of the proof the Myerson arbitration solution achieves the same welfare as the hypothetical institution of program (12) consists in showing that the solution (       ) of the minimization of  subject to the constraints  = 0  = 0
0 ·  · 1 0 ·  · 1 and 0 ·  · 1 is exactly equal to the equilibrium of the militarization and negotiation game in which disputes are settled with the optimal Myerson
arbitration strategies reported before Lemma A.
We begin by noting that setting  = 0 together with  = 0 and  = 0 yields  =
! +1 because  (2 ¡ 1) (2 ¡ 2 ¡ 1) ¸ 0 when  ·  ¡ 12 =
(1 ¡ )2 Hence, the solution must have an interior  2 (0 1)
To calculate the solution (       ) we proceed as follows.
First, we calculate the minimal value () that satis…es  = 0 and  = 0 subject to
the constraints 0 ·  · 1 and 0 ·  · 1
Solving for  and  as a function of   we obtain:
(2¡1)(2¡2¡1)
0
1 ¡  1 ¡  ¡  (1 ¡ 3 + (1 ¡ ))

1 ¡ 2 + (1 ¡ )
1
(1 ¡ ) ¡ (1 ¡ ) ¡  2
 () =
( + 1) (1 ¡ )

2
1 ¡ 2 + (1 ¡ )
 =
Because () decreases in  for all   ( + 1) we want to set  as large as possible.
2¡(1¡)
When  = 1 we obtain the solution  = 1¡
 which lies in [0 1] if and only
 1¡2+(1¡)
if  ¸ ( + 2) We note that this expression is part of the optimal Myerson arbitrator
strategies (      ) for ( + 2) ·  · ( + 1)
Further, setting  = 1 we obtain also:
 () =
1
(1 ¡ ) ¡ 
( + 1) (1 ¡ )

2
1 ¡ 2 + (1 ¡ )
Because  0 () / ¡ 12 ( + 1) (1 ¡ )  (2 ¡  +  ¡ 1)2  this expression strictly decreases
in 
Likewise, solving for  and  as a function of   we obtain:
1
(1 ¡ ) +  2  ¡ (1 + )
( + 1) (1 ¡ )
2
( + 1)(1 ¡ ) ¡ 2
2
(1 ¡ ) ¡  (1 ¡ 2 + (1 ¡ ))
=

(1 ¡ ) (( + 1)(1 ¡ ) ¡ 2)
() =

(17)
For  · ( + 2) the expression () increases in   We thus set  = 0 and obtain the
42
1¡
solution  = (+1)(1¡)¡2
 which lies in [0 1] if and only if  · ( + 2) Again, we note
that this expression is part of the optimal Myerson arbitrator strategies (      ) for
 · ( + 2) Further, when  = 0 we obtain also:
() =
1
(1 ¡ ) ¡ (1 + )
( + 1) (1 ¡ )
2
( + 1)(1 ¡ ) ¡ 2
(18)
Because  0 () = ¡ 12 (1 ¡ ) ( + 1) (1 ¡ ) (1 + 3 ¡ (1 ¡ ))  (3 ¡  +  ¡ 1)2  this expression strictly decreases in 
Because the function () strictly decreases in  on the whole range [0 ( + 1)]  the
inverse function () =  ¡1 () identi…es the minimal militarization probability  subject
to the constraints that  = 0  = 0 0 ·  · 1 and 0 ·  · 1
Direct calculations show that the inverse of the function () reported in expression
(10) for  · ( + 2) and in expression (1) for ( + 2) ·  · ( + 1) coincides with
the function () reported in expression (18).
We have shown that all the welfare-relevant parameters (      ) of the solution
of the minimization of  subject to the constraints  = 0  = 0 0 ·  · 1 0 ·  · 1
and 0 ·  · 1 take exactly the same values as       in the equilibrium of the
militarization and negotiation game in which disputes are settled with optimal arbitration
strategies.
This result yields Theorem 1 because (i) the optimal arbitration strategies satisfy all
the constraints of the program (12), that calculates the optimal choice      and 
of our welfare-maximization hypothetical institution (that is even capable of enforcing its
recommendations); (ii) the constraints that  = 0  = 0 0 ·  · 1 0 ·  · 1 and
0 ·  · 1 correspond to the constraints (13-16) that are weaker than the constraints of
program (12); and (iii) the solution (       ) of the minimization of  subject to the
constraints  = 0  = 0 0 ·  · 1 0 ·  · 1 and 0 ·  · 1 also maximizes welfare
 under the same constraints.
43
Dispute Resolution Institutions
and Strategic Militarization
Adam Meirowitz, Massimo Morelli, Kristopher W. Ramsay
and Francesco Squintani
Additional Material
Not Submitted for Publication
£
¤
Analysis for Militarization Cost Values  2
   
We complete the analysis of our game of militarization and con‡ict, with or without un£
¤
mediated or mediated peace talks, for militarization cost values  2
    We introduce
the notation ¹ = (1 ¡ ) 2
Proposition 2B. If the cost of arming    then the equilibrium of the militarization and
negotiation game that maximizes the players’ welfare  is such that each player militarizes
with probability  () = max f ¡ 2(1 ¡ ) 1g  strong players demand  =  weak
players demand  = 1 ¡  and war erupts only if both players are strong.
¹ and  · 4 The equilibrium of the militarization
Suppose that the cost of arming  2 ( )
and negotiation game that maximizes the players’ welfare  is such that each player militarizes with probability  () = ( + 2) strong players demand  = (1 + 2) + 12 ¡
 ( ¡ 1) (1 ¡ ) 4 weak players demand  = 1 ¡   and war erupts only if both players
are strong. When   4 instead  = 1¡(1¡) and  = [( + 2) (1 ¡ ) ¡ 2] [3(1¡)]
¹ then the equilibrium of the militarization and negotiation game
If the cost of arming  ¸ 
that maximizes the players’ welfare  is such that militarization does not take place,  = 0
and peace obtains.
¹ …rst. Recall from the proof of Proposition 2 that in this
Proof. We consider the case   
case, there does exist any value of  that equalizes the payo¤s  (; ) and (; ) associated with the optimal equilibria of the Nash demand game (see Proposition 1). Speci…cally,
for any   ( + 1) it is the case that  (; )  (; ) whereas for  ¸  ( + 1) 
1
 (; ) = 12¡  12 =  (; ) We also know from the proof of Proposition 2 that there
cannot exist any equilibrium of the Nash demand game with payo¤s ^ ( )  (; ) or
^
with (
)   (; ) for any  Hence, there cannot exist any equilibrium of the game of
militarization and con‡ict with arming strategy  · ( + 1) The optimal equilibrium of
this game is such that    ( + 1) and, just like in the optimal equilibrium of Proposition
2, each player militarizes with probability  () = maxf ¡ 2(1 ¡ ) 1g strong players
demand  =  weak players demand  = 1 ¡  and war erupts if only if both players
are strong. This payo¤s for militarizing and remaining weak in this equilibrium are, respec^
^
tively, ()
= (1 ¡ ()) + ()2 ¡  and ()
= (1 ¡ ())2 + ()(1 ¡ ) Because
 ()   ( + 1)  they are smaller than the payo¤s (; ) and  (; ) associated with
the optimal equilibria of the Nash demand game.
¹ Consider again the payo¤s  (; ) and (; )
Second, we consider the case  2 ( )
associated with the equilibria of Proposition 1. When    ( + 2)  solving the indi¤erence condition (; ) = (; ) we obtain:
() =
1
(1 ¡ ) ( + )
2
¹ This implies that
which strictly increases in  and is such that  (0) = (1 ¡ ) 2 = 
 (; )  (; ) for    ( + 2)  Because there cannot exist any equilibrium of the
^
Nash demand game with payo¤s (
)   (; ) or with ^ ( )  (; ) for any 
there cannot exist any equilibrium of the game of militarization and con‡ict with arming
strategy    ( + 2) 
When    and  ¸  ( + 2)  direct inspection of payo¤s expressions (3) and (4)
shows that (; )   (; ) By Proposition 2, by setting the strong players’ equilibrium
^
demands ^ above  =  it is possible to increase the payo¤s (;
) and reduce
^
 (; ) without a¤ecting the peace probability in the Nash demand game, as long as
^ · 1 ¡ (1 ¡ )  So, the optimal equilibrium of the game of militarization and con‡ict is
such that ^ (; ) = ^ (1¡)+2¡ = (1¡)2+(1¡) = ^ (; ) for  =  ( + 2) 
Thus, the optimal strong players’ demands are ^ = (1 + 2) + 12 ¡  ( ¡ 1) (1 ¡ ) 4
This expression increases in  and it is smaller than 1 ¡ (1 ¡ )  for  · 4 For   4 the
optimal strong players’ demands are ^ = 1 ¡ (1 ¡ )  so that the arming probability 
^
^
solves (;
) = (1 ¡ (1 ¡ ) ) (1 ¡ ) + 2 ¡  = (1 ¡ )2 + (1 ¡ ) = (;
) and
takes the formula reported in the Proposition we are proving.
¹ In this case, there is an equilibrium of the game of militaFinally, suppose that  ¸ 
rization and con‡ict in which militarization does not take place,  = 0 and peace obtains.
In fact, the payo¤s for militarizing and remaining weak are, respectively,  (; ) =  ¡ 
and  (; ) = 12; and (; ) = ¡ · (; ) = 12 for  ¸ ¡12 = (1 ¡ ) 2 =
2
¹

Proposition 4B. Suppose that the cost of arming    Then, every equilibrium of the negotiation game with un-mediated peace talks that increases the peace probability in emerged
disputes (i.e., after arming decision are sunk) leads to a strict increase of equilibrium militarization probability  and a strict decrease of ex-ante welfare  in the associated equilibrium of the whole game of militarization and negotiation.
¹ Then, there exists equilibria of the negotiation
Suppose that the cost of arming  2 ( )
game with un-mediated peace talks that increase the peace probability in emerged disputes,
and that lead to a strict increase of ex-ante welfare  in the associated equilibrium of the
whole game of militarization and negotiation.
Proof. The analysis for case    is identical to the case for  2 [ ] studied in
Proposition 4.
¹ Restricting attention to  2 [(+2) (+
Suppose that the cost of arming  2 ( )
1)) un-mediated peace talks reduce the probability of war among strong players to 1 ¡
  and increase the payo¤s of strong players to ^ (; ) = ^ (1 ¡ ) + [ 2 + (1 ¡
 )2] ¡  without changing the payo¤s of weak players  (; ) For  · 4 the arming
probability  = ( + 2) is at the lower bound of the admissible range. Increasing 
above zero, the indi¤erence condition ^ (; ) =  (; ) is still met at  = ( + 2) by
appropriately decreasing ^ 2 [ 1 ¡ (1 ¡ )] Thus un-mediated peace talks increase the
peace probability in emerged disputes, without increasing the militarization probability,
and hence lead to a strict increase of ex-ante welfare  in the associated equilibrium
of the whole game of militarization and negotiation. For   4 this argument holds a
fortiori, because when  = 0 it is the case that   ( + 2) and ^ = 1 ¡ (1 ¡ )
Hence, by increasing  above zero, the indi¤erence condition ^ (; ) =  (; ) is still
met appropriately decreasing  and holding ^ = 1 ¡ (1 ¡ ) …xed.
To calculate the optimal equilibrium of the whole game of militarization and negotiation
with un-mediated peace talks, we need to compare the optimal equilibrium for   ( +2)
with the optimal equilibrium with  2 [( + 2) ( + 1))
To calculate the optimal equilibrium of the whole game of militarization and negotiation
with un-mediated peace talks for   ( + 2) we …rst note that the maximum peace
1¡
probability in asymmetric dyads is ¹ = (+1)(1¡)¡2
 Supposing that the optimal peace
probability  reaches the upper bound ¹  the indi¤erence condition takes the form
^
 (; ) = (1 ¡ ) + 2 ¡  = (;
) = (1 ¡ )2 +  ((1 ¡ )(1 ¡  ) +  (1 ¡ )) 
Solving for  we obtain the expression
() =
¡
¢
1
1¡
( + 1)  ¡  +  +  2

2
3 ¡  +  ¡ 1
3
¹ () =  for  = ( + 2)  0 ()  0 for  
This function is such that (0) = 
( ¡ 1) ( + 3) and  0 ()  0 for   ( ¡ 1) ( + 3) Because equating () = ¹ yields
also the solution  = ( ¡1)( +1) we conclude that the equilibrium  strictly decreases in
¹ = ( ¡ 1) ( +1) This solution is admissible,
 and is such that () = ( +2) and ()
hence the optimal peace probability in asymmetric dyads  reaches the upper bound ¹ 
Inverting the expression () we obtain the formula:
3
1
1p
() =  + ( ¡ 1) +
( ¡ 1) [8 + [4 + ( + 1)2 ] ( ¡ 1)]
2
2
2
(19)
where () = 2 ( + 1)¡1 (1 ¡ )¡1 
The associated welfare is:
 = (1 ¡ )2 + 2 (1 ¡ ) (1 ¡  ) + 2 (1 ¡ )   +  2  ¡ 2
As a corollary to the next Proposition, it turns out that the optimal equilibrium of the
whole game of militarization and negotiation with un-mediated peace talks is such that the
arming strategy is   ( + 2) and hence that it satis…es the expression (19).
Proposition 6b. The optimal equilibrium of the militarization and negotiation game with
a Myerson mediator is such that the equilibrium militarization probability  () is strictly
decreasing and continuous in  and that the mediator recommends split (12 12) to weak
player pairs ( ) with probability one. For  2 [0 ] the arming probability is:
() = (1 + )
2 ¡ (1 ¡ )

2(2 + ) ¡ (1 + )2 (1 ¡ )
with  (0) = ( + 1) and () = ( + 1)( + ( + 1)2 ) and () = ( + 2) The
mediator recommends split ( 1 ¡ ) to asymmetric players pairs ( ) with probability
 2 (0 1) and (12 12) with probability 1 ¡  ; whereas it recommends split (12
12) to strong players pairs ( ) with probability  2 (0 1) and quits leading to war
otherwise. Myerson mediators strictly improve the chance of peace  and the welfare 
with respect to any equilibrium of the benchmark game of militarization and con‡ict with
un-mediated peace talks, or without communication.
¹ letting () = 2 ( + 1)¡1 (1 ¡ )¡1  the arming probability is:
For  2 ( ]
3
1
1p
¹
() =  + ( ¡ 1) +
( ¡ 1) [8 + [4 + ( + 1)2 ] ( ¡ 1)] for  2 ( ]
2
2
2
4
¹ = 0 The mediator recommends split (
with lim!+ (()) = ( + 2) and (())
1 ¡ ) to asymmetric players pairs ( ) with probability  2 (0 1) and quits leading
to war otherwise, and always quits when dealing with strong players pairs ( ) Myerson
mediators yield exactly the same outcome (and hence the same peace chance  and welfare
 ) as the optimal equilibrium of the benchmark game with un-mediated peace talks.
Proof. Recovering the analysis of Proposition 6, for the case in which   ( + 2)
the militarization cost value () which makes the players indi¤erent between arming and
remaining weak in the game with a Myerson mediator is reported in expression (10). This
function () strictly increases in  for   ( ¡ 1)( + 3) and strictly decreases in  for
  ( ¡ 1)( + 3) on the range  2 [0 ( + 2)) and it is such that (0) = ¹ and
(( + 2)) = 
¹ there exists a unique equilibrium arming probability  () 
We thus conclude that ( ]
¹ = 0 The inverse
strictly decreasing in  and such that () ! ( + 2) for  #  and ()
() =  ¡1 () of expression (10) in the range [(¡1)( +3) ( +2)) yields the expression
stated in the Proposition we are proving. This is the same expression as (19), the optimal
equilibrium militarization strategy  in the game with un-mediated peace talks, under the
constraint that   ( + 2) Thus, we conclude that (i) the optimal equilibrium of the
whole game of militarization and negotiation with un-mediated peace talks is such that the
arming strategy  is smaller than than ( + 2) and satis…es expression (19), and (ii) this
equilibrium achieves the same outcome as the optimal equilibrium of the militarization and
negotiation game with optimal Myerson mediation.
Turning to the case in which ( + 2) ·   ( + 1) we again recover the analysis
of Proposition 6, and see that the arming probability of the optimal equilibrium of the
militarization and negotiation game with a Myerson mediator satis…es expression (1). This
function strictly decreases in  and takes the values  (0) = ( + 1) and () = ( +
1)( + ( + 1)2 ) Simply extending the same arguments in the proof of Proposition 6,
we conclude that (i) for  2 [0 ] the optimal equilibrium of the game of militarization
and negotiation with optimal Myerson mediation is such that the militarization strategy
 takes the expression (1), and (ii) that the mediator strictly improves peace chance 
and welfare  relative to all equilibria of the game of militarization and con‡ict with or
without un-mediated peace talks.
5
Mediation and Peace
Johannes Hörner, Massimo Morelli and Francesco Squintani
Online Appendix not Submitted for Publication
[...]
Evidence on Commitment
One of the main assumptions of our model is the mediator’s commitment to lead to a
con‡ict escalation if this is prescribed by the optimal solution. In the real world, this
translates into the mediator’s commitment to quit and terminate the mediation, at least
with some probability. In this section we provide two types of evidence that mediators in
the real world are capable of keeping this commitment, and even that players prefer having
a mediator with a credible reputation of being able to keep this commitment. The …rst
type of evidence is from a data set that has settlement attempts as units of observation,
namely the Issue Correlates of War dataset (ICOW), by Hensel et al (2008). The second
type of evidence will be from an illustrative case study.
In fact, mediators often make clear to the players under which circumstances they will
quit. Such contingent plans of action often include deadlines. According to Avi Gil, one of
the key architects of the Oslo peace process, “A deadline is a great but risky tool. Great
because without a deadline it’s di¢cult to end negotiations. [The parties] tend to play
more and more, because they have time. Risky because if you do not meet the deadline,
either the process breaks down, or deadlines lose their meaning” (Watkins, 1998). Among
the many cases in which this technique was used, see for instance Curran and Sebenius
(2003)’s account of how a deadline was employed by former Senator George Mitchell in the
Northern Ireland negotiations. Committing to such deadlines might be somewhat easier for
professional mediators whose reputation is at stake, but they have been also used both by
uno¢cial and o¢cial individuals, including Pope John Paul II and former U.S. President
Jimmy Carter.27 Meanwhile, institutions like the United Nations increasingly set time
27
Bebchik (2002) describes how Clinton and Ross attempted to impress upon Arafat the urgency of
accepting the proposal being o¤ered for a …nal settlement, calling it a “damn good deal” that would not
be within his grasp inde…nitely.
1
limits to their involvement up-front (see, for instance, the U.N. General Assembly report,
2000).
Evidence from settlement attempts data
The ICOW data set considers each settlement attempt as a distinct observation.28 The key
source of variation is whether mediators resume the mediation process through a new settlement attempt following failure or whether they withdraw for good. The theory assumes
the mediator’s commitment to withdraw from mediation, expecting that this condition is
essential to successful mediation. Mediation attempts in the presence of commitment to
quit should be expected to be more successful, and mediators with such a reputation more
sought after to serve as a mediator compared to mediators that cannot commit to quit. We
probe the ICOW data for information that is consistent with these two hypotheses.
To ascertain whether these patterns exist, we construct rough indicators of mediation
termination and di¤erentiate cases according to the circumstances under which they terminated. The settlement attempt may end with 1) an agreement fully implemented; 2)
an agreement reached but not rati…ed by at least one party; 3) an agreement reached and
rati…ed but not complied with by at least one party; 4) no agreement reached and/or escalation of violent hostilities.29 We say a mediator has “quit” if the mediator does not initiate
a new mediation attempt involving the same two primary players within at least 10 years
of the end of the mediation failure. We consider this a “responsive quit” if the settlement
attempt ended under any conditions 2–4. A non trivial proportion of failed mediation
attempts satisfy this criteria and a signi…cant portion of the mediators in the sample will
have quit at least once. Mediators who have established a reputation for actually following
through on commitments to withdraw from the process in response to player transgressions
should be considered more e¤ective mediators and therefore should be more likely to be
invited as a mediator in future settlement attempts.
Variable frequency Rel. Frequency (total) Rel. Frequency (failed)
quit1
38
28.4% (134 total)
41.8% (91 total)
quit2
39
29.1% (134 total)
41.5% (94 total)
28
We use ICOW instead of other datasets because it’s level of analysis is appropriate for our purposes.
The International Crisis Bargaining dataset (ICB), Brecher and Wilkenfeld (1997 and 2000) for example,
would not be useful because it collapses all settlement attempts for each crisis into one observation.
29
We use two alternative de…nitions of agreement, leading to quit1 and quit2 variables, but they lead to
very similar results.
2
Table 1 describes how frequently mediators quit in the sample of 134 mediation attempts
present in the ICOW dataset. The relative frequency of quitting in the panel varies slightly
based on the de…nition of quitting used, which vary by how strict the criteria are for
coding the result as a responsive quit, but overall the data suggest that approximately 30%
of the mediation attempts resulted in the mediator quitting by our de…nition. Of failed
mediation attempts, mediators quit responsively in approximately 42% of cases. It is clear
that mediators do quit in a signi…cant portion of cases in which quitting is called for.
Variable frequency Rel. Frequency (total)
Quit1
116
86.6% (134 total)
Quit2
116
86.6% (134 total)
Table 2 demonstrates that an overwhelming majority of mediators in the sample quit
the process (by our de…nition) at least once in their career. 116 of the 134 mediation
attempts in the data were mediated by a third party that had quit at least once previously
in the panel. This suggests mediators that demonstrate they will withdraw in response
to belligerent transgressions are those asked again to mediate crises. The imprecision of
the measurement and the limited variation does not allow us to claim that this is airtight
evidence that the mediator’s capability to credibly threaten to quit when appropriate is a
key factor in determining the mediator selection, but the evidence is at least consistent with
the general perception that the ability to commit we assume in our model is an important
characteristic of real world mediation.
Illustrative Case Study: Ko… Annan in Kenya and Syria
When the contested December 2007 Kenyan Presidential election resulted in widespread
ethnic violence, threatening to escalate to full-scale civil war, the international community
rushed to establish peace-making e¤orts. After weeks of multiple uncoordinated mediation
attempts that failed to bring the players closer to a negotiated settlement, the African Union
appointed former UN Secretary-General Ko… Annan to head the Panel of Eminent African
Personalities, a coalition of political actors to bring about a solution to the escalating
violence. The most important pillar of Annan’s mediation strategy was the consolidation
of the disparate mediation e¤orts and interested third parties behind a single process.
He demanded, and received, assurances that the international community back the Panel’s
e¤orts and refrain from pedaling alternative or competing mediation attempts. Throughout
the negotiations, Annan constantly devised signals to communicate the lack of alternative
3
negotiating channels to the players in order to ensure their engagement with the Panel’s
e¤orts and proposals.
While working hard to overcome the challenges associated with bridging the bargaining
gap separating Kibaki and Odinga, Annan also made a point early on to communicate to
the players that the Panel would not remain involved inde…nitely. As the pace of progress
slowed, Annan reiterated that he ‘would not be available forever and that an alternative
had to be found’ (Lindenmayer and Kaye, 2009). When the two sides began stalling for
time, refusing to make meaningful concessions on the political issue, Annan announced
a suspension of the talks. In an interview with the Centre for Humanitarian Dialogue,
Gri¢ths (2008), Annan described the motivation for his decision:
“...Look, this is getting nowhere, so I’ve decided I’m suspending talks.” ...“I had done
my duty and believed the leaders should do theirs.”
Annan clearly used the suspension of the mediation process, and the threat of its termination, to coerce the parties into giving up more than they hoped at the negotiation table.
He even went so far to strengthen his signal by suggesting his successor, Cyril Ramaphosa
of South Africa. Kibaki and the PNU vehemently rejected this proposed replacement,
claiming Ramaphosa to be partial to Odinga’s claim. But nevertheless, the signal seems
to have been perceived as credible, as the players increased the urgency with which they
engaged with the Panel’s peace-making process (Lindenmayer and Kaye 2009).
Annan’s commitment to withdraw from mediation in the event the parties refused to
abide by his negotiating plan was a calculated complement to his demand to consolidate
the international community behind one mediation process. These two tactics served the
strategy to remove the players’ ability to shop around for alternative mediators and con‡ict
resolution avenues, leaving them with the option of following Annan’s lead or continuing a
…ght neither side wanted. This strategy …t the dispute well because it was clear that both
parties wanted to end the con‡ict, but that the possibility of alternative means to attain
their political goals tempted them away from conceding too much at the negotiating table.
Despite a mixed record of success (failure in Rwanda and Bosnia; success in Kenya),
Annan was asked again to step into the mediator’s role as Special Envoy for the U.N and
the Arab League in Syria’s escalating civil war. One of the prominent reasons cited for
his appointment was his recent success in Kenya. But, unlike in the Kenya case, in Syria
Annan faced a deeply divided international community. Though nominally unanimous in
support of Annan’s role and his six-point peace plan, the competing world powers almost
immediately took actions to undermine the mediation process. The U.S. and Western
allies began arming rebel forces and continued to call for Assad to step down while Russia
and China continued to prop up Assad’s regime. Without the international community
united behind the process, the situation deteriorated. Annan quit in response to continued
escalation of violence and both parties’ violation of the six-point plan. As such, Annan
4
maintained his credibility to commit to withdraw from his role in the event players become
uncooperative.
Mediation and Arbitration Without Commitment
We here explore the con‡ict resolution capabilities of mediators who pursue peace at all
costs in all circumstances. To provide a framework to our analysis, we focus on truthful
revelation mechanisms, as in the analysis of the mediators with commitment of section
??. Each player  privately sends a message  2 f g to the mediator, who then makes
a (public) recommendation. The only di¤erence with respect to section ?? is that, here,
the mediator does not have any commitment capability: given its (equilibrium) beliefs
with respect to the types of players as a function of the received message, she makes
recommendations that induces beliefs which leads to the equilibrium that maximizes the
chance of peace.
We argue that such mediators are ine¤ective. Speci…cally, we …rst show that there
do not exist equilibria in which the players reports their types truthfully and agree to
the mediator’s recommendations. Hence, mediators who seek peace in all circumstances
cannot improve upon un-mediated communication by means of standard truthful revelation
mechanisms. This result follows from Theorem 2 by Fey and Ramsay (2009), but because
the setting is slightly di¤erent, we present a proof.
The …rst step is to note that if there were an equilibrium, it would be one in which
peace is achieved with probability one. In fact, because the players would truthfully reveal
their types, the mediator can achieve peace with probability one by making the proposals
( 1 ¡ ) after reports ( )  (1 ¡  ) after reports ( )  and (12 12) otherwise.
Because the equilibrium achieves peace with probability one, the high-type’s incentive
compatibility constraint with double deviation reduces to:
Z
0
1
 (j) ¸
Z
1
maxf Pr[j ] + Pr[j ]2g (j)
(20)
0
and the low-type’s incentive compatibility constraint with double deviation reduces to:
Z
1
0
 (j) ¸
Z
0
1
maxf Pr[j ]2 + Pr[j ](1 ¡ )g (j)
(21)
These two constraints are stronger than the following high-type and low-type incentive
5
compatibility constraints without double deviation:
Z
1
0
 (j) ¸
Z
1
 (j) and
0
Z
0
1
 (j) ¸
Z
1
 (j)
0
which evidently, can only be satis…ed if
Z
1
 (j) =
0
Z
1
0
 (j) ´  · 12
Let us turn to the ex post participation constraint for the high type. For any  2 (0 1)
such that Pr[ ]  0 this constraint is:
 ¸ Pr[j ] + Pr[j ]2
(22)
Integrating this constraint, we obtain:
12 ¸  =
Z
1
0
 (j) ¸
Z
1
(Pr[j ] + Pr[j ]2) (j)
0
or, with a minor notational violation,
¸
 [ j]
[ j]
12 ¸
 +
2 (j)
 (j)
 (j)
0
= Pr[j] + Pr[j]2
Z
1
·
= 2 + (1 ¡ ) 
which contradicts
2 + (1 ¡ )   12 i.e.,   
We have shown that there do not exist equilibria in which the players reports their types
truthfully and agree to the mediator’s recommendations. Hence, mediators who seek peace
in all circumstances cannot improve upon un-mediated communication by means of standard truthful revelation mechanisms.
We now turn to consider arbitration without commitment. For comparability with
mediation without commitment, we set the analysis in a revelation game. The players
choose whether to participate and then report their types to the arbitrator, who imposes
peaceful splits. It is easy to show that there cannot exist any equilibrium in which the
6
players agree to participate and play any strategy (including mixed strategies) at the report
stage of the game.
In fact, arbitration without commitment establishes peaceful splits ( 1 ¡ ) for any
pair of messages (1  2 ) according to the symmetric distribution  ( 1 ¡ j1  2 ) Let
 (j) be the distribution of either player ’s split  given ’s message. In equilibrium,
letting   be the mixed strategy of a player of either type  and any message  2 (  )
and it must be that:
Z
Z
1
0
1
 (j) ¸
 (j0 )
0
for any other message 0  As in the above argument, these inequalities can only be simulR1
R1
taneously satis…ed if 0  (j) = 0  (j0 ) · 12 for all  and 0 in (  ) But
then, the interim participation constraint of strong players fails, because, again
2 + (1 ¡ )   12 when   
Hence, the …nding of Proposition 1 is con…rmed for the case of third party intervention
without commitment. The arbitrator is no more e¤ective than the mediator, even in
absence of commitment.
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8