Laissez-faire International Relations
Diplomacy as a Gaming Exercise
By Matt Sundstrom
1. The International System
3
2. Machine Game Exploration of Automatic Stabilization
6
3. Diplomacy
8
4. Exploring Automatic Stabilization: Game Results
17
5. Extending Simulation
24
Bibliography
Acknowledgements
Matt Sundstrom
May 30, 1990
Foreword 2002
I was introduced to Diplomacy in college, and I was hooked pretty quickly. It was
very much my kind of game. About the same time, I started classes in a relatively new
undergraduate program called Mathematical Methods in the Social Sciences (MMSS). I
describe the program to people as what an engineer might have to study, but the math
is tailored to the social sciences. Coursework included game theory, statistics and a
heavy emphasis on mathematical modeling. I felt a lot of what I was learning lent itself
to a study of the game. So I proposed to write my undergraduate thesis on the game as
a simulation of laissez faire international relations. Happily, my idea was approved.
While I was largely interested in studying Diplomacy as a player, writing an
academic thesis required I connect the game to more “serious” social science. The
game served well on both fronts. It may seem overly academic from a player’s
standpoint, but I still feel the substance applies to both the game and academia. Most
of the math attempts to formalize what we already think about while playing game…is
this move (stab) worth it? Will it work? What happens if it doesn’t?. From a gamer’s
standpoint, system evolution can be thought of in terms of winning outright, drawing,
surviving or being eliminated. Game results were presented and analyzed in terms of
simulation, but they can be very real from a player’s standpoint.
After I wrote this, I did not try very hard to stay involved with the hobby (maybe I’d
had enough for a year), and had a whole lot of other interests. I’ve recently started to
get back into it. A lot of the people I relied on over a decade ago are still going strong,
which was very good to see and helped me reconnect (thanks twice). I’m happy there
might be an audience within the hobby for the paper, because I had always wondered
how it might be received by players. The end of section three and section four may be
the most interesting, but I hope there are nuggets throughout. You’ll find several
endorsements of the beauty of the game in any event.
A lot has happened since 1990, but the text is largely the as the original version (I
tried to correct some typos or clarify things if I could). There is a lot I’d update and
expand upon now, especially with respect to playing the game. I’d invite your
questions, comments and thoughts.
Thanks for playing.
2
1. The International System
Much of gaming in the social sciences utilizes a simulated environment with live
players, in which the player's behavior is the subject of study for teaching, experimental,
or operational purposes.1 Separate disciplines can make constructive use of games for
a variety of problem analyses. One such field is international relations. Inherent in the
dynamics of the international arena are behavioral and systemic patterns that can
usefully identified be means of a simulation.2 At any moment, the international system
constitutes an important set of constraints and incentives within which national decision
makers must act, including the distribution of natural resources, cultural traits,
internation bonds and the structural patterns subsequently created. Given this
framework, international actors seek all or at least some of the following values:
security, power, glory, and wealth. National goals are defined in terms of these values, 3
and are pursued in the international arena.
Probably one of the most significant characteristics of international relations is the
fact that there does not exist any central coordinating mechanism or regime over the
system.4 States are left to their own devices in attempting to achieve their objectives. A
multistate system can thus be defined as being a regionally bounded and territorially
contiguous set of autonomous sovereign political entities that recognize no higher
secular authority, and whose members all have recourse to force.5 This image is often
likened to the free market in economics. Both can be viewed as predatory
environments where a process of natural selection is thought to be one of the principal
mechanisms that govern the system and the survival of its inhabitants. 6
In the absence of authoritarian restrictions on national behavior, the possibility for
the formation of coalitions among nations and their impact on the members of the
system is an important element of a multistate network. Within the international system,
all countries influence each other merely by sharing the same spatial, temporal, and
sociopolitical environment.7 Consequently, there exists an avenue for cooperative
1
Shubik, p.185
Jones & Singer, p.27
3 Bennett & Alker, p.232
4 Cusack, p.209
5 Bremer/Mihalka, p.303
6 Cusack/Stoll (1990a), p.262
7 Singer (1979a), p.51
2
3
behavior among states. Self-preservation and pervasive doubt imply that a state would
like to avoid the short end of any of these arrangements.8 In forming alliances, individual
nations generally seek both to deter a potential adversary and commit assistance or
neutrality in the event of a conflict.9 Most agree that alliances are intended to provide
their signatories with greater security than each would have alone.10 A bloc of nations
gains significance in the presumed unity of action among its members.11 It follows that
alliance patterns are an important explanatory variable in the international system.12
The preservation of a multistate system and its individual members under the
aforementioned conditions is of profound interest. Stability in this sense can be defined
as a steady number of states and a constant distribution of power among them.13 There
are two major schools of thought as to how this structure can be maintained,
respectively termed Realist and Idealist. Realism avoids reliance on anything not
naturally inherent to the system. One version of this philosophy, known as "laissezfaire" or "automatic stabilization", is based on the presumption that should any nation
desire to become predominant, it must, in order to protect its own interests, act to
prevent any other nation from accomplishing such an objective. As a result, the
international system can be policed solely by self-interest (again, much like the freemarket concept in economics).14 Equilibrium, in the sense of the preservation of a
pluralistic system, is expected to be the long-term outcome.15 In this scheme of things,
no major actor need be oriented to the preservation of the state system.16 Policy
making is unburdened by any conscious concern for the systemic consequences of
selfishly motivated behavior that involves the use of threats, alliances, and war as the
principal means in achieving the state's primary objective: an increase in power. 17
Historical examples of this type of setting include the city-states of Classical Greece,
Renaissance Italy, and Ch'un-ch'iu China.
8
Starr, p.61
Sabrosky, p164
10 Sabrosky, p.161
11 Bueno de Mesquita, p.115
12 Wallace, p.110
13 Bremer/Mihalka, p.304
14 Kaplan, p.690
15 Cusack/Stoll (1990b), pp.275-6
16 Bremer/Mihalka, p.305
17 Cusack/Stoll (1990a), p.276
9
4
A second version of the Realist school is referred to as " balance of power" or
"semi-automatic stabilization". In this case, one unique member of the system commits
itself to the process of equilibriation, supplementing the natural automatism of a laissezfaire network. Other nations may do as they choose.18 The behavior of Britain during
the 19th century is probably the most famous example of something close to this
philosophy in action.
Historically speaking, the Realist view of international relations has been the most
evident.19 The 20th century has seen the rise of an alternative perspective, categorized
as the Idealist school. Rather than viewing the individual state as the focus of national
interest, Idealists identify behavior that attempts to preserve the entire system as the
means to ensuring the security of the state.20 This doctrine, known as "collective
security", essentially requires countries to renounce the use of force as a means of
achieving national objectives and also to come to the aid of those states that have
become targets of aggression.21 Historical illustrations of this behavior are not readily
found (2002 update-the Gulf War etc.), although contemporary professional diplomats
such as Henry Kissinger have publicly subscribed to this theory. It is a viable force in
the contemporary study of international relations.
18
Claude, p.48
Starr, p.143
20 Gulick, p.31
21 Cusack, p.212
19
5
2. Machine game exploration of automatic stabilization
It is of interest to identify the logical consequences of a nation acting according to a
particular set of decision rules. Beyond historical studies, simulation can be used to
explore the implications of each of these theories. This methodology is further
appropriate, since international actions ultimately must be explained in terms of the
individual human being, or classes thereof.22 In this light, gaming can be usefully
employed in simulating the workings of a multistate system, and can be adapted to
focus on specific aspects of international interaction, in this case the preservation of a
pluralistic state structure.
In 1977, Bremer and Mihalka constructed a machine game designed to examine
the viability of laissez-faire in preserving pluralism in a multistate system. In this
exercise, the essential components of a multistate system were identified as 1) a
relatively large number of states, 2) each state having an initial amount of military power
and territory (in a closed area), 3) each state having knowledge of the geographical
position of all other states in the system, and 4) each state possessing the ability to
estimate the power of all other states.23 These characteristics were incorporated into a
gaming framework, with various rules included to determine player behavior. Over
several runs of the game, they found that in a network where political entities acted
according to the dictates of laissez-faire, the result for the vast majority was extinction
as one state developed an "empire".24
The degeneration of this game is not surprising, since all closed dynamic systems
will reach a steady state of some kind.25 In this particular case, the simulation can be
viewed as a Markov chain, whose only absorbing state is imperial domination.26 In
22
Singer (1979b), p.27
Bremer/Mihalka, p.306
24 Bremer/Mihalka, p.326
25 Bremer/Mihalka, p.326
26 The design of this machine game forces player activity to take place without reference to time beyond
the present round of play. The randomness of aggressive activity implies that history is of no impact.
Decisions are made irrespective of previous behavior patterns, and without regard to possible
consequences, save winning or losing the present round. In addition, once a state is eliminated from the
play, the membership of the system is forever reduced. The combination of these factors provides a
stepping stone for modeling the dynamics of this machine game as a Markov chain, in which the only
absorbing state is imperial domination by a single nation. The independence of separate iterations
implies that the chances for remaining in a state, which is defined as the present membership of the
system, will decline asymptotically toward 0. Let the probability for returning to "state" a be f i(xi1,...,xin),
23
6
terms of theoretical implications, this specific dynamics of this game and its progression
to imperial domination is the primary focus of interest. In 1990, Cusack and Stoll
extended the basic structure of this game in order to more thoroughly explore the nature
of automatic stabilization behavior within the simulation. Eight general areas of Realist
philosophy were identified as the primary factors of in the design of the updated game.
Specifically, the designers examined the impact of the initial distribution of power within
a multistate system, the degree of restraint among separate decision makers, the
accuracy of capability assessment, the destructiveness of war, the role of chance in
determining the outcome of a war, the indecisiveness of war, the relative losses of war
participants, and uneven growth over time due to internal sources.27 Each of these
factors were incorporated into the game in the form of parameterized equations, and
varied over separate runs so as to investigate their systemic implications.
Over the 8748 runs of the game, 43% retained a pluralistic character at the final
(1000th).28 Those games that did degenerate to empire did so with some rapidity. 29
However, the survival rate varied substantially between separate sets of the game,
ranging from 24% to 63%.30 The most significant factor in determining the ability of a
game to maintain a pluralistic character was the degree to which a large power ratio
was necessary to obtain a high probability of winning a war.31 In addition, the other
primary factors incorporated into the simulation also impacted on system endurance,
although to a lesser extent. A good fit between the variables used to predict the
endurance of a system and what transpired in the experiments was evidenced. This
suggests the central debates of Realism have focused on an important set of factors in
the determination of system endurance.32
where i is the iteration, and xi1,...xin are the variables generated during that round in determining player
behavior. If 0<fi(xi1,...,xin) <1, then ifi(xi1,...,xin)=0; i=1,2,...
27 Cusack/Stoll (1990b), p.277
28 Cusack/Stoll (1990b), p.302
29 Cusack/Stoll (1990b), p.302
30 Cusack/Stoll (1990b), p.302
31 Cusack/Stoll (1990b), p.312
32 Cusack/Stoll (1990b), p.312
7
3. Diplomacy
A central variable throughout the machine games of Bremer/Mihalka and
Cusack/Stoll is the estimation of power within the system by each nation. Changing the
parameters of this equation has a substantial effect on the play of the game. As an
exploration of automatic stabilization in a multistate network, the preservation of
pluralism in this simulation is profoundly impacted by the beliefs of each player with
respect to the power structure of the system. Another dominating feature of threat
perception in international relations is the estimation of intent.33 The findings of these
experiments can usefully be compared to those of a simulation in which intent is the
dominating variable, while relative power is common knowledge.
"Diplomacy"34 is the best known game designed to simulate the process of
international negotiations, specifically the diplomatic maneuvers of European Powers
preceding WWI.35 With this in mind, this game can be examined and formalized as a
simulation of international relations, with an emphasis on estimating intent. The
potential viability of automatic stabilization as pertains to the preservation of pluralism in
a multistate system, as illustrated by game records, can also be investigated.
Quickly stated, Diplomacy involves seven independent players each trying to attain
dominance from relatively equivalent starting points.36 Each nation on the Diplomacy
board represents one of the great powers of Europe in the early 20th century. 37 With
the exception of Turkey, each of these powers is generally acknowledged as a major
actor of the period.38 The field of play is a stylised map of Europe of this period.39 From
these origins, each player attempts to maintain and expand their territorial domain over
successive rounds of play. During the game, players are free to negotiate with other
players, possibly to form defensive pacts, neutralize certain regions, or to work in
concert against a specified enemy. These discussions are completely non-binding;
players are free to move in any fashion and disregard what they have previously said
33
Jones/Singer, p.27. Threat perception is formalized as a function of estimated capability and estimated
intent of a nation.
34 Diplomacy is the Avalon Hill Company’s trademark for its game of international intrigue (1976)
35 Bigelow, p.211
36 Calhamer (xerox)
37 Calhamer (1975), p.26
38 Singer/Small, p.45
39 Calhamer (1975), p.26
8
during negotiations. This reflects a central characteristic of the pre-1914 major-power
subsystem, namely the existence of an extensive alliance network, which eventually
involved all the major powers (except the U.S).40 In discussing this system, it is
insufficient to consider only the final composition of the contending coalitions as they
appeared in 1914, but also the development of these groups before WWI.41 Between
1900-1914, this subsystem underwent a major transformation, which significantly
altered the existing European balance of power.42 Diplomacy captures the essence of
this system in the condition of multiple and flexible checks and balances in the form of a
strategic game.43 However, the historical reference of this game possesses little
relevance beyond this. It provided a basis for the development of the game, but does
not have a substantial impact on play (in actuality, the initial conditions of the game are
a more accurate reflection of Napoleonic Europe44).
The specifics of scoring and movement are best explained by the rules of the
game (formerly an appendix-I hope you know them), but the general play of the game
bears discussion. Each player is limited to their own territory at the outset of the game,
but is empowered to move to control other regions, in the form of supply centers. In this
sense, there is an economic objective within the game.45 If such a move is contested by
another player, there needs to be actual superiority in order for either move to succeed.
At the outset of the game, for example, both the English and the French player can
move a fleet into the English Channel. However, if they both proceed in this fashion,
neither piece will move (a stand-off). If, on the other hand, the English player is able to
“support” this move in the second turn with a fleet from the North Sea, his move will
succeed, while the French player's fleet will not move. This allows for no element of
chance to determine game play. In addition, moves for a specific turn are all made
simultaneously, with no signaling outside of negotiations. The combination of these
factors makes strategy formation and communication with other players particularly
important to success within the game.
40
Sabrosky, p.142
Sabrosky, p.142
42 Sabrosky, pp.154-5
43 Calhamer (xerox)
44 Calhamer, personal interview 2/4/90
45 Calhamer (xerox)
41
9
The original intent of Diplomacy was largely geared toward entertainment and
playability. However, the end result provides for a surprisingly good simulation of
international negotiations. It can and has been used in a classroom environment in this
capacity.46 When viewed in terms of simulation design, this game is well adapted to an
experimental environment.
As a simulation of international relations, Diplomacy qualifies on many pertinent
criteria. Player goals of winning and survival can be linked to concerns of power and
security inherent among international actors. The pursuit of these objectives in both
arenas takes place without higher authorities to check the behavior of the participants,
save the other members of the respective systems. Diplomacy players are also allowed
to act in concert, but without being formally bound to any proposal or agreement. The
behavior of nations has often been portrayed in a similar fashion.
Diplomacy can also be depicted as possessing the essential components of a
multistate system. Each player is endowed with an initial amount of territory and power.
The geographical position and power of other nations represented in the game is
common knowledge. With respect to the number of states in the system, Diplomacy is
analogous to an oligarchic power structure. Although this number is not overwhelmingly
large, it is sufficient to facilitate a legitimate examination of this type of network.
A further analogy can be made between Diplomacy and the theoretical workings of
automatic stabilization. Although it is possible to have goals besides simply winning, 47
by and large each player is out for themselves, seeing as the primary object of the
game is to win. Accordingly, each player should prevent any other player from
approaching this point in order to protect its own interests. Everyone should also work
to guarantee their survival, as winning would be impossible upon elimination. From
these perspectives, another important feature of the game is the ability that players
have to adjust to changing conditions on the board. In this sense, incrementalism is of
some importance. In a game which proceeds at a slow tempo by small increments, the
situation may change character, but by a succession of small changes that can be
observed and adapted to.48 The unrestricted nature of negotiations in Diplomacy, as in
international relations, provides each player with the freedom to maneuver in this
46
Bigelow, p.209
For example, some players may decide to play according to dictates of power, specifically target
another player to lose, or attempt to see how long they can survive.
47
10
fashion over the course of a game. With communication, there is time for players to
bargain and attempt to avoid moves that involve mutual destruction.49
The relevance of Diplomacy as a simulation is crystallized in its similarities with a
multistate system dominated by self-interest among its members. As the inherent
conception and component parts of the game emphasize these tendencies, a viable
theoretical exploration is created. With these concerns in mind, Diplomacy can be used
as a gaming exercise, along the lines proposed by Bremer/Mihalka and Cusack/Stoll, in
examining the implications of automatic stabilization concerning the dynamics of a
multistate system.
Human participants bring both their personal characteristics and their own implicit
theories as to how nations should behave to a simulation.50 Decisions as to their
courses of action in a game merit discussion in analyzing the dynamics of the game. In
the case if Diplomacy, players are thrown into a strategic setting, with their behavior
determined accordingly.
Although the actual Diplomacy board has almost 80 spaces, it is possible to view
the play of the game in terms of the players and their positions relative to each other in
the game, focusing primarily on the potential impact of each other in the system.
Abstracting from the board, a depiction of potential influence levels can be created. If
there exists a space (land or water) for instance, which two separate players can reach
in the least number of moves relative to everyone else, these territories can be
contested without direct interference. Russia and England, for example, can both land
a piece in Norway in two moves, a speed that no other player can match (fig. 3.1).
Fig. 3.1: Border network
E
R
G
A
F
I
T
48
Schelling, p.170
Schelling, p.170
50 Guetzkow/Valadez, p.261
49
11
Of further interest at the outset of the game are those situations in which two
players can act in concert against a third i.e. two separate fronts can be opened against
a common target without direct interference from other players. Again, the example of
Russia and England can be used, as they are both able to move against Germany
without first having to remove an intermediary. The level of potential interaction
between players at the outset of the game can constructively be viewed in these terms.
In conjunction with the multiple possibilities for action, strategy formation in
Diplomacy is profoundly influenced by the non-binding nature of its negotiations. This
characteristic has significant systemic implications, the most important of which is the
pervasive presence of uncertainty and incomplete information among players. The
problem of choosing a strategy is inextricably intertwined with belief. Each player must
decide on a course of action based on what they believe to be the "actual" game. 51 In
conditions of risk and uncertainty, modern Bayesian decision theory states that rational
behavior is equivalent to expected utility maximization using a subjectively assessed
probability distribution.52
These pre-game concerns supply the foundations for strategy formation. During
the game, judgements as to specific statements, actions, and moves have to be made.
In a multi-player game, theoretical interest is on the question of coalition formation and
its effect on the outcomes of the game.53 A coalition is defined as a set of players who
decide to act together as one group relative to the rest of the players. 54 A coalition
structure is a partition of the set of players into a number of coalitions, each aiming to
enhance the interests of its members.55 The issue of coalition membership is
inseparable from the distribution of benefits.56 A Diplomacy player, in theory, could
become a member of 64 different coalitions.57 Narrowing down these alternatives will
depend on what each player believes can be gained by membership in each (or even by
feigning such participation), and in adapting this behavior as the game progresses.
51
Rapaport, p.238
Harsanyi, p123
53 Rapaport, p.196
54 Hart/Kurz, p.235
55 Roth, p.228
56 Roth, p.228
57 The number 64 is obtained simply by counting these possibilities. A player can join up to 6 2-player
coalitions, 15 3-player, 20 4-player, 15 5-player, 6 6-player, and 1 7-player. The identity coalition is also
included.
12
52
As coalition structure impacts the game, it is necessary to identify those factors
that affect its emergence. Each player is obviously interested in channeling the
development of the game in his or her favor, and as such will attempt to direct the
formation of this network in his or her favor if at all possible. Guiding the decision logic
of each player is the prediction of opponents' behavior without any effort to influence
them, and preferences as to the behavior of these actors.58 The ability to persuade
becomes an integral part of the contest.59 In a strategic setting, moves are also
important, as they possess an information content not found in mere speech.60 A
strategic move can be said to influence the choices of other players by affecting
expectations as to how oneself will behave.61 The development of a reputation amidst
these issues, and thus the ability to negotiate effectively, depends on the tradeoff
between the costs of maintaining an image and the benefits that accrue from it.62
It would not be very useful to visualize a simulation that focused on intent in terms
of independent iterations, although it may be modeled as such. One could rob a bank,
for example, and benefit tremendously, if there were no negative consequences to be
had in the future. Without reference to time, concerns of reputation are lost, and the
game is relegated to being a sequence of independent prisoner's dilemmas. Strategy
formation in Diplomacy is better viewed in terms of a "supergame", which is defined as
an infinite game with n players in which the tth move {t=1,2,...} is the playing of a tth
game in a sequence of ordinary games with strategy sets Si1, Si2, ...,Sit,...and payoff
functions it(sit)(stSt), {t=1,...,i : i=1,...,n}. The general definition of a strategy for the ith
player is defined as...
sit=fit(s1,s2,...,st-1);
=si1
t=2,3
t=1
where fit, {t=2,3,..}, is a sequence of functions that maps all preceding ordinary game
strategies of all players into the tth ordinary game strategy of the ith player. si1 is the ith
player's initial move.63 In other words, each player makes an initial move based entirely
58
Singer(1979a), pp.51-2
Calhamer (xerox)
60 Schelling, p.117
61 Schelling, p.160
62 Fudenberg/Kreps, p.541
63 Friedman, p.4
59
13
on perception and belief, after which the moves of other players can be incorporated
into the decision process.
As these theoretical generalizations are the prevailing concerns of the game, they
can be used in formalizing game play. Each Diplomacy player will attempt to maximize
his utility in every round of the game, based on a subjective assessment as to the actual
game. As the capability of each player is common knowledge at each stage of the
game, it is intent that is the primary object of uncertainty and threat perception.
Strategy formation can be viewed as a function of the perceived intentions of other
players. At the same time, decision as to one's own course of action is profoundly
influenced by the perception of other player's beliefs.
A key component in estimating the intent of the other participants in the game is
the belief structure concerning the assessments of reputations. From any one player’s
standpoint, these are based on a subjectively constructed relationship between
communication with other players and the actual moves made in the relevant round by
the same players. These are perfectly assessed by each player (they know how they
feel about the other players in the game), and updated as information, in the form of
communication or moves, is received (equation 1.a). The scheme is complicated when
estimating other players’ beliefs concerning reputations. In this instance, a player is
forced to guess the decision process of every other player as to the importance of
reputation. Consequently, this information is not perfect, and can only be incorporated
into strategy formation as an estimate (equation 1.b).
REPit(-i) = f[REPit-1(-i), DIRCOMit-1(-i), s-it(i)]
(1a)
ESTREPit(-i) = f[ESTREPit-1(-i), DIRCOMit-1(-i), sit-1(-i)]
(1b)
where...
REPit(-i) : player i's assessment of the reputation of player -i
DIRCOMit(-i) : player i's assessment of communication with player -i in round t
s-it(i) : player i's assessment of strategy used by player -i in round t
ESTREPit(-i) : player i's belief as to assessment of his own reputation by player -i in
round t
DIRCOMit(-i) : player i's belief as to assessment by player -i of their communications in
round t
sit(-i) : player i' belief as to assessment of his own strategy in round t by player -i
14
The assessment of reputations within the game is adjusted from round to round as
information is received. It is a key element in the construction of a belief as to the actual
game, and accordingly in estimating the intent of other players. These decisions are
tempered by the capabilities of each player in a given round, which, as previously
stated, are common knowledge. More often than not, however, the set of choices
available to each player are very high in number.64 Players must somehow reduce the
size of these sets, lest they be relegated to random guessing in selecting a course of
action. Some strategies can be eliminated by virtue of redundancy. Others can be
discarded as being of no benefit to a player. Still, the set of strategies that are viable is
not small. At this point, reputation and communication can be effectively employed in
attempting to ascertain the "true" game. When combined with possible payoffs, in terms
of changes in capability and reputation, an educated guess as to the intent of each
player can be made (equation 2).
ESTINTit(-i)=max [-it(s-it) + DIRCOMit(-i)REPit(-i) + INDCOMit(j)REPit(j)] :
ji,-i
(2)
s-itS-it
where...
ESTINTit(-i) : player i's estimation as to intent of player -i in round t
S-it : set of strategies available to player -i in round t
DIRCOMit(-i) : player i's assessment of communications with player -i in round t
INDCOMit(j):player i's assessment of communications with player j as pertains to
player -i
Having ascertained the "actual" game, player attention shifts to personal strategy
selection within this framework. An attempt will be made to maximize expected utility, in
terms of his own capabilities and reputation in later rounds (equation 3).
max E[(sit|s-it)] = [ [ESTREPik(-i) + CAPik(sit|s-it)]
sitSit
k=t+1,t+2,...
(3)
k -iN
where...
(sit|s-it) : payoff of strategy sit given opposing strategies s-I (for all –i)
CAPit : capability of player i in round t
: constants
64
At the outset of the game, for example, each player has over 300 possible opening moves.
15
These equations are simultaneously solved for all players i, -i, and j. Changing the
specifics of the various weighting parameters within the system allows for a diversity of
playing styles to be reflected (2002 note:  weights the importance of what you think
player –i will think of you after the move,  weights the importance of the power you
expect to have).
Implicit throughout the preceding discussion are the opportunities players have to
cooperate with one another. By no means is the set of available strategies limited to
those that can only be used by a single player. The payoffs that can be gained from
joint actions are very much a part of the assessments of intent within the game.
Likewise, the payoffs that can be had by defecting from such an agreement are also
incorporated into this structure. Diplomacy can be viewed as a diplomatic variation of a
multiplayers prisoners dilemma,65 the implications of which have a significant impact on
cooperative behavior within the game, and accordingly, on the game itself.
65
Bigelow, p.212
16
4. Exploring automatic stabilization: Game results
The data used in this study is almost exclusively derived from Postal Diplomacy.
Although the game was originally designed to be played in a face-to-face setting, it
lends itself very well to the use of mail. These games still have 7 players, but also
include a "Gamemaster", to whom moves are mailed and then processed. He, in turn,
publishes the results of each round, most often in the form of a small flyer or magazine.
Between filing deadlines, which are usually about four weeks apart, players are free to
communicate with each other, either in person, over the phone, or by mail. As in faceto-face games, these negotiations are non-binding; each player is free to submit
whatever orders they wish. These games typically take from two to three years to
complete (not necessarily ending in victory).
It should be noted that the caliber of play in Postal Diplomacy tends to exceed that
of face-to-face games.66 Rather than being confined to 15 minute negotiating sessions,
postal players usually have several weeks to examine their options and communicate
with other players. As a result, fewer mistakes and oversights occur, and strategies are
more thoroughly and carefully assessed and discussed. In this sense, and in others, it
appears that postal games are the most accurate reflection of international
communication channels. Very rarely do the leaders of seven separate nations
assemble in the same place, and certainly not over the time span supposed in the
evolution of a multistate system. In addition, discussions between nations tend to
proceed along bilateral, rather than multilateral, channels.67 Postal Diplomacy mirrors
each of these attributes.
The data examined in this study is in two forms, summations of which are included
as appendices, as well as in the text of the paper. One set is a compilation assembled
by Randolph Smyth. It included 2292 game ends, and is largely used in investigating
general tendencies toward hegemony. More detailed game results, in the form of
approximately 100 supply center charts, have been provided by the Boardman Number
Custodian, who is presently Don Williams. Almost every Postal Diplomacy game start is
reported to him, and results in the form of supply center charts are archived by him and
published in a magazine entitled Everything. Custody of the position has changed
66
Williams, personal interview 4/5/90
17
hands several times, but the records have been kept intact with the transitions. The
most recent issue is volume 82. This practice dates back to the 1960's and the inventor
of Postal Diplomacy, Dr. John Boardman.68 Over 2000 games have been recorded
during this period, and the practice is still going strong.
The 2000+ games compiled by Smyth (table 4.1) probably provide the most
exhaustive overview of game ends, in terms of final power structure. Victory by a single
power occurs in over 1/2 the games played, and 75% of the games have no more than
two victors. A draw involving a majority of the players happened in barely 10% of the
games, with a 7-way draw taking place only twice (<.1%).
Table 4.1: Number of draw players
#DRAW PLAYERS
#GAMES REPORTED
%GAMES REPORTED
1
1368
59.8
2
372
16.2
3
303
13.2
4
173
7.5
5
64
2.8
6
10
0.4
7
2
0.1
Total
2292
100.0
These results are not overly surprising, since Diplomacy is by and large doomed to
an absorbing state of hegemony, similar to that of the games of Bremer/Mihalka and
Cusack/Stoll. The evolution of this system is much more important in exploring the
workings of automatic stabilization in this setting. As victory is achieved when one
player controls over 50% of the supply centers on the board, an examination of this
progress, in terms of change in the power distribution within the game, is in order.
Using supply center charts, it is possible to trace shifts in relative power within the
game, as well as identify any periods of stabilization.
At the outset of the game, all players are in control of three supply centers, except
Russia who has four. The standard deviation (denoted s) of this set is 0.36.69 The
67
Calhamer (xerox)
Calhamer (1975), p.26
69 The standard deviation in the number of supply centers controlled by each player provides a good
summary of power distribution within the system. As it increases, a wider distribution of this control is
implied, and vice-versa.
68
18
behavior of this measure within the game facilitates an analysis as described above
(table 4.2). In examining this data, a continuous divergence in the distribution of relative
power within each system can be identified through 1909. Despite relatively equivalent
starting points, the game progresses uninterrupted to be dominated by a select group of
players. This occurs even with the loss of countries from the system. After 1909, a
leveling in the distribution of power within the game can be noticed. Curiously, there is
a profound drop in the number of games played beyond 1909. Most of these games did
not even end in victory, but in player declared draws (17% and 28% of sample
respectively; tables 4.3a and 4.3b). Although games declared as draws are not
substantially different from the overall summary of games results, those that ended in a
"quick win" do distinguish themselves. This category is characterized by a much
speedier divergence in the relative power amongst the players than is noticed
elsewhere in the sample. This progress is also not interrupted upon the loss of a player
from the game, which is a characteristic of some games. 1985K is a typical game of
this set (table 4.4).
19
Table 4.2: Relative power distribution-overall70
Year
(s)
n
n71
(c)
1901
0.80
0.26
115
7.00
1902
1.35
0.43
115
6.97
1903
1.88
0.55
115
6.71
1904
2.41
0.79
115
6.42
1905
2.79
0.87
113
5.94
1906
3.15
1.05
112
5.48
1907
3.58
1.10
106
5.13
1908
3.75
1.23
94
4.71
1909
4.13
1.32
76
4.46
1910
3.70
1.44
54
4.11
1911
3.89
1.85
38
4.00
191272
3.52
1.32
21
4.03
where . . .
Year: year in game
(s): average standard deviation of games studied
n: standard deviation of s of games studied
n: Number of games studied
(c): average number of countries in game
70
The games summarized in this chapter were taken from Everything, volumes 70-75. Some
exclusionary criteria was employed in an effort to obtain the best possible sample of games. No game
that was declared a draw before 1907 was included. I felt these games had not been allowed to run their
full course. These games were no different from games ending later, and were likely ended more due to
lack of interest than to a stalemate. I did not feel anything was lost. Games in which the supply center
total for a given year was less than that of the previous year were also not included. It is a quirk of the
game that a supply center, once under control, can never again not be under control of some player.
Games whose records had this characteristic were incomplete in their information, and considered bad
for the sample (I commend Don Williams on his efforts to eliminate this problem in present reporting).
71 Once a game was won or declared a draw, it could no longer be included as part of the sample for
subsequent years. Accordingly, n declines.
72 In theory, Diplomacy has no specific end year. 1912 was selected as the end of my analysis simply
because most games are not played beyond this point. The decline in n tells the story.
20
Table 4.3a: Relative power distribution-Draws declared pre-1910
Year
(s)
n
n
(c)
1901
0.78
0.27
32
7.00
1902
1.44
0.43
32
7.00
1903
1.95
0.58
32
6.66
1904
2.50
0.74
32
6.38
1905
2.60
0.87
32
5.84
1906
2.97
0.93
32
5.50
1907
3.21
1.03
31
5.09
1908
3.46
1.25
25
4.75
Table 4.3a: Relative power distribution-pre-1910 victories
Year
(s)
n
n
(c)
1901
0.84
0.27
20
7.00
1902
1.43
0.47
20
6.95
1903
2.23
0.68
20
6.70
1904
2.99
1.01
20
6.45
1905
3.55
0.98
18
6.00
1906
4.27
1.15
16
5.72
1907
4.69
1.07
12
5.35
Table 4.4: Supply center chart for 1985K
Player
01
02
03
04
05
06
07
Austria
5
6
6
5
5
3
2
England
5
8
9
11
13
15
19
France
6
6
7
9
7
8
4
Germany
3
0
Italy
4
4
3
1
0
Russia
5
6
6
4
4
3
4
Turkey
5
4
3
4
5
5
5
0.88
1.37
2.13
3.55
3.75
4.49
6.18
(s)=
21
The only evidence for possible stabilization within Diplomacy play is found in
games extending beyond 1912. Between the years 1909-1912, the assessment of the
average standard deviation of power within a game is relatively constant. However, the
results of these games before 1909 are included as a part of the overall summary. A
separate examination of these games is therefore in order (table 4.5). The change in
the relative distribution of power within the system for games going beyond 1911 is not
noticeably different from the overall summary. The same divergence can be seen,
along with an equalization in the average standard deviation in supply centers in the
years beyond 1908. However, the increase in the variation of relative power suggests
that this is not a singular trend. Further investigation shows games that are on the high
side of this distribution often end in victory shortly after 1911, in much the same fashion
as illustrated in 1985K only in a longer period of time. It is the games on the low end of
the scale that are the equalizing factor. This behavior is illustrated in 1984H (table 4.6).
Table 4.5: Relative power distribution-games played past 1911
Year
(s)
n
n
(c)
1901
0.78
0.26
39
7.00
1902
1.29
0.41
39
7.00
1903
1.76
0.43
39
6.82
1904
2.15
0.50
39
6.38
1905
2.63
0.64
39
6.05
1906
2.87
0.82
39
5.56
1907
3.13
1.04
39
5.05
1908
3.36
1.00
39
4.74
1909
3.69
1.09
39
4.59
1910
3.33
1.30
39
4.31
1911
3.65
1.56
38
4.16
1912
3.37
1.46
33
3.88
22
Table 4.6: Supply center chart for 1984H
Player
01
02
03
04
05
06
07
08
09
10
11
12
Austria
5
5
6
5
6
6
5
5
5
5
6
6
England
5
6
5
7
8
8
10
11
11
11
11
11
France
5
6
7
8
9
9
9
9
9
9
9
9
Germany
4
2
2
0
Italy
5
5
4
4
2
1
1
1
0
Russia
5
4
3
1
0
Turkey
5
6
7
9
8
9
9
8
9
9
8
8
0.35
1.36
1.81
2.69
2.64
3.12
3.37
3.49
2.18
2.18
1.8
1.8
(s)=
Games of this sort are not altogether frequent, accounting for 10% of the original
sample (50% of games played beyond 1911). However, this number may be low, given
the large number of draws declared before this point is reached. It may be that if,
instead of being declared a draw, a game were allowed to continue, further examples of
stabilizing behavior could be found. From this sample alone, potentially 40% of all
games may exhibit this characteristic.
Having identified at least two different types of games, attention shifts to possible
explanations for these results. As the game outcome is heavily dependent on
assessing intent within the system, this has a significant impact on the evolution or
degeneration of a pluralistic structure. In those games that end in outright victory, it
may be possible that separate players could be analyzing the game from entirely
different belief structures, rendering it inconsistent.73 Accordingly, players do not always
select the best option with respect to the true game, and are unable to recover from this
error. Assuming players act rationally according to their own assessments, there must
be some flaw in the belief structure if the system degenerates. If a stable structure is
attained, however, the belief structure may be very close to that of the true game. If this
is the case, it becomes necessary to identify in greater detail than can be done here the
reasons for this divergence in belief. This would be a great stride in explaining the
dynamics of this simulation.
73
Harsanyi, pp.164-5
23
5. Extending simulation
The focus of this paper has in large part been on the interaction of self-interested
entities in a multistate system and the preservation of pluralism therein. Implicit to this
direction has been a natural emphasis on the selfish behavior in Diplomacy. Given the
nature of the game, it is difficult to identify other philosophies for action. However, if this
could be done, further insight into the workings of a multistate system could be gained.
Cusack has demonstrated the potential of such an approach. In 1989, he added
balance of power and collective security actors to the system, examining whether these
different rules for power management enhance the survival of their practitioners.74 He
found that collective security fared better than both laissez-faire and balance of power in
preserving pluralism and maximizing the size of the system over time.75 Employing
different styles of play in Diplomacy could produce a similar extension. Rather than
adopting the Realist view of the world, players could be assigned specific roles, such as
pure balance of power or collective security motivated play. Although some hobbyists
do occasionally adopt different approaches to a game, it is not inherent to the network
presently in place.
Extending or varying the structure of the game could prove to be very useful in the
study of international relations, and has been done in the hobby. One of the most
obvious changes that can be made is in the number of players. Rather than being
restricted to 7 players, the game could be made to include up to 34 separate nations
(these initial conditions are very similar to those used by Bremer/Mihalka). Realignment
of the initial conditions can also be made elsewhere. If desired, the field of play could
easily be manipulated to reflect some other configurations of states. The whole world
could be used instead of Europe. Postal games, such as WWIII and Youngstown XII,
do exactly this. Borders or information flows can be changed so as to create different
avenues for interaction. A Postal Diplomacy variant known as Gunboat is played with
no communication between the players. A specific list of possible structural changes
could go on for a while. Any one of these variants could be employed in a further study
of the dynamics of a multistate system.
74
75
Cusack, p.209
Cusack, p.226
24
These types of changes also appear to be particularly useful in studying the role of
individual decision-making in an automatic stabilization setting. It is one thing to identify
the evolution of a system, but quite another to explain it. If the Realist philosophy is to
be accepted or rejected, some statement of justification should be made. Further
investigation into the specifics of strategy formation is the final piece of the puzzle in
attempting to explain the dynamics of the game in play. It is my understanding that
there is an attempt within the hobby to somehow create a computerized player or
tactical advisor that can assess the multiple possibilities for action and identify a best
strategy. This will be an important step in expanding the role of simulation in this field,
and I hope this paper can serve as a step in that direction.
25
BIBLIOGRAPHY
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Collective Insecurity: The War of the Pacific in a World Politics Simulation" in
Problems of World Modeling. Karl Deutsch et al eds. Ballinger: Cambridge, MA,
1977, pp. 215-302.
Bigelow, Bruce E. "Simulations in History." Simulation and Games. June, 1978, pp.
209-20.
Bremer, Stuart A., and Mihalka, Michael. "Machiavelli in Machina: Or Politics among
Hexagons" in Problems of World Modeling. Karl Deutsch et al, eds. Ballinger:
Cambridge, MA, 1977, pp. 302-37.
Brooker, R.G. "Truth as a Variable." Simulation and Games. 19, March, 1988, pp. 4358.
Bueno de Mesquita, Bruce. "Systemic Polarization and the Occurrence and Duration of
War" in Explaining War. J. David Singer ed. Sage Publications: Beverly Hills,
1979, pp. 113-38.
Calhamer, Allan. Series of articles from Games and Puzzles. Xerox of personal
articles provided by author.
_____. Personal interview, 2/4/90.
_____. "Diplomacy" in Modern Board Games. David Pritchard, ed. William Luscombe
Publisher Ltd.: London, 1975, pp. 26-44.
Claude, Inis L. Power in International Relations. Random House: New York, 1962.
Cusack, Thomas R. "The Management of Power in a Warring State System" in Power
in World Politics. Richard J. Stoll and Michael D. Ward, eds. Lynne Reiner
Publishers Inc.: Boulder, 1989, pp. 209-26.
Cusack, Thomas R., and Stoll, Richard. "Adaptation, State Survival, and System
Endurance: A Simulation Study" in International Political Science Review. 11,
April, 1990, pp. 261-78.
_____. (forthcoming) Exploring Realpolitik; Probing International Relations Theory with
Computer Simulation. Lynne Reiner Publishers, Inc.: Boulder, CO.
deLeon, Peter. Scenario Designs-An Overview. Rand: Santa Monica, California, 1973.
Friedman, James W. "A Noncooperative Equilibrium for Supergames." Review of
Economic Studies. 113, Jan., 1971, pp. 1-12.
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Fudenberg, D., and Kreps, D.M. "Reputation in the Simultaneous Play of Multiple
Opponents." The Review of Economic Studies. 54, October, 1987, pp. 541-68.
Guetzkow, Harold et al. Simulation in International Relations. Prentice-Hall: Englewood
Cliffs, NJ, 1963.
Guetzkow, Harold, and Valadez, Joseph. "Simulation and Reality: Validity Research"
in Simulated International Processes. Harold Guetzkow and Joseph Valadez, eds.
Sage Publications Inc.: Beverly HIlls, 1981.
Gulick, Edward V. Europe's Classical Balance of Power. Cornell University Press:
Ithaca, NY, 1955.
Harsanyi, John C. Papers in Game Theory. D. Reidel Publishing Co.: Dordrecht,
Holland, 1982.
Hart, S., and Kurz, M. "Stable Coalition Structures" in Coalitions and Collective Action.
Manfred J. Holler, ed. Physica-Verlag: Wurzburg, 1984, pp. 235-58.
Jones, Susan D., and Singer, J. David. Beyond Conjecture in International Politics.
F.E. Peacock: Itasca, IL, 1972.
Kaplan, Morton. "Balance of Power, Bipolarity, and other Models of International
Systems." American Political Science Review. 51, September, 1957.
Rapaport, Anatol. Fights, Games, and Debates. University of Michigan Press: Ann
Arbor, MI, 1960.
Roth, A.E. "Stable Coalition Structures: Aspects of a Dynamic Theory" in Coalitions and
Collective Action. Manfred J. Holler, ed. Physica-Verlag: Wurzburg, 1984, pp.
228-34.
Sabrosky, Alan. "Interstate Alliances: Their Reliability and the Expansion of War" in The
Correlates of War II. J. David Singer ed. The Free Press: New York, 1980, pp.
161-98.
Schelling, Thomas C. The Strategy of Conflict. President & Fellows of Harvard
College: Cambridge, MA, 1966.
Shubik, Martin. "Gaming: Theory and Practice, Past and Future." Simulation and
Games. 20, June, 1989, pp. 184-9.
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27
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1965. [48]
28
ACKNOWLEDGEMENTS
These were my acknowledgements in 1990. They deserve it again. A lot of
familiar names.
Harold Guetzkow, Professor Emeritus of political Science at Northwestern University.
There was so much more I wish that I could do along the lines he proposed.
Nevertheless, what has been done owes much to his vast expertise and advice. Thank
you, Professor Guetzkow, and I hope I can continue this work.
Allan Calhamer, designer of Diplomacy. Not only did he provide the game that I so
enjoy and has been the focus of this year’s work, he was especially helpful in getting me
started and with providing me insights into the game and its design. Thank you, Mr.
Calhamer, and I hope you enjoy this.
Larry Peery, editor of Diplomacy World, and Jim Burgess, Professor of Economics at
Union College. I often found myself having trouble attempting to build a bridge between
the hobby and academia. It was the assistance and expertise of both of these
gentlemen in both areas that in large part made this link possible. I hope they agree.
Thank you, Larry, and I hope all goes well with your book, and thank you, Jim.
Don Williams, Boardman Number Custodian. I was thrilled to find out that record
keeping was done within the hobby, and could not have asked for a more helpful person
to be in charge of it. I would further like to compliment and thank him for his devotion to
the hobby, and hope that it continues. Thank you, Don.
John Boardman, professor of Physics at Brooklyn College. It might not seem like a
natural connection, but Professor Boardman is responsible for the creation of postal
Diplomacy and maintaining game records. I know you were surprised to find a link
between your creation and academia. Hopefully, it was worthwhile. Thank you,
Professor Boardman.
Randolph Smyth, ‘zine pubber. Although not initially on my wavelength with respect to
record keeping, he was more than willing to adapt his work for this project. Thank you,
Mr. Smyth.
Zoe Pietrusiak and all of my fellow Evans Scholars who helped me through the year.
The number reading was tedious, but instrumental to the completion of this paper. Zoe
has put up with me all year, and offered assistance wherever she could. Thank you,
Zoe.
Finally, Michael Dacey, Professpor of Geography at Northwestern University. Credit
here goes to his involvement with and dedication to a program that I have enjoyed
immensely during my four years at Northwestern (yes, it’s true). I wish you and the
program continued success.
29