Birger Wernerfelt
© 2001 by Birger Wernerfelt. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit including © notice is given to the source.
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Birger Wernerfelt*
May 1, 2001
*Professor of Management Science, MIT Sloan School of Management, Cambridge, MA
02142, 617-253-7192, bwerner@mit.edu
. I am grateful for comments from Oliver Hart,
Duncan Simester, Steven Tadelis, Miguel Villas-Boas, and seminar participants at MIT. Of course, the usual disclaimer applies.
JEL Codes: D2, L2
Key Words: Theory of the Firm, Coordination, Communication.

The paper is a study of barriers to coordination in terms of agents’ incentives to search for and communicate complementary information. In particular, I look at the value of commitment by comparing game forms in which a contract is negotiated prior to, versus after, search and communication. The comparison depends on three effects. (1) The bargaining power effect: Since the decision to communicate reveals information about preferences, it implies a loss of bargaining power when the players negotiate ex post. This hurts the incentives to communicate and therefore the incentives to search. (2) The incentive transfer effect: If the gains from adjustment accrue unevenly, ex ante negotiation may leave one of the players without incentives to communicate and search. With ex post negotiation, that player can bargain for a share of the gains. (3) The bargaining efficiency effect: The negotiation process itself may be more efficient ex post because more information has been revealed. The net effect depends on the magnitude of the gains and their accrual. If negotiation normally leads to agreement, it is better done ex ante in cases where adjustments yield smaller, more evenly accruing, gains. When the gains are larger and accrue less evenly, ex post negotiation implements more communication and search.
2

Division of labor makes it necessary for agents to coordinate, but at the same time gives them opportunities to acquire different information. The paper is a study of barriers to dynamic coordination, adjustment, in terms of agents’ incentives to search for and communicate complementary information. More specifically, I look at the effects of commitment. When adjustment requires one player to communicate information to the other, should the terms of trade be negotiated before or after communication? The answer depends on the relative magnitudes of three effects. Communication prior to negotiation is
(1) -unattractive, because senders prefer their opponent to know as little about their preferences as possible (the bargaining power effect),
(2) -attractive, because the ability to negotiate for a share of the gains from an adjustment can give a player incentives to help implement it (the incentive transfer effect), and
(3) -attractive, because the revealed information contributes to the efficiency of the negotiation process (the bargaining efficiency effect).
Put differently, if bargaining normally leads to agreement, early negotiation is good because players do not worry about loosing bargaining power, and it is bad because payoffs can not be contingent on adjustment.
The relative magnitudes of these effects depend on the importance of using payoffs to provide incentives for adjustment, relative to the value of bargaining power due to asymmetric information. The former factor weighs more when non-contractible gains from adjustment are larger and accrue less evenly, and the latter factor weighs more when gains from individual adjustments are smaller and accrue more evenly.
3

Application
Consider a “marketing” manager, who knows about the kinds of products consumers want, and a “manufacturing” manager, who knows about the kinds of products that can be made. While the two managers know how to make and market an “old” product, they may be able to do better if they can identify a “new” product, which would bring in higher revenues. We assume that the revenues accrue to the marketing manager. The new product may be more costly to produce or market and it may even be infeasible in the sense that it is impossible to make or sell. However, if it is feasible, the two managers can identify it by communicating.
Let us first think of a situation in which the manufacturing manager’s salary is fixed ex ante. In this case, his interest in the new product depends only on whether it is harder for him to produce. If it is, he can claim that the new product can not be manufactured.
Revenues and marketing costs do not play a role. So an opportunity could be missed because an employee with indispensable information can not be paid to cooperate.
Suppose next that the manufacturing manager’s salary is negotiated after he has had a chance to communicate about the new product. In this case, his decision to communicate or not reveals information about his relative costs for the new and the old product. He will be tempted to communicate if the new product is cheaper for him, but since the marketing manager knows this, she will be able to negotiate for a share of his cost savings. So concerns about bargaining power may cause the manufacturing manager to withhold communication even if the new product is cheaper for him. On the other hand, large revenues will affect his incentives to communicate, since he can hope to negotiate for a share of them.
4

Plan of the Paper
In Section II, I formulate the basic model, introduce the two specific game forms representing ex ante and ex post negotiation. To illustrate the three effects, I compare their ability to implement search and communication in three extreme cases. Some links to the theory of the firm are discussed in Section III.
.
Two players, A and B, she and he, may cooperate on an “old” project or a “new” project. The essential feature of the model is that the new project only is feasible if (i) both players search for and find it, (ii) one player communicates his finding to the other, and (iii) the latter selects the new project over the old. The only ex ante difference between the players is that prior to side-payments, a fraction r a
of the revenues received for the project accrue to A, while B gets (1- r a
). We will initially let B decide whether or not to communicate and if he does, give A the choice between the two projects. In the Appendix, I show that the results are robust to reversal of the roles.
A project is defined by two tasks that the players have to carry out to implement it.
The first of these tasks has to be carried out by A and the second has to be carried out by B.
The players are both indispensable in the sense that both are necessary to implement any project. Neither has an outside option other than doing nothing, and receiving zero. In order to focus on cooperation conceived as information exchange, I have chosen to abstract from moral hazard in the determination of productive efforts. That is, I am effectively assuming that the players’ levels of effort are unaffected by the game form governing the relationship. This is probably not a realistic assumption. It seems plausible that higher
5

effort levels can be enforced when the players negotiate with better knowledge of their tasks. For purposes of the following, this would imply an upward shift in the efficiency of the game form with ex post negotiation. However, the qualitative results of the analysis would not change.
The feasibility of the old project is guaranteed, and the nature of the tasks is known.
However, the costs of the tasks, C oa
for player A, and C ob
for player B, are the private information of those players. We assume that C oa
and C ob
are i.i.d. draws from a distribution F over the unit interval. It will initially be convenient to assume that F is symmetric around ½ and has no mass points. The revenues of the old project are R o
.
The players gather information under moral hazard. Specifically, if a player incurs a positive search cost s, he or she finds the new project with prob
DELOLW\ ,WLVLPSRUWDQW
WKDW VLQFHRWKHUZLVHDGHFLVLRQQRWWRFRPPXQLFDWHEHFRPHVDVLQIRUPDWLYHDVD decision to communicate.) Without search, there is no chance of finding the new project.
(To keep things simple, I assume that it is not observable whether a player searches.) The new project is only feasible only if both players find it. In that case its costs, C na
and C nb
, are i.i.d. draws from the same distribution as those of the old project. New projects are more attractive in expectation because their revenue R n
•5 o
. In addition, a new project offers a fresh cost draw. If a new project is found, the players will learn from information
WKDWWKH\UHFHLYHWKURXJKWZRVLJQDOVWKDWZHZLOOODEHO DQG 7KHVLJQDO KDVWZR components. It reveals C na
, and it contains partial information about the tasks that define
WKHQHZSURMHFW:HODEHOWKLVODWWHUFRPSRQHQW DQGDVVXPHWKDWLWFDQEH communicated, but does not reveal any information about C na
7KHVLJQDO PD\RQO\EH received by player A.
7KHVLJQDO ZKLFKPD y be received by B only, has a similar
6

structure. It reveals C nb
,
DQGLWFRQWDLQVSDUWLDOLQIRUPDWLRQ DERXWWKHWDVNVWKDWGHILQHWKH new project.
/LNH FDQEHFRPPXQLFDWHGDQGLWGRHVQRWUHYHDODQ\LQIRUPDWLRQDERXW
C nb
. The tasks that define the new project are unforeseen ex ante and to learn the nature of these tasks a player needs to know both
DQG
7KHSOD\HUVPD\FRPPXQLFDWH DQG WRHDFKRWKHU
and the truthfulness of communication is observable, but not verifiable. So while the receiver of a message can tell whether it is true or not, the parties cannot contract on the veracity of communication.
Without this critical assumption, contracts can trivially solve the problem. Fortunately, this
“softness” of information (see Tirole, 1986) is a very natural assumption in the context of division of labor. (Think of a pair of marketing and manufacturing managers or two coauthors.) If only A
NQRZV RQO\
B
NQRZV DQGRQHFDQQRWPDNHVHQVHRIRQHZLWKRXW the other, then it is hard to see how a third party can rule on claims about either. The fact that receipt of messages is non-verifiable prevents the players from agreeing to bilateral communication, thus implementing ex post symmetric and complete knowledge of payoffs.
I take this contractability argument even further and assume that outsiders understand so little about the projects, that contracts cannot depend on whether an implemented project is new or old. Alternatively, I assume that we focus the analysis on those projects for which this is true. This implies that the players can do no better than to negotiate a contract over w, a transfer from A to B if a project is implemented. (A somewhat related argument is made by Stein, 2000).
6LQFHRQO\RQHSOD\HUQHHGVWRNQRZ ¶DQG ¶ZHDVVXPHWKDWRQO\RQHSOD\HU may communicate. If there is communication, the receiving player can choose between the new and the old project. In this context, it is important that the costs of the old project are
7

private information. Without this assumption, communication may be discouraged simply because bargaining over the old project may be more efficient. More subtly, it serves to encourage communication because a player reveals information about the costs of the old project by choosing it after receiving communication about the new project. So the communicating player gets some information in return for what he or she gives up by communicating.
It is assumed that communication reveals information only in the weakest possible way. It may be reasonable to assume that the content of communication reveals something about costs. However, I make the weaker assumption that no information is revealed beyond that contained in the choice to communicate. This conservative assumption means that communication results in a rather indirect loss of bargaining power.
In modeling the effect of information on bargaining power, I have two concerns.
First, I would like to make rather weak assumptions about how power varies with informational asymmetries. Secondly, I want to separate the distributive effects from the pure efficiency effects of information. To accomplish this, I assume that bargaining, independently of when it takes place, consists of a single take-it-or-leave-it offer that is made by A with probability p, and else by B. I model p as a function of two arguments,
“how little B knows about A’s costs”, and “how little A knows about B’s costs”. One could think of these as posterior probability distributions that are ordered by some measure of dispersion. However, in the following, I will be looking at situations in which the arguments are identical, plus a case in which a single real number can serve as a sufficient statistic for how much is known about a player. So the analysis is consistent with a lot of ways of measuring these arguments. For now, it suffices to say that p
8

(i) -is increasing in the first argument and decreasing in the second,
(ii) -satisfies the symmetry condition p(x,y)=1-p(y,x), and
(iii) -is linear in probabilities such that if B
DVVLJQVSUREDELOLWLHV
-
WRVWDWHVDQG in which he knows x
1
and x
2
, respectively, about A’s costs, and x
1
and x
2
are nested in the sense that one could be a posterior resulting from the other, then
S S[
1
,y)+(1-
S[
2
,y), and similarly for A’s beliefs about B’s costs.
The second condition implies that p(x,x)=1/2. The third condition could be weakened considerably, but has the advantage of making the analysis notationally much more transparent. It is unpleasantly strong and is inconsistent with many reasonable measures of the arguments of p. However, as we will see, it is much less offensive in the special cases we will be looking at.
The negotiation mechanism itself is clearly arbitrary and, in general, less than second best. For purposes of the analysis, its two most critical properties are (1) that payoffs responds to informational advantages, and (2) that bargaining becomes more efficient when the players have better information. These are properties are satisfied by most reasonable models of bargaining, such as the sealed bid model of Chatterjee and Samuelson (1983).
Let me now define two game forms. One in which the players commit to a contract negotiated before search and communication, and one in which there is ex post negotiation.
It is clearly possible to look at a number of other game forms. In particular, one could imagine a game form with some intermediate degree of commitment (Aghion and Tirole,
1997; Rogoff, 1985) to an ex ante negotiated contract. However, as a first cut, I will focus on a comparative analysis of the two extreme cases with full and no commitment.
9

The “Ex Ante Negotiation” and “Ex Post Negotiation” Game Forms
Because either player can be asked to communicate, there are two versions of each of these game forms. I will show in the Appendix that their performances are identical. In this Section I will assume that B communicates, such that A gets to select the project.
The “ex ante negotiation” game form is defined by the following six stages:
EA1. The parties write a contract, which says that B will carry out an unspecified task at
A’s request. In return, B gets the unconditional transfer t, as well as w if the project is implemented. The players set w to maximize joint payoffs, and negotiate t according to the bargaining mechanism described above.
EA2. The players may invest s in search.
EA3. The parties learn their costs for the old project and may find the new project and thus
DQG UHVSHFWLYHO\
EA4. B may communicate to A.
EA5. A may ask B to perform a specific task (or the game will end).
EA6. The players may carry out their tasks, and if so, payoffs are distributed. (Otherwise, there are no payoffs.)
The “ex post negotiation” game form is defined by the following six stages:
EP1. Each player may expend search costs s.
EP2. The players learn their costs for the old project and may find the new project and
WKXV DQG UHVSHFWLYHO\
EP3. B
PD\FRPPXQLFDWH WR
A.
10

EP4. A announces whether she wants them to carry out the old or the new project. The
ODWWHUEHLQJIHDVLEOHRQO\LIVKHNQRZVERWK DQG
EP5. The parties may write a contract, which says that B will get w to carry out the task associated with the chosen project. They then determine w according to the bargaining mechanism described above.
EP6. If agreement is reached, the players carry out their tasks, and payoffs are distributed.
We will compare these two game forms under several extreme circumstances.
1. R n
=R o
and R o
large: Ex Ante Negotiation is Best.
In this subsection, we will isolate the bargaining power effect by looking at a case in which the revenues are identical, but very large. This means that (i) preferences between projects are only based on costs, and even the largest cost differences are swamped by minor variations in bargaining power, and (ii) all bargaining is efficient. (The latter implication requires that, given the “fatness” of F’s upper tail, revenues are so large that expected payoffs are maximized by making offers that are accepted with probability one.)
With ex ante negotiation, communication can not influence bargaining power, so the equilibrium is very simple. Given a choice between the old project and a new project, A will simply select whatever is cheaper for her, and B will communicate whenever the new project is cheaper for him. So in the end, ¼ of all new projects are implemented, accounting for ½ of those that ideally should be implemented.
11

Result 1EA: If R n
=R o
, R o
is large, and s<
2 œ>]
-z(1-F)]dF, the game form with ex ante negotiation has an equilibrium in which both players search. B communicates if and only if
C nb
”& ob
, and if he does, A will select the new project if and only if C na
”& oa
.
Proof: We will analyze the game backwards. In stage 5, A will continue if her payoffs, r a
R o
-w, are greater than her costs for the project. Given a choice between the old project and a new project, A will simply select whatever is cheaper for her. So if she has the option, A will select the new project with probability 1/2. In stage 4, if B has received
KHZLOO communicate whenever the new project is cheaper for him, or with probability 1/2.
Assuming that both players search, we first look at A’s incentives in stage 2. Her expected payoff consists of three terms. They represent her surplus (i) if B does not communicate or A does not find the new project, (ii) if B communicates, and A decides not to ask for the new project, and (iii) if they implement the new project. In case (i) A’s expected costs are
œ
zdF, in case (ii) they are
œ
z(1-F)2dF, and in case (iii) they are
œ z(1-
F)2dF. Her expected payoff reduces to
[1-
2
+(1/2)
2
][r a
R o
-w-
œ
zdF]+(1/2)(1/2)
2
[r a
R o
-w-
œ
z(1-F)2dF]+
(1/2)(1/2)
2
[r a
R n
-w-
œ
z(1-F)2dF]-s =
r a
R o
-w-
2 œ>]
z(1-F)]dF -s. (1)
If A does not search, her expected payoffs are r a
R o
-
œ
zdF-w. So if B searches, A will do so if
V 2 œ>
z/2-z(1-F)]dF. (2)
Turning now to B, his payoff from searching when both players do so, is given by
(1-
2
)[(1-r a
)R o
-w-
œ]G)@
1/2)
2
[(1-r a
)R o
+w-
œ
z(1-F)2dF]+
(1/4)
2
[(1-r a
)R o
+w
œ
zF2dF]+(1/4)
2
[(1-r a
)R o
+w-
œ
z(1-F)2dF]-s =
12

(1- r a
)R o
+w-
2 œ
[z/2+z(1-F)]dF-(1-
2
)
œ]G)
-s. (3)
So in this game form B’s search incentives are exactly as A’s. There is an equilibrium, in which both players will search if
V 2 œ>
z/2-z(1-F)]dF. (4)
Finally, in stage 1, if the players set w=(r a
-1/2)R o
, both of them will want to continue at all later stages. Q.E.D.
The game form with ex post negotiation is much more complicated. However, the analysis is simpler when we can assume that all offers are accepted. It is further simplified if revenues are very large, such that concerns for bargaining power dominates preferences based on cost differences between projects. Under these circumstances, it will turn out that there is no communication and thus no search in equilibrium. The reason is that A can exploit B’s communication strategy to select a bargaining scenario in which she has more power. If only B-types with very low C nb
and very high C ob
communicate, all A-types will select the new project and thus be in a superior informational position. Conversely, if most
B-types cummunicate, all A-types will select the old project and thus force bargaining over the old project knowing a lot about C ob
. As a result, the only equilibrium is one in which no
B-types communicate and no new projects are implemented.
Result 1EP: If R n
=R o
and R o
is large, the game form with ex post negotiation has no equilibria in which B communicates. There is thus no search either.
13

Proof: We first need a bit of notation. The key components of a candidate equilibrium are a communication strategy for B and a selection strategy for A. Any pair of such strategies, combined with a pair of choices, give each player a posterior probability distribution over the costs of the other. There are five relevant scenarios:
(1) B communicates and A selects the new project,
(2) B communicates and A does not select the new project because she prefers not to,
(3) B communicates and A does not select the new project because she did not find it,
(4) B does not communicate because he prefers not to, and
(5) B does not communicate because he did not find the new project.
If both players know the scenario, we use (x i
,y i
), i=1,2...5, to denote the arguments of
p in these five scenarios. Furthermore, we let (C na1
,C nb1
) denote the highest costs A and B possibly could have in scenario 1, while (C oai
, C obi
), i=2,3,4,5, denote the highest possible costs in the other scenarios. Because B can not distinguished scenarios 2 and 3, x
2
=x
3
, and because A can not distinguished scenarios 4 and 5, y
4
=y
5
. The costs satisfy similar conditions.
Whoever makes the offer at the bargaining in stage 5 will take almost all the surplus, leaving the other player just enough to cover the highest cost she or he possibly could have.
So for example in scenario 1, A will bid w a
= C nb1
-(1-r a
)R n
and B will bid w b
= r a
R n
-C nb1
.
Given that revenues are so high that all offers are accepted, when A compares scenarios (1) and (2) in stage 4, she will select the former if
p(x
1
,y
1
)(R n
-C nb1
-C na
)+[1- p(x
1
,y
1
)](C na1
-C na
)>
[
S
(x
2
,y
2
)+(1-
S
(x
3
,y
3
)] (R o
–C ob2
-C oa
)+[1-
S
(x
2
,y
2
)-(1-
S
(x
3
,y
3
)](C oa2
-C oa
). (5)
This can always be written in the form
14

C na
<C oa a
, where -1
” a
”
(6)
So A’s strategy can only be sustained if it belongs to this class.
Looking next at B’s communication decision in stage 3, he compares scenarios 1, 2, or
3, versus 4 or 5. Again using that revenues are so high that all offers are accepted, his preferences depend on the probability, call T( a
), that A will select the new project. Given this, B will communicate if
7
{p(x
1
,y
1
)(C nb1
-C nb
)+[1-p(x
1
,y
1
)](R n
-C na1
-C nb
)}+[ (1-T)p(x
2
,y
2
)+(1-
S[
3
,y
3
)](C ob2
-C ob
)+
[1-
7
- (1-T)p(x
2
,y
2
)-(1-
S[
3
,y
3
)](R o
–C oa2
-C ob
)>
[
S[
4
,y
4
)+(1-
S[
5
,y
5
)](C ob4
-C ob
)+ [1-
S x
4
,y
4
)-(1-
S[
5
,y
5
)](R o
–C oa4
-C ob
). (7)
This can always be written in the form
C nb
<C ob b
, where -1
” b
”
(8)
So we can restrict our attention to pairs ( a b
), and these
¶ s can serve as sufficient statistics for the arguments of p. We have thus ended up in a setting where the linearity property (iii) of p is much less problematic. For example, if B believes that a
is equally
OLNHO\WREH DQG
–
WKHQ
p( *,0)+1/2p(- *,0)=1/2.
In scenario 1, when the players bargain over the new project, more is known about a player with a smaller . So with minimal abuse of notation, we can write p(x
1
,y
1
S a b
).
If a
is large, less is known about C na
, and A has more power. Conversely, if b
is small, more is known about C nb
, and A again has more power. In scenario 2, when B has communicated but A rejected because she preferred the new old project, we can find an expression for p by using the symmetry of F. First, the distribution of C ob
is just that of 1-
C nb
. , and second, the distribution of C na
for A’s that select the new project when a
= a
*,
15

is identical to the distribution of C oa
for A’s that do not, when a
=- a
*. So we can write p(x
2
,y
2
)=p(a
, b
). The figures below illustrate two examples.
Figure 1 Figure 2
A-
7\SHVDQGVHOHFWLRQRIQHZSURMHFWV a
<0 B-Types and Communication: b
>0
C o
C o
-
C n
C n
In scenario 3, where B communicates and A rejects because she did not find the new object, nothing is learned about C oa
, so p(x
3
,y
3
)=p(1, b
). In scenario 4, where B chooses not to communicate, p(x
4
,y
4
)=p(1,b
), and in scenario 5 where B fails to find the new project p(x
5
,y
5
)=p(1,1). We can also find T( ), the probability that a player prefers the new project, as an increasing function such that T(-1)=0 and T(1)=1.
When A decides on a
, her dominant concern is to maximize the probability that she gets to make the offer and appropriate the surplus. We can write this probability as
7 a
S a b
>
-
7 a
)]p(a
, b
)+(1-
S b
) (9)
For intermediate values of a
, (9) involves a gamble (with probabilities T and 1-T) between two inferior options. This is dominated by taking the higher p for sure, either by a
=-1, such that T( a
)=0, or by a
=1, such that T( a
)=1. Intuitively, A does not want to separate.
Given this, we go back to stage 3 of the game and look at the probability that B gets to make the offer. If a
=1 and T( a
)=1, B will make the offer with probability
7 b
)[1-p(1 b
)]
>
-
7 b
)][1-p(1,b
)]+(1 (10)
16

Just like (9), (10) involves a gamble between two inferior options for intermediate values of b
(with probabilities T and 1-T). This is dominated by taking the higher p for sure, either by b
=-1, such that T( b
)=0, or by b
=1, such that T( b
)=1.Like A, B does not want to separate.
Similarly, when a
=-1, T( a
)=0, B will make the offer with probability
7 b
)[1-p(1 b
)]
>
-
7 b
)][1-p(1,b
)]+(1 (11) which is identical to (10). This leaves us with 1 and –1 as the only candidate values of b
.
Given that the search costs s are positive, neither player will search, and there will be no communication. Q.E.D.
Summarizing Results 1EA and 1EP, we see that ex ante negotiation implements efficient new projects half the time, while none are implemented under ex post negotiation.
The bargaining power effect favors ex ante negotiation.
2. R n
>>R o
, R o
large, and r a
=1: Ex Post Negotiation is Best.
To illustrate the incentive transfer effect, we now look at another extreme situation. We assume that R n
is much larger than R o
, and that all revenues accrue to A. This means that it is critical to implement the new project, but that B has no direct incentives to do so. (If r a
<1, this game form does much better, since B has strong incentives to communicate and search.) We continue to assume that R o
is very large such that all offers are accepted.
17

Result 2EA: If R n
is much larger than R o
, R o
is large, r a
=1,
DQGV 2 œ])
-1)dF, the game
form with ex ante negotiation has an equilibrium in which both players search. B will communicate if and only if C nb
”& ob
, and if he does, A will always select the new project.
Proof: In stage 5, A will continue if her payoffs are greater than her costs for the project.
Since R n
- R o
is large, A will always prefer the new project if she has a choice. In stage 4 B will communicate whenever the new project is weakly cheaper for him, which happens with probability 1/2. This is the same communication strategy as when R n
=R o
. When r a
=1, the increased value of R n
has no impact on communication with ex ante negotiation.
We next look at A’s incentives in stage 2. Her expected payoff if she searches consist of three terms, representing her surplus (i) if one of the players do not find the new project,
(ii) if B decides not to communicate, and (iii) if they implement a new project. In the case where both players search, this is
(1-
2
)(Ro-w-
œ]G) 2
(R o
-w-
œ]G) 2
(R n
-w-
œ]G
F)-s=R o
-
œ]G)
-w+
2
(R n
-R o
)/2-s.(12)
If A does not search, her expected payoffs are R o
-
œ]G)
-w. So given that B searches, A will do so if
V 2
(R n
-R o
)/2. (13)
Turning now to B, his expected payoff, when both players search, is given by
(1-
2
)(w-
œ]G) 2
(w-
œ]G) 2
[w-
œ]
-F)2dF]-s=w-
œ> 2
z(1-F)2-(1-
2
)z]dF-s. (14)
If B does not search, he can expect w-
œ]G)
. So given that A searches, B will do so if
V 2 œ])
-1)dF. (15)
18

Since R n
- R o
is large, we see that B’s search incentives are much weaker than A’s.
Therefore, both players will search if (15) holds, and neither player will search if this does not. Q.E.D.
In this case the game form with ex post negotiation is much simpler.
Result 2EP: If R n
is much larger than R o
, R o
is large, r a
=1, and s<
2
(R n
-R o
)/2, the game
form with ex post negotiation has an equilibrium in which both players search. B always communicates and A always selects the new project.
Proof: In the postulated equilibrium neither party learns anything about the costs of the other. So the prior beliefs never updated and p=1/2. Appealing to the size of revenues, as in the proof of Result 1EP, we disregard costs as well as payoffs when the other player makes the offer. So if A has a choice, she expects R n
/2 from the new project and R o
/2 from the old project. She will therefore always choose the new project in stage 4. Going to stage 3, if B communicates, he will be able to negotiate for revenues R n
/2 with probability
DQG
R o
/2 with probability 1-
,IKHGRHVQRWFRPPXQLFDWHKHFDQH[SHFW
R o
/2. So consistent with the hypothesized equilibrium, all B types will communicate and all A types will select the new project. In this game form B can expect to bargain for a share of R n
, and his communication strategy is therefore responsive to revenues even though r a
=1. The bound on search costs finally follows from the facts that each player can expect R o
2
(R n
-R o
)/2-
s if they search, and R o
/2 if they do not. Q.E.D.
19

Comparing Results 2EA and 2EP, we see that ex post negotiation always implements the new project, while ex ante negotiation only implements it half the time. The incentive
transfer effect favors ex post negotiation.
3. R n
=R o
and R o
small:Ex Ante Negotiation May Be Best.
We now illustrate the bargaining efficiency effect. In the previous subsections, we have assumed that R o
is so large that all bargaining processes are efficient. It is never an equilibrium for a player to make a low bid and risk not trading. We will now change this and see how the information revealed by communication can increase the efficiency of the bargaining process. If the bargaining efficiency effect is very small, we saw in Results 1EA and 1EP, that ex ante negotiation will still be best if R n
=R o
. However, we will here show by example that the bargaining efficiency effect can be so large that ex post negotiation is best, even with a small bargaining power effect working against it. To this end, we will completely neutralize concerns for bargaining power by fixing a constant p=1/2, and appeal to continuity to argue that the results continue to hold for “almost” constant p-functions.
Since we are just looking for an example, we assume that costs are drawn from a simple multinomial distribution F’, that assigns equal probabilities to costs being C
1
-
2
&
2
-
&
3
RU&
4 where
Result 3EA: If R o
= R n
U a
FRVWVDUHGUDZQIURP)¶DQGV WKHJDPH
form with ex ante negotiation has an equilibrium in which both players search. B will communicate if and only if C nb
equals C
1 or C
2
, and if he does, A will select the new project
20

if and only if C na
equals C
1 or C
2
unless (C na
, C oa
)=( C
2
, C
1
). The players only trade if both their costs are C
1 or C
2
.
Proof: Suppose that w=1/2. In this case players only want to trade if their costs are C
1 or
C
2
, and the communication and selection strategies are obvious except for the claim that B will communicate when (C nb
, C ob
)=( C
2
, C
1
). If this B type does not communicate, he
ZLOOWUDGHZLWKSUREDELOLW\òDQGJDLQ LIKHGRHV+RZHYHULIKHFRPPXQLFDWHVKHZLOO
WUDGHWKHQHZSURMHFWZLWKSUREDELOLW\JDLQLQJ DQGWUDGHWKHROGSURMHFWZLWK
SUREDELOLW\JDLQLQJ 6RWKHH[SHFWHGUHWXUQIURPWKHODWWHU is higher and the claim is true. If we mechanically calculate the players’ payoffs, we find that A and B can expect
DQG UHVSHFWLYHO\IRUDWRWDOVXUSOXVRI 6LQFHWKH\HDFKFDQ
H[SHFW LIWKHUHLVQRVHDUFKLWLVQHFHVVDU\W hat s<(81Q.E.D.
Result 3EP: If R o
= R n
U a
FRVWVDUHGUDZQIURP)¶DQGV WKHJDPH
form with ex post negotiation has an equilibrium in which both players search. B will communicate if and only if C nb
”& ob
, and if he does, A will select the new project if and only if C na
”& oa or (C na
, C oa
)=( C
2
, C
1
).
Proof: Under the hypothesized equilibrium, A will offer w a
= C
2
if her own costs are C
1 or
C
2
, and w a
=C
1
if her own costs are C
3 or C
4
. Similarly, B will offer w b
= 1-C
2
if her own costs are C
1 or C
2
, and w b
=1-C
1
if her own costs are C
3 or C
4
. If A’s with C na
=(C
1
,C
2
,C
3
,C
4
VHOHFWWKHQHZSURMHFWWKH\FDQH[SHFWVXUSOXVHVRI UHVSHFWLYHO\
Conversely, if C oa
=(C
1
,C
2
,C
3
,C
4
), they can expect
UHVSHFWLYHO\IURP
21

the old project. So the postulated selection strategies constitute an equilibrium. If B’s with
C nb
=(C
1
,C
2
,C
3
,C
4
) communicate, A will select the new project with probability 11/16 and these B types can expect surp
OXVHVRI UHVSHFWLYHO\IURPWKHQHZ project. If A does not select the new project, B’s with C ob
=(C
1
,C
2
,C
3
,C
4
) can expect
VXUSOXVHVRI UHVSHFWLYHO\IURPWKHROGSURMHFWDIWHUFRPPXQLFDWLRQ,I they do not communicate, B’s with C ob
=(C
1
,C
2
,C
3
,C
4
) can expect surpluses of
UHVSHFWLYHO\IURPWKHROGSURMHFW2QHPD\YHULI\WKDWWKHSRVWXODWHG communication strategies constitute an equilibrium. If we mechanically calculate the players’ payoffs, we find that A and B
FDQH[SHFW DQG UHVSHFWLYHO\IRU
DWRWDOVXUSOXVRI 6LQFHWKH\HDFKFDQH[SHFW LIWKHUHLVQRVHDUFKLWLV necessary that s<(354Q.E.D.
Let us now compare the equilibria from 3EA and 3EP. When R n
=R o
=1 ex post negotiation implement more communication (probability 5/8 vs.1/2), and expected total
VXUSOXVHVDUHKLJKHU YV 1HLWKHUJDPHIRUPLPSOHPHQWVDOOHIILFLHQW projects, but because it does better, ex post negotiation also implements more search (for values of s
XSWR YV &RQVHTXHQWO\H[SRVWQHJRWLDWLRQLVWKHPRUH efficient in this example.The bargaining efficiency effect favors ex post negotiation.
Each of our three effects is known from other contexts. The bargaining power effect is related to the idea that offering a contract reveals information about the offerer (Aghion and Bolton, 1987; Hermalin and Katz, 1993). Interestingly, a number of papers have shown
22

how a commitment not to renegotiate can be sustained by a commitment not to acquire certain pieces of information (Spier, 1992; Dewatripont and Maskin, 1995). The bargaining power effect makes the causality goes the other way: A commitment not to renegotiate influences the amount of information revealed. The incentive transfer effect plays a role in models in which incentive systems may cause agents not to reveal information that is of value to their principals (Rotemberg and Saloner, 1993; Dewatripont and Tirole, 1999). It is also, in an ironic way, the opposite of the well-known hold-up problem. If only A has search costs, ex post negotiation can be bad, because it may prevent her from getting enough expected surplus to warrant the specific investment of s. In the present model both players need inducements, so it is efficient to spread the surplus in ex post negotiation, rather than concentrate it in ex ante negotiation. Finally, the bargaining efficiency effect is exploited in a lot of screening mechanisms.
Together, the bargaining power effect and the incentive transfer effect imply that ex ante negotiation is better when adjustments yield smaller and more evenly accruing benefits. This is illustrated in Figure 3 below.
Figure 3
Most Efficient Coordination Regimes
Uneven accrual of gains
Ex Ante
Negotiation
Ex Post
Negotiation
Big gains per adjustment
23

Notwithstanding the above, it is clear that a large part of modern market economies are organized such that parties negotiate after finding out what they are trading. I will now argue that the employment relationship is a prime example of ex ante negotiation and that the model therefore throws light on the theory of the firm.
Interpretation as Firms and Markets
In a paper that is more controversial than influential, Wernerfelt (1997) defines the employment relationship as a game form used for trading sequences of human asset services. In this game form, the parties engage in once-and-for-all wage negotiation, the boss describes desired services sequentially, and either party may terminate the relationship at will. He contrasts the game form with negotiation-as-needed, and ex ante agreed upon price lists. The argument is then based on exogeneously specified adjustment (negotiation and communication) costs. The wage contract is assumed to be more costly that agreements on individual adjustments or items on a price list. So if adjustments are frequent and diverse, the employment relationship is the more efficient game form.
One of the problems with this argument is that most obvious adjustment costs are not driven by incentives. They consist of time and effort spent on conflict resolution. In the broader scheme of things, there is quite a bit of indirect evidence that conflict is costly and is avoided. In particular, a lot of biological analogies suggest that a pattern of once-and-forall conflict resolution followed by cooperation is a rather common, and thus presumably efficient, phenomenon. For example, when a new wolf first joins a pack, it has to engage in considerable conflict to establish its place in the social rank-order. After these initial
24

negotiations, conflict is set aside, and the pack cooperates on hunts. Independent of how it is found and killed, prey is then shared according to rank within the pack. However, arguments driven by exogeneous costs are less satisfactory than those in which the costs are endogeneous. In particular, some professional norms consider it critical that the effects can be derived from incentives.
The adjustment-costs in the present paper, consisting of withheld communication, failure to select superior alternatives, and under-investment in search, are derived from incentive concerns. So it is tempting to look at the analysis as contributing examples of incentive-driven adjustment-costs to the theory of the firm.
Interpreted in this light, the results suggest that firms are better coordination regimes when the gains from individual adjustments are smaller and accrue more evenly. The first condition could be taken to imply that the firm is more efficient when it is less important to implement adjustments. However, I do not believe that this is the right interpretation.
Among equally productive environments, those with smaller gains from adjustments will have more frequent opportunities. So the question really is whether improvements occur in many small, or a few large steps. Also the second condition could be related to the frequency of adjustment. Supergame arguments would suggest that it is easier to share gains that come in a lot of smaller batches. One can thus argue that the model is consistent with the prediction that firms are more efficient when more frequent adjustments are needed.
There are some empirical findings supporting this interpretation. First, Simester and
Knez (2001) have rather directly documented that the bargaining power effect plays a role in the firm versus market choice. They describe how a firm restricts the flow of information
25

to arms length suppliers, but allows open communication with internal suppliers of the same parts (see also Tushman, 1978). More indirectly, Monteverde (1995) shows that integration is more likely when up- and downstream engineers need to communicate more.
Even more indirectly, we can compare incremental and radical new product development.
When improvements are incremental, the new product’s revenues will be only marginally higher than those of the old product, and the firm should be best. For more radical changes, the new product may command much higher revenues, and the market will be more efficient. This general prediction, that more radical innovations tend to occur between, rather than within firms, is supported by literature in the area of innovation management
(Freeman, 1991; Hagedoorn, 1995; Powell, Koput, and Smith-Doerr, 1996).
Let me therefore relate the analysis to the literature on the theory of the firm.
Contribution to the Literature on the Theory of the Firm
The paper contributes to at least three different questions asked in this literature.
What is the basis for the comparative advantage of the firm?
In addition to the above-mentioned paper by Wernerfelt (1997), the analysis is related to a recent piece in which Bajari and Tadelis (2000) perform a comparison of costplus and fixed price contracts. Fixed price contracts give steeper incentives, but since adjustments lead to ex post bargaining with incomplete information, they are burdened with an inefficiency. Because cost plus contracts can be adjusted costlessly, there if a trade off between incentives and adjustment costs. As a result, cost-plus contracts, interpreted as firm-like, are more efficient when adjustments are more likely. This is essentially the same
26

prediction as that made in the present paper. However, the argument here relies on different forces and is one layer deeper. We looked at the process by which candidate adjustments are identified, and saw that fewer candidates may be identified in the presence of ex post bargaining.
Summarizing, the models of Wernerfelt (1997), Bajari-Tadelis (2000), and the present paper, are driven by different adjustment costs. In the former paper the costs are exogeneous, in Bajari-Tadelis they are due to the inefficiency of incomplete information bargaining, and in the present paper, the costs appear in the form of incentive barriers to communication and cooperation. In spite of these differences, all three papers are consistent with the prediction that firms perform relatively better when adjustments are smaller and more frequent.
A recent paper by Gertner (1999) is related in a different way. Like we do here, he formalizes coordination in terms of communication and argues that players are more likely to withhold complementary information in markets. In spite of this similarity, however, the argument ends up being quite different from that made here. Gertner defines the firm as a game form with a neutral arbitrator while the market is an asymmetric game form in which one party has control. So information is sent to a neutral party in the firm, but an adversary in the market. Ergo, less information is sent in the market. In the present paper, information is always sent to an adversary, but either after or before negotiation. Depending on parameter values, we find that there may be more communication in the firm or in the market. The fact that the firm and market game forms are defined so differently leads the two papers to make contrasting predictions. Gertner predicts that firms should be used when arbitration is cheap, while my main prediction is the institutional choice depends on
27

the distribution of gains from adjustment. On the other hand both papers predict that concerns about bargaining power ceteris paribus will hamper communication across firm boundaries.
Who is the Boss?
The basis for authority in the firm has been a topic of much discussion. As is done in the papers mentioned above, we here portray the boss as the player with superior information. The information endowment is exogenous in Wernerfelt (1997), but endogenous in the present paper. This view of the boss is implicit in some of the classical literature on the firm, such as Simon (1951) and Arrow (1974). On the other hand, it contrasts with the property rights stream (Grossman and Hart, 1986; Hart and Moore, 1990; and Hart, 1995), according to which the boss gets her role from asset ownership.
Why do employees have low-powered incentives?
More narrowly, the paper also contributes to the literature that explains the advantages of flat incentives in firms. The observation of the stylized fact goes back to at least Williamson (1985), and several other rationalizations have been offered. Many of these, i.e. Holmstrom and Milgrom (1994), derive the advantages of flatter incentives by relying on multi-tasking concerns at the individual level. Bajari and Tadelis (2000) argue that renegotiation is more efficient when incentives are less steep. The present paper, along with the above-mentioned piece by Gertner, argues that flat incentives facilitate cooperation between agents. In fact, one interpretation is that the market spreads incentives to foster broader initiatives, while the firm flattens incentives to encourage cooperation.
28

Further Research
We have only looked at a few corners of the parameter space. A lot of interesting interactions remain to be investigated. The most natural idea may be to perform some sort of comparative statics on F. The bargaining power effect should be more important when the players have less information about each others’ costs. Another interesting direction for future theoretical research is to introduce more asymmetry between the players. It does, for example, seem reasonable to assume that the player to whom revenues accrue is better informed about their magnitude. Other possibilities are to look at differences in search (or effort) costs. Such investigations would help us identify in more detail the determinants of the allocation of organizational roles.
Beyond this, the analysis is still partial. The distribution of non-contractible gains may to some extent be a design variable itself. In the context of the cost-revenue example, it may be possible to let revenues accrue to either player, or to write some sort of sharing agreement. Similarly, the co-specialization of information could perhaps be avoided by designing more modular tasks. It is also tempting to look deeper into the nature of the commitment that separates the two game forms. If renegotiation is costly, one would expect more of it when the gains from adjustment are larger and accrue less evenly. Since we found that the Market is most efficient in such cases, it seems that the results could be consistent with some types of endogenous renegotiation.
29

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31

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32

I will here look at game forms that are identical to those analyzed in Section II, except that the players’ roles are reversed. To make the contrast as stark as possible, we assume that r a
=1.
Ex ante negotiation when B selects the project
This game form is defined as follows:
EAB1. The parties write a contract, which says that A will carry out an unspecified task at
B’s request. In return, A gets the unconditional payment -t, as well as R o
-w if an old project is implemented, and R n
-w if a new project is implemented. The players set w to maximize joint payoffs, and negotiate t by flipping a fair coin and letting the winning player make a take-it-or-leave-it offer.
EAB2. The players may invest s in search.
EAB3. The players learn their costs for the old project and may find the new project and
WKXV DQG UHVSHFWLYHO\
EAB4. A may communicate to B.
EAB5. B may ask A to perform a specific task.
EAB6. The players carry out their tasks, and if so, payoffs are distributed.
By proceeding as before, we find.
Result 4EAB: When B selects the project, the game form with ex ante negotiation has an equilibrium in which the players’ search incentives and expected playoffs are the same as when A selects the project. In this equilibrium, A will communicate if and only if R na
-
C na
•5 o
- C oa
. If A communicates, B will select the new project if C nb
”& ob
.
33

Proof: We will analyze the EAB game backwards. In stage 5, B will continue if her payoffs, w, are greater than her costs for the project. Given a choice between the old project and a new project, he will select the new project if C nb
”& ob
. In stage 4, A will communicate whenever R na
-C na
•5 o
- C oa
, such that the new project gives him weakly larger payoffs.
Looking next at the EA game, A will select the new project is R na
-C na
•5 o
- C oa
, and B will communicate if C nb
”& ob
. Either way the game forms implement the same set of new projects. Q.E.D.
The Result implies that in the game form with ex ante negotiation (the firm), the
accrual of non-contractible payoffs does not affect who should select the project. In particular, one cannot use the allocation of organizational roles to manipulate search incentives. Instead, one would guess that the players’ relative information is an important factor in determining the most efficient allocation of roles. If the boss is a player with more information, less needs to be communicated.
Ex post negotiation with B Selecting the Project
This game form is defined by:
EPB1. Each player may expend search costs s.
EPB2. The players learn their costs for the old project and may find the new project and
WKXV DQG UHVSHFWLYHO\
EPB3. A
PD\FRPPXQLFDWH WR
B.
EPB4. B announces whether he wants them to carry out the old or the new project. The
ODWWHUEHLQJIHDVLEOHRQO\LIKHNQRZVERWK DQG
'.
34

EPB5. The parties may write a contract, which says that B will get w to carry out the task associated with the chosen project. To determine w, the players flip a fair coin and the winning player makes a take-it-or-leave-it offer.
EPB6. If agreement is reached, the players carry out their tasks, and payoffs are distributed.
Perhaps not surprisingly, we can show - by direct re-labeling of the endogenous functions and variables - that this game form performs just like that in which A selects the project. So also in the game form with ex post negotiation (the market), the accrual of
non-contractible payoffs does not affect who should select the project. Combining the two results, we see that the identity of the player selecting the project does not affect the relative efficiency of the two coordination regimes.
35