GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 294

A Formal Behavioral Model of Firm Boundaries: Why Does
Authority Relation Mitigate Ex Post Adaptation Problems?

Yusuke Mori

December 2012GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, JapanA Formal Behavioral Model of Firm Boundaries: Why Does
Authority Relation Mitigate Ex Post Adaptation Problems?∗
Yusuke Mori†This version: December 25, 2012

Abstract
We explore why authority within firms helps trading parties immediately settle ex post
adaptation problems despite the possibility of a subordinate’s disobedience to the orders of
his boss. By employing three crucial behavioral assumptions (reference-dependent preference, self-serving bias, and shading), we point out that the choice of governance structure
affects trading parties’ expectations about outcome of ex post adaptations and show that asubordinate is likely to obey orders of his boss because he is expected to do so. Nevertheless,our study also points out that such a positive aspect of authority comes with subordinate’s
psychological disutility.
Keywords: Reference-dependent preference; self-serving bias; contracts as reference points;
transaction cost; ex post adaptation
JEL Classification: D23; L22∗

I am grateful to Reiko Aoki, Kohei Daido, Junichiro Ishida, Akifumi Ishihara, Shinsuke Kambe, Shintaro Miura,

Tomoharu Mori, Fumitoshi Moriya, Takeshi Murooka, Sadao Nagaoka, and Yasuhiro Shirata for their beneficial
comments, and especially to Hideshi Itoh for his suggestions and encouragement. I also thank the participants at
Contract Theory Workshop, Contract Theory Workshop East, 2012 Japanese Economic Association Autumn Meeting,the 6th Annual Meeting of the Association of Behavioral Economics and Finance, and the seminar at Hitotsubashi
University for their helpful comments. This paper received the Osaka University Institute of Social and Economic
Research/Moriguchi Prize. Any remaining errors are my own.
†

Graduate School of Commerce and Management, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo 186-8601,

Japan. E-mail: cd101008@g.hit-u.ac.jp

1

1 Introduction
Transaction cost economics (TCE), such as Williamson (1985, 1996), asserts that under bilateralmonopoly caused by relationship-specific investment or other factors, firms are likely to choose
vertical integration. It follows because while non-integrated parties have to engage in costly negotiations for the ex post adaptations to unanticipated disturbances, which leads to bargaining
inefficiencies (delay in reaching agreement and bargaining breakdown), integrated firms can implement these by fiat without such costly negotiations. This assertion is supported by a numberof empirical studies (see Lafontaine and Slade, 2007 for a survey of these studies).
The discussion above implicitly assumes that authority within organizations is effective andsubordinates always obey their boss’s orders. This implicit assumption has been frequently questioned (e.g., Hart, 1995), but TCE has not provided any formal justification for it.
This paper develops a formal model that explores the effectiveness of authority in the context
of ex post adaptations. Especially, we focus on the situation where trading parties in bilateralmonopoly due to relationship-specific investment engage in the division of trade value, which ismost likely to cause conflicts between them. We show that authority helps trading parties reachagreement on the division of the value immediately despite the possibility of a subordinate’s
disobedience to the order of his boss (i.e., integration achieves immediate agreement more easily
than non-integration).
There is some recent studies which point out that reference points affect ex post renegotiation,and hence, make-or-buy decisions (e.g., Hart and Moore, 2008, and Herweg and Schmidt, 2012).
We also focus on how reference points affect make-or-buy decisions and our study employs three
behavioral assumptions about how reference points affect each party’s utility and how they are
set: reference-dependent preference, self-serving bias, and shading. It is worth noting that these2assumptions are crucial for the result.1 That is, relaxing any of these assumptions leads to theresult that authority relationship does not affect the timing of agreement or brings the opposite
result: non-integration can realize the immediate agreement more easily than integration. The
evidence that supports each of these assumptions will be presented in Section 3.
Trading parties in our model have the following four characteristics. First, as in the literatureon reference-dependent preference, such as Köszegi and Rabin (2006, 2007), the parties’ utility isreference dependent and their reference points are given by their expectations about the relevant
outcomes.
Under this assumption, since non-integration and integration employ different adaptation processes, each governance structure leads to different reference points (i.e., the process by which
adaptation outcomes are determined affects the parties’ reference points). Under non-integration,
as mentioned above, ex post adaptation is implemented through bargaining, and hence, the parties’ reference points are given by the expected outcome of bilateral bargaining. Under integration, on the other hand, ex post adaptation is implemented by fiat. That is, a party who has decision rights (boss) unilaterally gives an order to her subordinate and he can only choose whether
to obey it or not. Thus, the parties’ reference points are the expected outcome of an ultimatum
game (i.e., the boss takes most of the trade value).
Second, each party has a self-serving view regarding who is to incur sunk relationshipspecific investment (Babcock et al., 1995). More specifically, while a party who does not invest
thinks that her partner who has invested (he) is to incur the whole investment cost, he believes
that his sunk investment is to be compensated. Although his belief about the sunk cost mightseem unreasonable, Macleod (2007) points out a concept of fairness based on the idea that par-1

What is important here is that each party cares about his partner’s gain-loss. Our result thus does not change if

we employ another form of other-regarding preference instead of shading, such as altruism. See Appendix D.

3

ties should be compensated for their sunk investments. Such self-serving views result in thedivergence of reference points between the parties, which causes delay in reaching agreement.
Third, those who obtain the payoffs that are smaller than their reference point payoffs undertake activities that lower their partners’ payoffs. Such behavior can be considered punishment
for unfair treatment; it is called shading in the literature on contracts as reference points, suchas Hart and Moore (2008), Hart (2009), and Hart and Holmstrom (2010). It is worth noting that
our model can be easily extended to analyze another form of other-regarding preference, namely
altruism, which is discussed in Appendix D.
Fourth, while the value shrinks because of delay in reaching agreement, each party does notcare about the cost of delay (behaves as if there were no discounting). This assumption does
not only reflect the experimental fact of Binmore, Swierzbinski, and Tomlinson (2007), but also
substantially simplifies our analysis. The case where the parties do care about discounting will
be dealt with in Appendix C.
Some reader might suspect that such behavioral aspects matter at the level of individuals,
but not at the level of organizations (i.e., make-or-buy decisions). Nevertheless, we believe thatthese aspects affect organizational-level decisions. For example, some literature points out thepresence of “boundary-role person” (Adams, 1976) who performs “The specialized class of roles
that carry out the function of interaction between the organization and various elements in its
environment” (Perry and Angle, 1979, p. 489). This implies that since those who make decisions
at the level of organizations is an individual (boundary-role person), his decisions can be affectedby these behavioral aspects.
Our model presents two reasons why integration achieves immediate agreement on the division of the value more easily than non-integration despite the possibility of the disobedience toorders. First, disobedience to an order under integration provokes severer punishment than rejec4

tion of an offer under non-integration.2 Under non-integration, trading parties are autonomous,and hence, they are entitled to reject any offer that their partners make as they please (namely,
their reference point payoffs are balanced). Thus, the rejection of an offer does not cause a proposer a huge amount of feeling of loss (anger) under non-integration. Under integration, on theother hand, ex post adaptation is implemented by fiat. That is, a boss determines how to divide
the trade value, and a subordinate is supposed to obey her orders. The boss’s reference point
payoff is thus quite large. However, if a subordinate disobeys the boss’s order, as Barnard (1938)
points out, the authority relationship between the parties is terminated, and hence, the adaptation
outcome is determined as if they are autonomous parties (i.e., their payoffs are balanced). Thismeans that if the order is rejected, the boss is compelled to obtain a far smaller payoff than her
reference point payoff, which provokes a huge amount of anger. Since the boss’s anger leads tosevere retaliation against the subordinate, he is less willing to reject the order.
The second reason is that under integration, the utility improvement for a subordinate from
disobedience is not sufficient to offset damage from the severe punishment. As mentioned above,
the parties’ reference points under integration are the expected outcome of an ultimatum game,and hence, the subordinate expects a small payoff. Thus, he can enjoy a large payoff improvementfrom rejecting the order, but such a payoff improvement is “too much” for him (i.e., disobedience
does not lead to a large utility improvement), which makes him less eager to reject the order.
We use this result to analyze firm boundaries and point out a trade-off between immediateagreement and the aggregate sense of loss. That is, while integration can economize inefficiencies

2

To facilitate the comparison between non-integration and integration, we assume that under integration, a boss

does not fire a subordinate who disobeys her order. Intuitively, this assumption suggests that dismissal is not always
costless: a fired employee can engage in actions that inflict damage on his ex-boss in revenge (e.g., sabotage, leakage,and theft).

5due to delay in reaching agreement, it incurs larger shading costs (i.e., deadweight loss caused byshading) than non-integration. The reason for this is as follows. As mentioned above, the party
who invests believes that his sunk investment will be compensated regardless of the choice of thegovernance structure. Nevertheless, under non-integration, each party expects a positive share ofa trade surplus (namely, the trade value minus the investment cost) from bargaining, and thus,
the party who invests expects to incur some portion of the investment cost. Under integration,on the other hand, a party who receives an order from the boss expects that the whole surplus
will be taken by the boss, and hence, if the party who invests does not have decision rights, hedoes not take the investment costs into account when he sets his reference point. This discussion
suggests that the divergence between the parties’ reference points because of the self-serving
view regarding who is to incur the investment costs is larger under integration than under nonintegration. This makes the aggregate sense of loss and shading costs under integration larger
than those under non-integration.
The rest of the paper proceeds as follows. The next section relates our study to the existing
literature. Section 3 introduces the model and Section 4 examines which governance structure
achieves immediate agreement on the division of the value more easily. Section 5 presents a
reduced form analysis of firm boundaries and shows the trade-off between immediate agreement and the aggregate sense of loss. Section 6 contains concluding comments. Furthermore,
Appendix A shows that the three behavioral assumptions (reference-dependent preference, selfserving bias, and shading) are all crucial to our result: integration achieves immediate settlementof the division of the value more easily than non-integration. Appendix B examines the case inwhich the parties are risk-averse. Appendix C assumes that the parties care about discounting
and checks the robustness of our result. Appendix D extends our model to analyze altruism.

6

2 Related LiteratureThis paper employs the approach that a contractual arrangement, namely the choice of governance structure (the presence of authority), determines each party’s reference point, which is
influenced by self-serving bias. Hence, we first relate our study to Hart’s contracts-as-referencepoints approach, which points out that contracts serve as reference points. We then review someexisting studies that share similar interests to ours. Lastly, since this paper derives implications
for firm boundaries, some approaches to them are reviewed.
The models of contracts as reference points are presented in Hart and Moore (2008), Hart(2009), and Hart and Holmstrom (2010). These studies employ two important assumptions.
First, “each party feels entitled to the best outcome permitted by the contract” (Hart and Moore,
2008, p. 33). Second, those who obtain less than their reference points undertake retaliation
against their trading parties. Such retaliation is called shading.
Our study is deeply related to contracts-as-reference-points approach in the sense that contractual arrangements affect each party’s reference point and each party can engage in shading.
Nevertheless, in our study, while each party’s reference point is influenced by self-serving bias,
he is not naive enough to believe that he is entitled to the best outcome permitted by the contract.
That is, all trading parties set their reference points with the same rule, which helps their reference points converge, but cannot share the same reference point due to each party’s self-serving
belief about who is to incur a sunk investment.
It is worth noting that our approach is quite different from that of Köszegi and Rabin (2006,2007) in the following senses. First, while reference points are endogenously determined in theirapproach, they are exogenously given in ours. Second, punishment for unfair treatment (shading)plays an important role in our study, but it is not considered in their studies. Nevertheless we7

borrow Köszegi and Rabin’s assumption that each party’s reference point is his “expectations
about the relevant outcome” (Köszegi and Rabin, 2007, p. 1051) and their utility function.
We next relate our paper to the existing studies that share similar interests to ours: Gallice(2009), Van den Steen (2010), Akerlof (2010), and Herweg and Schmidt (2012). Gallice (2009)
develops a model of Köszegi and Rabin’s reference-dependent preferences with self-serving bias.
However, Gallice (2009) is silent about how and what bias affects each party’s reference point.
As mentioned above, we assume that parties’ self-serving views regarding the sunk investment
result in the divergence of their reference points even if they share views on how each party sets
his reference point.
Van den Steen (2010) develops a theory of interpersonal authority. He shows that it is costly
for employees to disobey orders (and to get fired) because concentrating asset ownership into an
employer’s hands (i.e., integration) improves her outside option and lowers their outside options.
While Van den Steen (2010) focuses on ownership structure, it is not central to our study. In ourstudy, the choice of governance structure only affects the ex post adaptation process and eachparty’s reference point.
Akerlof (2010) presents a formal model of compliance, norms (senses of duty to comply),and punishment. In his model, a failure in compliance (failure in following norms) provokes
anger that leads to punishment. He points out that norms are contextual: self-interest behavior
is viewed as fair in market contexts, but not within an organization. Our model also assumes
that unfair treatments provoke anger and what is fair depends on the adaptation process: bilateralbargaining (non-integration) or fiat (integration).3
Herweg and Schmidt (2012) explore how loss aversion affects the outcome of ex post contract
renegotiation and show that loss aversion interrupts efficient renegotiation. Both their study and3

A similar discussion can be found in Hart and Moore (2008, p. 35).

8

ours assume that contractual arrangements affect reference points and point out that loss aversion
matters. However, there are some differences between their study and ours. First, self-serving
bias is not considered in Herweg and Schmidt (2012), but it plays an important role in our study.
Second, while Herweg and Schmidt (2012) focus on inefficiencies due to maladaptation, ourstudy focuses on delay in reaching agreement on the division of the value and shading cost (i.e.,
deadweight loss caused by shading).
We lastly review some approaches to firm boundaries: TCE and the property-rights theory.
While the former approach, as in Coase (1937) and Williamson (1996), focuses on authority,
the latter approach, as in Grossman and Hart (1986), Hart and Moore (1990), and Hart (1995),
stresses the choice of ownership structures.
TCE asserts that authority helps integrated firms to avoid costly ex post renegotiation, butdoes not explain how it does this. Mori (2011), for example, develops formal models of ex
post adaptation in the spirit of TCE and shows that inefficient ex post bargaining, which takes
place only under non-integration, creates a trade-off between rent seeking and bargaining costs.
In Mori (2011), however, as in the literature on TCE, integration is assumed to avoid bargaining
costs without offering a formal justification for the assumption. This study adopts TCE’s idea that
authority is the most important aspect of integration (internal organizations) and complements its
arguments by showing that the presence of authority (i.e., the choice of governance structure)affects each party’s expectation, and hence, the timing of agreement.
Our study is quite different from the existing studies on the property-rights theory with respect to how ownership structures affect parties’ outside options. Matouschek (2004), for example, develops a formal model following the property-rights theory and examines the optimal
ownership structure that minimizes ex post inefficiency caused by too much or too little trade.
In Matouschek (2004), disagreement payoffs depend on the ownership structure (namely, while9non-integration or integration maximizes the aggregate disagreement payoff, joint ownershipminimizes it). Our study, on the other hand, assumes that ownership structure does not affectparties’ outside options. Furthermore, while the property-rights theory has often been employed
to examine ex ante inefficiency (underinvestment problems), our study assumes that there is no
ex ante inefficiency (namely, the investment has been efficiently sunk) and focuses on ex post
inefficiencies.

3 The Model
This section presents the model that examines which governance structure realizes immediateagreement on the division of trade value between two trading parties. We compare two polar
governance structures (non-integration and integration) by employing three behavioral assumptions: reference-dependent utility, self-serving bias, and shading. We first present an overview ofthe model and then introduce some behavioral assumptions.
Two risk-neutral trading parties (parties 1 and 2) trade one unit of a good and are to engage inthe division of trade value.4 The trade requires party 2’s relationship-specific investment I (party
1 does not invest) and creates value π. We assume that the trade is efficient and the parties cannot
earn anything outside the current trade relationship. More specifically, the condition π/2 − I>0
holds, which means that the Nash bargaining solution yields a positive payoff even to a party
who incurs the whole sunk investment. In order to focus on ex post inefficiency, we assume thatex ante investment I is efficiently sunk (i.e., no ex ante inefficiencies).
The game proceeds as follows. First, a governance structure is chosen (non-integration or
integration) to maximize the sum of the two parties’ utility. Second, the parties set their reference
points regarding how the value will be divided. A process to divide the value is then initiated.
4

We refer to party 1 as “she” and party 2 as “he” for the purpose of identification only.

10

We assume that under integration, party 1 (resp. party 2) becomes a boss (resp. a subordinate).5
The process of the value division consists of party 1’s division offer x = (x1 , x2 ), where xi
represents party i’s share of the value, and party 2’s acceptance decision.6 If party 2 accepts theoffer, the surplus is divided as the accepted offer specifies; otherwise, the game continues. This
process does not necessarily mean that party 1 makes a take-or-leave-it offer. Since we focus
on which governance structure realizes immediate agreement, we only need to examine whether
the first offer is accepted. Thus, we can interpret this process to capture the first period of an
infinite-horizon alternating-offers bargaining.
For simplicity, we assume that each party does not care about discounting (the cost of delay
in reaching agreement). Note that this assumption does not mean that there is no discounting.
Namely, while the value actually shrinks because of delay in reaching agreement, each party
ignores discounting (behaves as if there were no discounting). This assumption does not only
simplify our analysis substantially, but also reflects the discussion in Binmore, Swierzbinski,
and Tomlinson (2007). They conduct an experiment of Rubinstein’s bargaining and point out
that “Much preliminary effort was devoted to trying to present the shrinking of the cake....But
subjects then largely ignored the discounting altogether” (p. 10, n. 4). We will study the casewhere parties do care about discounting and generalize our main result in Appendix C.

5This assumption implies that the party who has decision rights and the one who is to make the investment are

different (e.g., a buyer firm merges with a seller firm which possesses a specific asset to produce a required input).
We believe that this assumption is appropriate because “the literature typically reserves the expression ‘make or buy’
to contexts where firms integrate backward” (Lafontaine and Slade, 2007, p. 631, n. 5). If party 2 has decision rights
under integration, integration should always be chosen as the optimal governance structure. See also footnote 14.
6

The assumption that party 1 has the right to send an offer under both governance structures is employed only

to facilitate the comparison between non-integration and integration. Thus, we can instead assume that under nonintegration, the right to send the offer is assigned to each party with equal probability without changing our result.

11

Behavioral Assumptions
This subsection introduces three behavioral assumptions, namely reference-dependent utility,
self-serving bias, and shading (other-regarding preference), and presents evidence that supports
them.7 We emphasize that these assumptions are all crucial to our result: integration can realize
immediate agreement more easily than non-integration. In Appendices A and B, we show that
our result does not hold if any of these assumptions is relaxed. Appendix A shows that noreference-dependence, no self-serving bias, or no shading leads to the result that the choice ofthe governance structure does not matter. Appendix B focuses on the case in which the parties arerisk-averse and have no reference-dependent preference, and shows that such a change leads tothe opposite result: non-integration achieves immediate agreement more easily than integration.
Furthermore, Appendix D shows that our result holds even if we employ another form of otherregarding preference instead of shading: altruism.
Party i’s utility is assumed to be reference-dependent and affected by party j’s shading. Thatis, we combine Köszegi and Rabin’s reference-dependent utility and the utility function of thecontracts-as-reference-points approach. Let ri = (rii , rij ) denote party i’s reference point (rijrepresents i’s belief about party j’s reference point payoff). Party i’s utility when an adaptation
outcome is y = (yi , yj ) is thus given by
Ui (y | ri , rj ) = yi + n(yi | rii ) + θ min{n(yj | rjj ), 0}
wheren(yi | rii ) =

7




 η(yi − rii )if yi ≥ rii ηλ(yi − rii )if yi <rii .

While we understand that it is important to explore whether these three behavioral assumptions can coexist, it isbeyond the scope of this paper, and hence, we leave it for future research.

12

The first term of the utility function denotes party i’s intrinsic payoff, the second term, n(·),
represents his gain-loss utility (η represents weight on gain-loss payoff and λ>1 is sensitivityof loss aversion), and the third term is the loss caused by party j’s shading (θ>0 denotes anexogenous common punishment intensity, namely shading parameter). We assume that θ ≤(1 + ηλ)/ηλ, which means that each party does not have an incentive to accept a payoff whichis smaller than his reference point payoff to avoid his partner’s shading. Since we want to show
clearly the crucial effect of loss aversion on our result, our gain-loss function n(·) rules out
diminishing sensitivity, which is one of the features of gain-loss utility.
Shading can be interpreted as a punishment for unfair treatment. (We can extend our model
to consider altruism, which will be dealt with in Appendix D.) That is, when party i obtains apayoff smaller than his reference point payoff, he experiences a sense of loss, which provokes
anger and drives him to punish his partner (i.e., to engage in shading). Thus, if he obtains apayoff greater than or equal to his reference point payoff (i.e., if he does not incur any loss), hedoes not undertake any shading (θ min{n(yi | rii ), 0} = 0 when yi ≥ rii ).8 As in the contractsas-reference-points approach, we assume that shading behavior does not inflict any cost on those
who shade. Intuitively, shading makes people who are treated unfairly believe that justice has
been done, and hence, brings them private benefit large enough to offset the cost of shading.
Note that we use the term “shading costs” as deadweight loss due to shading.
It is worth noting that the first and second terms (resp. third terms) of the utility function constitute a utility function that corresponds to the utility function of Köszegi and Rabin’s approach8

The literature on contracts as reference points does not deal with gain-loss utility. Hence, shading in the literature

on contracts as reference points depends not on gain-loss utility but on the difference between a party’s payoff and hisreference point payoff (i.e., the shading term in the literature on contracts as reference points is given by θ min(yi −rii , 0)).

13

(resp. the contracts-as-reference-points approach). In other words, we introduce shading intoKöszegi and Rabin’s utility function. We believe that such formalization is plausible because it
is well known that the threat of punishment affects people’s behavior substantially. For example,
the laboratory results of ultimatum games are contrary to the theoretical prediction. That is, while
theory predicts that the proposer gives the receiver the smallest monetary unit possible and thereceiver accepts, subjects playing the role of receiver often reject small but positive offers in ultimatum experiments. Bolton and Zwick (1995) conduct an ultimatum experiment and show thatpunishment for unfair treatment explains more of the deviation from the theoretical prediction in
ultimatum games than the obtrusive effects of experimenter observation.
As in Köszegi and Rabin’s approach, each party’s reference point in our model is his expectation about the relevant outcome. However, while Köszegi and Rabin’s approach assumes
rational expectations, our model assumes that each party expects the relevant outcome in a biased
way. More specifically, the parties correctly infer how their partners set their reference points,
but perceive the game structure self-servingly.
We assume that each party has a self-serving view regarding the sunk investment I. Thatis, while party 1, who does not invest, thinks that party 2, who is supposed to invest, is to incur
his sunk investment, party 2 believes that his sunk cost is to be compensated. In other words,
party 1 (resp. party 2) believes that the parties are to divide a gross value π (resp. a net value
π − I). Party 2’s belief about his sunk cost might seem implausible. However, Macleod (2007,
p.187) suggests that “one can develop a concept of fairness based on the idea that it is optimal
to reward sunk investment, and, hence, ‘fair’ bargains should take this into account.” Formally,
party 1 believes that each party’s outside option is given by
w1 = (w11 , w12 ) = (0, −I),14

where wij denotes party i’s belief about party j’s outside option. Note that each party cannot
obtain anything outside the current relationship. Party 2, on the other hand, is confident that theparties’ outside options are
w2 = (w21 , w22 ) = (0, 0).
This assumption reflects the fact that each party’s role (in this case, whether a party has invested
or not) affects his expectation in a self-serving way even if the same information is shared (Babcock et al., 1995).
The ways in which parties set their reference points are assumed to be different under eachgovernance structure; this stems from the difference in processes of the value division between
non-integration and integration. Under non-integration, as Williamson (1996) notes, “the autonomous stages would need to bargain these [adaptations to unanticipated disturbances] throughto agreement” (p. 17), and hence, each party’s expectation regarding the outcome of the bilateralbargaining serves as his reference point. We thus assume that each party uses the Nash bargaining
solution as his reference point; this is common knowledge.
Under integration, on the other hand, “the unified firm can implement adaptations to unanticipated disturbances by fiat” (Williamson, 1996, p. 17). In other words, the person who has
decision rights (boss) can order any division to her subordinate (he) and he can only decide
whether to accept the order or not. That is, ex post adaptation proceeds something like an ultimatum game, and hence, each party expects that the boss obtains most of the value (i.e., theequilibrium outcome of the ultimatum game is used as his reference point).
From these assumptions, party i’s reference point under governance structure g, which isdenoted by rig , is given as follows: under non-integration,m m
r1m = (r11
, r12 ) =

)
(π π
, −I
2 2

(
m m
r2m = (r21
, r22 ) =15

π−I π−I,22),and under integration,9hhr1h = (r11, r12
) = (π, −I)hhr2h = (r21, r22
) = (π − I, 0) .

Party 1’s (resp. party 2’s) payoff is listed first (resp. second). We assume that each party knows
about self-serving bias. That is, each party knows that his partner has a different reference point(e.g., under non-integration, party 1 knows that party 2’s reference point is r2m ).
Some readers might think that it is inappropriate to assume that while the parties minimize ex
post inefficiencies (i.e., they recognize the presence of self-serving bias) in the stage where theychoose the governance structure, they do not take into account such a bias when they constructtheir reference points. Nevertheless, this assumption is reasonable because even if people learn
about the bias, it does not cause them to modify their expectations. As Babcock and Loewenstein(1997, p. 115) note, “When they learned about the bias, subjects apparently assumed that theother person would succumb to it, but did not think it applied to themselves.”
We then explain what will happen if party 2 rejects party 1’s offer/order. For simplicity, we
assume that after party 2 rejects party 1’s offer/order, each party obtains a continuation payoff.
As mentioned above, since each party is affected by self-serving bias, party 1 believes that partym = π/2 − I, which is her belief about party
2’s continuation payoff cannot be larger than r12

2’s reference point payoff when the trading parties are autonomous. Party 2 is also influenced by
self-serving bias (i.e., before observing party 1’s offer/order, party 2 believes that his continuationm = (π − I)/2), but he can update his belief about his continpayoff cannot be smaller than r22

uation payoff by observing party 1’s offer/order. That is, party 2 infers what party 1 seriously
believes about continuation outcome from her offer/order, and expects that real continuation out9

What is important here is that party 1 is expected to obtain a larger payoff under integration than non-integration

due to her authority. Thus, the assumption that the equilibrium outcome of the ultimatum game serves as reference
points under integration is not crucial to our result. See also Section 4.2.

16

come is to be specified somewhere between r1m and r2m (through a negotiation, for example).
Hence, party 2’s belief about his continuation payoff after observing party 1’s offer/order, P ,satisfies1011
ππ−I− I<P ≤.
2
2
It will turn out that party 1 optimally offers what her reference point specifies, and hence, thisassumption about party 2’s continuation payoff P implies that he has an incentive to reject party
1’s optimal offer regardless of the choice of governance structure.
We assume that each party’s belief about party 2’s continuation payoff does not depend on thegovernance structure chosen at the beginning. Some readers might wonder why this assumption
is appropriate while the parties’ reference points are employer-favored under integration. This
assumption stems from Barnard’s (1938) arguments about authority. Barnard (1938, p. 163)
asserts, “Disobedience of such a communication [directive communication] is a denial of its authority for him. Therefore, under this definition the decision as to whether an order has authority
or not lies with the persons to whom it is addressed and does not reside in ‘persons of authority’or those who issue these orders.” This suggests that a subordinate’s rejection of an order terminates the authority relationship. Hence, after party 1’s order is rejected, the process of the value
division becomes the same under non-integration and integration, which leads to the same belief
about each party’s continuation payoff between the two governance structures.

10

Including P > (π − I)/2 does not change our result.

11This setting does not rule out party 1’s belief update. For example, party 2’s counter offer, which is not modeled,might help her modify her belief about continuation outcome. However, since we focus on whether the first offer is
accepted, such update does not matter.

17

4 Which Governance Structure Achieves Immediate Agreement?
This section explores how the choice of the governance structure affects the timing of the settlement of ex post adaptation (the division of the trade value) and shows that integration realizes
immediate agreement more easily than non-integration despite the possibility of subordinates’
disobedience to their boss’s orders. This result can be intuitively explained by the following two
discussions. First, a subordinate (party 2) believes that his disobedience to an order provokes
severe punishment from his boss (party 1). Second, since the subordinate does not expect a large
payoff from the outset, he is not so interested in payoff improvement from disobedience.
This section proceeds as follows. Subsection 4.1 studies each party’s optimal behavior andexamines when immediate agreement is realized under each governance structure. Subsection
4.2 then compares two governance structures and presents our main result and its intuition.

4.1 Each Party’s Optimal Behavior
This subsection analyzes party 1’s optimal offer/order, which is studied in Subsection 4.1.1, andparty 2’s optimal acceptance/compliance decision, which is examined in Subsection 4.1.2.

4.1.1 Party 1’s Offer/OrderWe first examine party 1’s optimal offer/order and show that she optimally offers/orders what her
reference point specifies. Note that party 1 believes that party 2’s continuation payoff is given bym (i.e., her belief about what he is entitled to obtain as an autonomous party).
r12
m or x <r h is not optimal for party 1
Since θ ≤ (1 + ηλ)/ηλ holds, any offer/order x1 <r111
11
m under non-integration(such an offer only leads to her loss). Hence, we must examine x1 ≥ r11
h under integration. Furthermore, under integration, party 1’s optimal order is equivand x1 ≥ r11
h = π). We thenalent to her reference point because there is no room for her to demand more (r11

18

m +∆
only need to study the optimal offering strategy under non-integration such that x1 = r11(∆ ≥ 0).
m + ∆ under non-integration. If party 2 accepts such an offer,Suppose party 1 offers x1 = r11

party 1’s utility is given by
m
m
m
m
m
U1m (x | r1m , r2m ) =r11
+ ∆ + n(r11+ ∆ | r11
) + θn(r12− ∆ | r22
)
(
)
I
m
=r11
+ ∆ + η∆ − θηλ+∆ .
2m , r m ). If party 2 accepts the offer,
Note that party 1 knows party 2’s reference point r2m = (r2122
m + ∆. Furthermore, since her payoff r m + ∆ is larger than her
party 1 obtains a payoff r1111m ), she enjoys the gain η{(r m + ∆) − r m } = η∆. However, since thereference point payoff (r111111
m + ∆ forces party 2 to obtain r m − ∆, which is smaller than his reference point
offer x1 = r1112m ), party 1 expects him to shade by θηλ{(r m − ∆) − r m } = θηλ{(I/2) + ∆}. Thus,
payoff (r221222
m + ∆ instead of x = r m if the following condition holds:
party 1 offers x1 = r11
1
11

θ≤

1+η
.
ηλ

(1)

If this condition holds and party 2’s acceptance is guaranteed, it is optimal for party 1 to choose
x1 = π, namely, she demands the whole surplus.
However, even if condition (1) holds, since party 2 knows party 1’s reference point r1m , shem will be rejected (and obtain continuation payoff r m ). Given this,expects that an offer x1 >r11
11
m only delays agreement, and hence, party 1 offers x = r m under nonmaking an offer x1 >r11
1
11m.
integration.12 If condition (1) does not hold, it is obviously optimal for party 1 to offer x1 = r11

We thus find that it is optimal for party 1 to offer/order what her reference point specifies. Let
m , r m ) (resp. xh = r h = (r h , r h )) denote party 1’s optimal offer underxm = r1m = (r11
12
1
11 12
12

We assume that when the parties face choices that yield them the same expected payoffs, they prefer the choicethat achieves faster agreement.

19

non-integration (resp. integration).

4.1.2 Party 2’s Acceptance/Compliance Decision
We then study party 2’s acceptance/compliance decision given party 1’s optimal offer xm =
(π/2, π/2 − I) under non-integration and order xh = (π, −I) under integration. Note that party
2’s reference point is r2m = ((π − I)/2, (π − I)/2) under non-integration and r2h = (π − I, 0)
under integration.
We first study party 2’s optimal acceptance strategy under non-integration. If party 2 accepts
the offer xm = (π/2, π/2 − I), his utility is
m

U2 (x

π
| r1m , r2m ) = − I + n
2

(

π
π−I
−I |
2
2

)
+ θn

(π
2

|

π) π
ηλ
I ≡ U2m .
= −I −
2
2
2

Note that party 2 knows party 1’s reference point r1m . If he rejects the offer, on the other hand,
his utility is
(
)
(
π−I
π)
U2 ((π − I − P, P ) | r1m , r2m ) = P + n P |+ θn π − I − P |
2
2
)
(
{
}
π
π−I
′
− P − θηλ− (π − I − P ) ≡ U2m .
= P − ηλ22Party 2 then accepts the offer if′

U2m ≥ U2m

⇔

θ ≥1+

1
≡ θm .
ηλWe next analyze party 2’s compliance strategy under integration. Notice that party 1’s optimal order, which is equal to her reference point, is given by xh = r1h = (π, −I).
If party 2 accepts the order (π, −I), he obtains
U2 (xh | r1h , r2h ) = −I + n (−I | 0) + θn(π | π) = −(1 + ηλ)I ≡ U2h .

20

If party 2 rejects the order, his utility is given by
U2 ((π − I − P, P ) | r1h , r2h ) = P + n(P | 0) + θn(π − I − P | π)′

= (1 + η)P − θηλ {π − (π − I − P )} ≡ U2h .
Thus, party 2 (the subordinate) does not reject the order if the following condition holds:
U2h ≥ U2h

′

⇔

θ≥

(1 + η)P + (1 + ηλ)I≡ θh .
ηλ (P + I)

4.2 Immediate Agreement and Governance Structures
This subsection derives our main result that integration is more likely to realize immediate agreement than non-integration based on the discussions in the previous subsection.
We can determine that θh <θm , which means that non-integration requires severer punishment than integration for party 2’s rejection to realize immediate agreement. There are two
reasons for this. First, party 2’s rejection under integration provokes party 1 to greater anger thanthat under non-integration. Since party 1 offers/orders what her reference point specifies, party
2’s rejection results in party 1’s aggrievement. Furthermore, because party 1’s reference pointh = π) is much larger than that under non-integration (r m = π/2)
payoff under integration (r1111

and party 2’s belief about his continuation payoff P is independent of the choice of the governance structure, party 2 expects that his disobedience leads to party 1’s larger sense of aggrievement under integration (ηλ {π − (π − I − P )} = ηλ(P + I)) than under non-integration(ηλ {π/2 − (π − I − P )} = ηλ(P + I − π/2)). Party 1’s larger aggrievement results in severer
punishment for party 2, which makes him less willing to disobey the order.
Second, while party 2’s disobedience under integration leads to a larger payoff improvement
than under non-integration, the former has less impact on his utility than the latter because of loss
aversion. Under integration, if party 2 rejects party 1’s order, he can enjoy his payoff improve21

ment P − (−I) = P + I. Since party 2’s reference point payoff is 0, his payoff improvement
leads to gain P and reduction in loss I. Party 2’s utility improvement from rejecting the orderis then ηP + ηλI (λ>1). Under non-integration, on the other hand, party 2’s payoff improvement P − (π/2 − I) leads to loss reduction only, and hence he enjoys the utility improvement
ηλ{P − (π/2 − I)}. Intuitively, under integration, party 2 does not expect a large payoff, andhence, his payoff improvement from rejecting the order is “too much” for him and does not leadto a large utility improvement. Such an insignificant utility improvement is not enough to offset
the huge cost of the rejection discussed above (i.e., party 1’s shading), and thus, party 2 is lesseager to disobey the order.
The second reason suggests that each party’s belief that party 1 takes the whole surplus underintegration is not critical to our result. That is, integration realizes immediate agreement moreeasily than non-integration as long as the following conditions hold:
m
m
h
h
r12
< P < r22
and r12< r22< P.

These conditions imply that while the continuation payoff (P ) does not contribute to party 2’sutility improvement substantially under integration, it does so under non-integration.
We then have the following proposition:
P ROPOSITION 1: Integration achieves immediate agreement more easily than non-integration.
That is, non-integration requires severer punishment for party 2’s rejection than integration torealize immediate agreement: θh < θm . Thus, the governance structure that achieves fasteragreement is summarized as follows: Non-Integration or Integration

if θ<θh or θm ≤ θ,
if θh ≤ θ<θm .

Integration

22

This proposition implies that there are three cases. The first case is that both governancestructures fail in reaching immediate agreement (i.e., the case in which θ < θh holds). The secondcase is that only integration realizes immediate agreement (namely, the case in which θh ≤ θ <θm holds). The last case is that both governance structures achieve immediate agreement (that is,the case in which θm ≤ θ holds). The next section analyzes these cases separately, and hence,for convenience, we call these Cases 1, 2, and 3, respectively.
This proposition also suggests that integration can never do worse than non-integration withrespect to the timing of agreement, but the choice of the governance structure does not matter
when the punishment for party 2’s rejection is sufficiently severe or mild (i.e., θ is either sufficiently high or low). This is quite intuitive. If the punishment for rejection is too severe (namely,θ is sufficiently high), such severe punishment makes party 2 unwilling to reject the offer/orderregardless of the choice of the governance structure. If the punishment for rejection is too mild
(θ is sufficiently low), on the other hand, party 2 does not care about such a negligible threat ofpunishment and rejects the offer/order as long as he can improve his payoff by doing so.
This result explains how integration facilitates immediate agreement and presents a formal
justification for the implicit assumption of TCE: integration can avoid costly ex post bargaining.
Hart (1995) observes “If there is less haggling and hold-up behaviour in a merged firm, it isimportant to know why. Transaction cost theory, as it stands, does not provide the answer” (Hart,
1995, p. 28). Our result suggests that integration can avoid costly renegotiation because eachparty’s expectation of the relevant outcome is different between the two governance structuresdue to the difference in the adaptation processes between them.
This section focused on immediate agreement ignoring transaction cost-minimization (i.e.,
minimizing ex post inefficiencies such as the costs of delay, the sense of loss, and shading costs).
We examine these inefficiencies and study firm boundaries in the next section.
23

5 Which Governance Structure Minimizes Transaction Cost?
This section presents a reduced-form analysis of firm boundaries. Specifically, we examine thecosts of delay, the sense of loss, and shading costs under each governance structure and study
which governance structure minimizes these inefficiencies in Cases 1, 2, and 3. We then pointout a trade-off between immediate agreement and the aggregate sense of loss (shading costs).
As mentioned previously, while the value actually shrinks because of bargaining delay, theparties ignore discounting. We thus assume that although the parties behave as if there were no
discounting, the surplus shrinks to δπ − I because of delay in reaching agreement, where δ is asource of the cost of delay and can be interpreted as a discount factor. (We discuss the case inwhich the parties care about discounting in Appendix C.)
Case 1 (θ<θh ): In this case, the parties cannot reach agreement immediately regardless ofthe choice of the governance structure (the cost of delay is the same between the two governancestructures). Hence, we need to examine the sense of loss and shading costs.
As mentioned previously, the continuation outcome after party 2’s rejection is determined
to be somewhere between r1m and r2m , and thus, under non-integration, the negotiation afterm − rm ) =party 1’s offer is rejected can be seen as the division of the aggregate loss ηλ(r1121m − r m ) = (ηλ/2)I between the parties. Hence, the aggregate shading cost (i.e., the sum
ηλ(r2212of each party’s shading) is θ(ηλ/2)I.
m =Under integration, on the other hand, given party 2’s disobedience, he obtains at least r12

π/2 − I, and hence, enjoys gain at least η{(π/2 − I) − 0} = η(π/2 − I). However, party 1
experiences a loss larger than ηλ[π − {(π − I) − (π/2 − I)}] = (ηλ/2)π because she believes
that she can obtain π, but party 2’s disobedience forces her to receive at most (π −I)−(π/2−I).
Thus, under integration, the aggregate loss is equal to or greater than (ηλ/2)π − η(π/2 − I) and24

the aggregate shading cost is at least θ(ηλ/2)π.
This discussion implies that in Case 1 there is no reason to choose integration because integration does not facilitate agreement and incurs a larger sense of loss and shading cost than
non-integration.
Case 2 (θh ≤ θ<θm ): Unlike Case 1, only integration can realize immediate agreement. In
other words, integration can save the cost of delay (1 − δ)π that non-integration cannot avoid.
While integration can avoid the cost of delay, it suffers from a larger loss and shading costthan non-integration. As shown in Case 1, since the offer is rejected, non-integration incurs theaggregate loss (ηλ/2)I and the aggregate shading cost θ(ηλ/2)I. Under integration, on the other
hand, party 1’s order, which is equal to her reference point, is accepted, and hence, only party 2
experiences loss ηλ(0 − (−I)) = ηλI and engages in shading θηλI.
Thus, integration should be chosen if the cost of delay under non-integration is larger than theexcess of the aggregate loss and shading cost under integration over those under non-integration.
That is, the optimal governance structure is summarized as follows: Non-integration
if θ ≥ max [θh , θ2 ]Integration

otherwise,

where
θ2 ≡

2(1 − δ)π− 1.
ηλI

θ2 equalizes the cost of delay with the excess of the aggregate loss and shading cost under integration over those under non-integration.
Case 2 is the case where θh ≤ θ < θm . Hence, if θ2 < θh holds, integration should not bechosen. That is, if integration can be the optimal governance structure, the following condition

25

must hold in addition to the condition above:θ2 ≥ θh⇔1−δ ≥{(1 + η + ηλ)P + (1 + 2ηλ)I}I.
2(P + I)πCase 3 (θm ≤ θ): Case 3 is similar to Case 1 in that the choice of the governance structure
does not affect the timing of agreement (namely, immediate agreement is reached regardless ofthe choice of the governance structure). Hence, we again need to focus on the sense of loss andshading costs, as in Case 1.
Under non-integration, party 2 accepts the offer, and hence, only party 2 experiences loss
ηλ{(π − I)/2 − (π/2 − I)} = (ηλ/2)I and undertakes shading θ(ηλ/2)I. Under integration,on the other hand, as in Case 2, immediate agreement is reached, and thus, only party 2 feels
aggrievement ηλI and shades by θηλI.
The above discussion suggests that non-integration should be chosen in Case 3, as in Case 1.
From Cases 1, 2, and 3, we have the following proposition:
P ROPOSITION 2: Integration should be chosen as the optimal governance structure (thatminimizes the transaction costs) if and only if the following conditions hold:1−δ ≥{(1 + η + ηλ)P + (1 + 2ηλ)I}I2(P + I)π(2)

andθh ≤ θ < θ 2 ,
where
θ2 ≡

2(1 − δ)π− 1.
ηλIThis result implies that integration should be chosen when the punishment for party 2’s rejection (θ) is intermediate and the cost of delay is larger than the sense of loss and shading cost. The
26

explanation as to why integration should be chosen when θ is intermediate has been presented
in the intuition of Proposition 1. Furthermore, even if only integration can realize immediateagreement (i.e., θ is intermediate), it should not be chosen when the cost of delay is insignificant(namely, δ is sufficiently close to 1) and the excess of loss and shading costs under integration
over those under non-integration are quite large (i.e., either η or λ or both are large). This is what
condition (2) means.
The right-hand side of condition (2) (resp. θ2 ) is decreasing (resp. increasing) in π. Thisimplies that larger trade value makes integration more likely to be chosen, which is consistent
with the main assertion of TCE. Furthermore, this observation is also consistent with empiricalstudies on TCE, such as Monteverde and Teece (1982), Masten (1984), and Joskow (1988) (seeLafontaine and Slade (2007) for the review of these studies). These empirical studies provide
support for the hypothesis that the more relationship-specific a trade becomes, the larger quasirent gets, and hence, the more likely it is that integration should be chosen.

A Trade-Off between Immediate Agreement and Shading Costs
The above discussions suggest that integration always suffers larger shading costs and sense ofloss than non-integration. This stems from the fact that the level of divergence between two
parties’ reference points under integration is larger than under non-integration. That is, whilem and r m is I/2, the difference between r h and r h is I. This can be
the divergence between r12
22
12
22

explained by the fact that under integration, party 2 sets his reference point without internalizing
investment cost I.
Under either governance structure, party 2 believes that his investment cost I is to be compensated. Nevertheless, under non-integration, party 2 somewhat internalizes the investment costwhen he sets his reference point because he obtains a positive share of the surplus π − I from27

ex post bargaining. Under integration, on the other hand, party 2 expects that he cannot obtainh = 0), and hence, there is no room for him to internalize theany portion of the surplus (i.e., r22

investment cost I.
This implies that there is a trade-off between immediate agreement and the aggregate sense ofloss. That is, the belief that party 1 (boss) takes the entire surplus under integration makes party
2 less willing to reject her order than under non-integration (see Section 4), but also makes him
set his reference point without internalizing the investment cost, which leads to larger aggregate
loss and shading costs than under non-integration.13 14

6 Conclusion
This paper examined the question of why authority (integration) helps ex post adaptations tobe settled immediately. We showed that, despite the possibility of subordinates’ disobedienceto their boss’s orders, integration can realize immediate settlement of the adaptation because
each party’s reference point under integration is employer-favored due to the ex post adaptation
process under integration. This employer-favored reference point makes a subordinate less eager
to reject his boss’s order for the following two reasons. First, it is very costly for the subordinate
to reject the order from his boss because disobedience to the order results in the boss’s hugeamount of anger and severe punishment. Second, it is not so rewarding for the subordinate to13

Even if party 2 obtains some portion of the surplus under integration, this trade-off continues to emerge as longmmhh
as the following conditions hold: r12< P < r22
and r12
< r22
< P.
14

As mentioned in footnote 5, if party 2 becomes the boss under integration, integration dominates non-integration.
′′

This is because in such a case, both parties share the same reference point under integration: r1h = r2h = (0, π−I) ≡′rh . Since the same reference point is shared between the parties, party 1, who is now the subordinate, accepts party′

2’s order, which is equal to rh , without incurring any sense of loss. Hence, integration completely avoids ex post
inefficiencies (delay in reaching agreement, sense of loss, and shading costs).

28

reject the order because he does not expect a large adaptation payoff from the outset.
We further showed that integration incurs larger aggregate loss and shading cost than nonintegration. This follows because, under integration, the expectation that party 2 cannot obtainany portion of the surplus makes him set his reference point without internalizing the investment
cost. These discussions suggest that the employer-favored reference points create a trade-off
between immediate agreement and shading costs.
In conclusion, we make a brief comment on some extensions: asymmetric shading parameters, endogenous reference points, and the limit of firm scope. First, we discuss the case in which
the parties have different shading parameters. While our model assumes that the parties share thesame shading parameter θ, asymmetric shading does not affect our result because party 2’s shading does not matter. Hence, any change in either party’s shading parameter does not substantiallyaffect our analysis and results.
We next discuss endogenous reference points. Our model takes each party’s reference point
as exogenous. Nevertheless, we can extend our model to deal with endogenous reference points
by employing the assumption of imperfect recall, which can be found in Bénabou and Tirole(2004). For example, suppose party 1 is completely rational, but party 2 forgets that he canbe biased and sets his reference point self-servingly with positive probability. Since party 1 isrational, she takes party 2’s bias into account when she sets her reference point. In such a case,as in Köszegi and Rabin’s approach, party 1’s reference point is given by her probabilistic belief
concerning the relevant outcome.
Finally, we can extend our model to analyze the limit of firm scope. Suppose party 1 facessome other transactions similar to the trade in which parties 1 and 2 engage and that θ is decreasing in the number of transactions she conducts: θ′ (n) ≤ 0, where n represents the number oftransactions she handles. The intuition of the latter assumption is that the more transactions party29

1 conducts, the smaller effort and the less time she can provide to each transaction (i.e., the harder
it is for her to punish those who disobey her orders). Under these assumptions, an integrated firm
can become larger as long as θh ≤ θ(n) and condition (2) hold (see Proposition 2). That is,party 1 can acquire at most n∗ trading partners where n∗ satisfies θ(n∗ + 1) < θh ≤ θ(n∗ ). This
discussion is consistent with diminishing returns to management (e.g., Coase, 1937).

Appendix A: Relaxing Three Behavioral Assumptions
This appendix shows that three behavioral assumptions (reference-dependent utility, self-serving
bias, and shading) are all crucial to our result: integration realizes immediate agreement moreeasily than non-integration. Sections A.1, A.2, and A.3 examine the no-reference-dependence
case, the no-self-serving bias case, and the no-shading case, respectively. All these cases yield
the same result: the choice of the governance structure does not affect the timing of agreement.

A.1 No Reference-Dependence
We first explore the no reference-dependence case. Suppose the adaptation outcome is y =(yi , yj ). In the case where there is no reference-dependence, the utility of party i who has areference point ri is given by
Ui (y | ri , rj ) = yi + θ min(yj − rjj , 0).
Since there is no reference-dependence, each party’s utility function does not include a gain-loss
term and each party’s shading depends on the difference between his payoff and his reference
point payoff (namely, the shading term does not include η, which denotes weight on gain-loss
payoff, and λ, which represents the sensitivity of loss aversion). In other words, the utility
function above is similar to that of contracts as reference points. Since parameters η and λ are30not used, we assume that θ ≤ 1, which means that each party does not have an incentive to giveup any payoff to avoid his partner’s shading and corresponds to the assumption θ ≤ (1 + ηλ)/ηλin the main model.
Note that the optimal offer/order of party 1 does not change. We thus need to examine
party 2’s optimal acceptance/compliance decision only. Under non-integration, while party 2’s
acceptance payoff is given by
U2 (xm | r1m , r2m ) =ππm− I − θ · 0 = − I ≡ UN
RD ,
2
2

his rejection payoff is
U2 ((π −I −P, P ) | r1m , r2m ) = P −θ

}
{
(π
)}
m′
− (π − I − P ) = P −θ P −
−I
≡ UN
RD .
2
2

{π

Note that party 1 optimally offers (π/2, π/2 − I), party 2’s reference point is ((π − I)/2, (π −′mmI)/2), and party 2’s belief about his continuation payoff is P . Comparing UN
RD and UN RD

implies that party 2 does not reject the offer if θ ≥ 1.
Under integration, on the other hand, if party 2 accepts the order, he obtainsh
U2 (xh | r1h , r2h ) = −I − θ · 0 = −I ≡ UN
RD .

Note that party 1’s optimal order is (π, −I) and party 2’s reference point is (π − I, 0). If party 2
rejects the order, his utility is given by′hU2 ((π − I − P, P ) | r1h , r2h ) = P − θ{π − (π − I − P )} = P − θ(P + I) ≡ UNRD .

We find that when θ ≥ 1, party 2 does not reject the order under integration.
This discussion implies that if there is no reference dependence, the choice of the governancestructure does not matter (i.e., does not affect party 2’s acceptance/compliance decision). In
the no-reference-dependence case, the marginal benefit from payoff improvement is 1 and its
31

marginal cost is θ, and hence, party 2 rejects the offer/order as long as the former is larger
than the latter: θ < 1. As mentioned in Section 4, one of the reasons why integration achieves
immediate agreement more easily than non-integration is that while the utility improvement fromrejection under non-integration consists of loss reduction only, that under integration includes not
only loss reduction but also gain. No reference dependence (no loss aversion) makes both gain
and loss equally important for both parties and eliminates the difference between the effects ofgains and losses on each party’s utility.

A.2 No Self-Serving Bias
We next study what will happen if there is no self-serving bias. As in the previous subsection,
party 1’s optimal offer/order does not change, and thus, we focus on party 2’s optimal behavior.
Suppose both parties share the same view regarding each party’s outside option: w1′ = w2′ =(0, −I).15 Both parties then share the same reference point. That is, under non-integration, theirreference points are
r1m = r2m =

)
(π π
m
, − I ≡ rN
SSB ,
2 2

and, under integration,hr1h = r2h = (π, −I) ≡ rN
SSB .

Party 2’s acceptance payoff under non-integration is thusm
U2 (xm | rN
SSB ) =(π)
(π π ) π
π
π
m
−I +n
− I | − I + θn|
= − I ≡ UN
SSB .
2
2
2
2 2
2

Since party 2 has the same reference point as party 1, accepting the offer leads to no aggrieve-

15

Assuming w1′ = w2′ = (0, 0) does not affect the result.

32

ment. If he rejects the offer, he obtains
(
)
(
π
π)
m
−
I
+
θn
π
−
I
−
P
|
U2 ((π − I − P, P ) | rN
)
=
P
+
n
P
|
SSB
2
2
{
(π
)}
m′
= P + η(1 − θλ) P −
−I
≡ UN
SSB .
2
′

m
m
The comparison between UN
SSB and UN SSB suggests that party 2 does not reject the offer

if θ ≥ (1 + η)/ηλ holds. Similarly, under integration, if party 2 accepts the order, his utility ishh
U2 (xh | rN
SSB ) = −I + n(−I | −I) + θn(π | π) = −I ≡ UN SSB .

If party 2 rejects the order, he obtains:′hh
U2 ((π−I−P, P ) | rN
SSB ) = P +n(P | −I)+θn(π−I−P | π) = P +η(1−θλ)(P +I) ≡ UN SSB .

Hence, we find that party 2 does not reject the order if θ ≥ (1 + η)/ηλ holds. These discussions
imply that the choice of the governance structure does not affect the timing of the agreement
when there is no self-serving bias.
This result is explained as follows. Without self-serving bias, both parties share the same ref¯ g
¯
¯ g
¯
¯
¯
¯
erence point, and hence, ¯rN
SSB1 − (π − I − P ) and rN SSB2 − P become the same, wheregrN
SSBi represents party i’s reference point payoff under governance structure g. Party 2 thus

rejects the offer/order if the marginal benefit from rejecting the offer/order (i.e., 1 + η) is larger
than or equal to the marginal cost from doing so (namely, θηλ).

A.3 No Shading
Lastly, we examine the case in which there is no shading. This case corresponds to the one inwhich there is no punishment for rejecting an offer/order and party i’s utility function is characterized as follows:
Ui (y | ri ) = yi + n(yi | rii ),33

wheren(yi | rii ) = η(yi − rii )if yi ≥ rii ηλ(yi − rii )if yi <rii .

Since there is no shading, party i’s utility does not depend on his partner’s reference point. This
formulation corresponds to the simple version of Köszegi and Rabin’s reference-dependent utility
function.
Since there is no punishment for party 2’s rejection of an offer/order, he rejects any offer/order that yields him a smaller payoff than his continuation payoff. Given that party 1 believes that party 2’s continuation payoff is given by r1m (her reference point when the parties
are autonomous), she optimally offers xN S = (π/2, π/2 − I) under both non-integration andintegration.
Under non-integration, if party 2 accepts the offer, he receivesπU2 (xN S | r2m ) = − I + n

(

2

π
π−I
−I |
2
2

)
=

π
ηλ
m
−I −
I ≡ UNS,
2
2and if he rejects it, his utility is(
U2 ((π − I − P, P ) | r2m ) = P + n

π−I
P |
2

)

(
= P − ηλ

π−I
−P
2

)

′

m
≡ UN
S.

Note that there is no shading even if the offer that corresponds to party 1’s reference point is′

m is smaller than U m , which means that party 2
rejected. By assumption P > π/2 − I, UN
S
NS

always rejects the offer.
Under integration, on the other hand, if party 2 accepts the order, his utility is given by16
U2 (xN S | r2h ) =
16

(π
)
(π
)
π
h
−I +n
− I | 0 = (1 + η)
− I ≡ UNS.
2
2
2

From the discussion of the optimal ordering strategy, some readers might suspect that without shading, eachparty’s reference point under integration becomes the same as that under non-integration. Nevertheless, such a change
does not affect our discussion.

34

If he rejects the order, he enjoys′hU2 ((π − I − P, P ) | r2h ) = P + n(P | 0) = (1 + η)P ≡ UNS.

′

h < U h always holds. That is, under integration, party 2 rejects the
Since P > π/2 − I, UNS
NSorder for certain.
The above discussion implies that the governance structure does not matter if there is no
shading. This is quite intuitive: party 2’s rejection cannot be prevented without any punishment
for it.

Appendix B: Risk-Averse Parties
We here examine a different type of no reference dependence. More specifically, in this appendix,
we assume that the parties are risk-averse instead of assuming that they have reference-dependent
preferences and are risk-neutral.
Suppose that each party i has concave utility function m(x), which is twice differentiable(m′ (·) > 0 and m′′ (·) < 0), and his overall utility is
Ui (x = (xi , xj ) | ri , rj ) = m(xi ) + θ min{m(xj ) − m(rjj ), 0}.
This utility function is similar to that of contracts as reference points. This change in the assumption does not affect party 1’s optimal offer, and thus, we need to analyze party 2’s behavior
only.
Under non-integration, party 2’s acceptance utility ism
U2 (xm = r1m | r1m , r2m ) = m(r12).

m , r m ), andNote that party 1’s optimal offer is equivalent to her reference point, xm = r1m = (r111235

m , r m ). If party 2 rejects the offer, his utility isparty 2 has a reference point r2m = (r2122m
U2 ((π − I − P, P ) | r1m , r2m ) = m(P ) − θ{m(r11) − m(π − I − P )}.

Party 2 does not reject the offer under non-integration if his acceptance utility is larger than orequal to his belief about the continuation utility:
m
m
m(r12
) ≥ m(P ) − θ{m(r11) − m(π − I − P )}

⇔

θ ≥

m)
m(P ) − m(r12
′
≡ θm
.
m
m(r11 ) − m(π − I − P )Under integration, party 2’s compliance utility ishU2 (xh = r1h | r1h , r2h ) = m(r12),

and his rejection utility ishU2 ((π − I − P, P ) | r1h , r2h ) = m(P ) − θ{m(r11) − m(π − I − P )}.

Hence, party 2 does not reject the order if the following condition holds:
h
h
m(r12
) ≥ m(P ) − θ{m(r11) − m(π − I − P )}

⇔

θ ≥

h )
m(P ) − m(r12≡ θh′ .
h ) − m(π − I − P )m(r11We thus determine
′
θm
< θh′

because m(·) is concave and the following relationships hold:
h
m
m
h
r12
< r12
< P ≤ π − I − P < r11< r11.

This discussion implies that non-integration achieves immediate agreement more easily than integration, which means that our main result cannot be obtained by assuming risk-averse parties.
36     
 

m(⋅)

 
 

 

r12h

r12m

P π −I − P

r11m

r11h



   Figure A: Each Party’s Utility Improvement/Decrease from Party 2’s Rejection(a) (resp. (b)) represents party 1’s utility decrease (resp. party 2’s utility improvement) underintegration. (c) (resp. (d)) denotes 1’s utility decrease (resp. 2’s utility improvement) under
non-integration.

In the model in Section 4, party 1’s punishment for rejecting the order under integrationis severer than her shading under non-integration because both parties’ reference points are
employer-favored under integration. In the risk-averse case, however, the same factor leads to the
opposite result. This is illustrated in Figure A. Since the parties have concave utility functions,the same amount of payoff increase/decrease affects their utility differently. Under integration,
the amount of party 2’s payoff improvement from rejecting the order (P − (−I) = P + I) is
the same as that of party 1’s payoff decrease (π − (π − I − P ) = P + I). Nevertheless, theamount of party 2’s utility improvement from his rejection, which corresponds to (b) in Figure
A, is far larger than that of party 1’s utility decrease from it, which is denoted by (a) in Figure
A. Under non-integration, on the other hand, party 1’s utility decrease from party 2’s rejection(π/2−(π −I −P ) = P +I −π/2), which is denoted by (c) in Figure A, is not so small comparedwith party 2’s utility improvement from it (P − (π/2 − I) = P + I − π/2), which corresponds to(d) in Figure A. Hence, integrated firms require much severer punishment for party 2’s rejection37

to offset party 2’s benefit from it than autonomous trading parties do.

Appendix C: Parties Who Care about Discounting
This section studies the case in which the parties care about discounting and checks the robustnessof our result. To achieve this, we change the setting in the following way (the rest of the settings
are the same as in the main model). First, the parties do care about discounting. That is, theyshare a common discount factor δ and their payoffs are discounted if they cannot reach agreement
immediately; this is common knowledge.
Second, we assume that the following condition holds:17δπδπ − I− I<δP ≤.
2
2
The first inequality implies that party 2 has an incentive to reject party 1’s offer/order that corresponds to party 1’s reference point (each party’s reference point will be specified below). The
second inequality means that party 2 does not expect more than what he thinks he is entitled to obtain (namely, his reference point payoff). This condition also implies that I/(π − 2P ) ≤ δ(≤ 1).
This appendix proceeds as follows. Section C.1 specifies each party’s reference point andparty 1’s optimal offer/order under each governance structure. Section C.2 studies party 2’s
optimal acceptance/compliance decision under each governance structure. Section C.3 presents
the result, which is a modified version of Proposition 1.

17

We continue to assume that the following condition holds:π
π−I− I<P ≤.
2
2

38

C.1 Reference Points and Party 1’s Optimal Offer/OrderWe first specify each party’s reference point and party 1’s optimal offer/order under each governance structure. It is common knowledge that the parties care about discounting, and hence, theirreference points are different from those in the main model. Since both parties expect that party
1 sends the offer which makes party 2 indifferent about whether he accepts it and party 2 accepts
such an offer, party 1’s reference point under non-integration is
(

(
π−I −

m∗ m∗
r1m∗ = (r11
, r12 ) =

)
)
δπ
δπ
−I ,
−I .
2
2

Note that the expected bargaining outcome is given by the Nash bargaining solution and party
1 believes that party 2 is to incur his sunk investment (i.e., she believes that the parties’ outside
options are w1 = (w11 , w12 ) = (0, −I)).
As mentioned in the main model, it is optimal for party 1 to offer what her reference point
specifies. Thus, her optimal offer is given by
(
m∗

x

m∗
= (xm∗
1 , x2 ) =

(
π−I −

)
)
δπ
δπ
−I ,
− I = r1m∗ .
2
2h∗ , r h∗ ) = (π, −I),
Under integration, on the other hand, party 1’s reference point is r1h∗ = (r1112which is the same as in the main model, because there is no room for her to demand more. The
optimal order, which is equal to party 1’s reference point, is thus given byh∗h∗xh∗ = (xh∗
1 , x2 ) = (π, −I) = r1 .

We then determine party 2’s reference point. Party 2 infers that party 1’s offer makes him
indifferent about whether he accepts it. However, he believes that the parties’ outside options are
w2 = (w21 , w22 ) = (0, 0). Thus, his reference point under non-integration is given by(m∗ m∗
r2m∗ = (r21
, r22 ) =

(
π−I −
39

δπ − I2)δπ − I,
2).

Party 2’s reference point under integration, on the other hand, ish∗ h∗r2h∗ = (r21
, r22 ) = (π − I, 0).

C.2 Party 2’s Acceptance/Compliance
We first study party 2’s optimal acceptance decision under non-integration given party 1’s optimal
offer xm∗ and the parties’ reference points, r1m∗ and r2m∗ . If he accepts the offer, he obtains payoffδπ/2 − I, which leads to his sense of loss ηλ{(δπ − I)/2 − (δπ/2 − I)} = ηλI/2, and incurs
no shading from party 1. Party 2’s utility is thus given by
U2 (xm∗ | r1m∗ , r2m∗ ) =

δπ
−I +n
2

(

δπ
δπ − I
−I |
2
2

)
+θ·0=

δπ
ηλ
m
−I −
I ≡ UDis.
2
2

If he rejects the offer, on the other hand, his utility is()()δπ − Iδπ
U2 ((δπ − I − δP, δP ) | r1m∗ , r2m∗ ) = δP + n δP |+ θn δπ − I − δP | π −
2
2
)
{(
)
}
(
3δ
δπ − Im′− δP − θηλ1−
π + I + δP ≡ UDis.
= δP − ηλ22Note that party 2’s belief about the continuation outcome is discounted since the parties careabout discounting. We thus find that party 2 does not reject the offer if the following condition
holds:m′m
UDis≥ UDis⇔{()}(1 + ηλ) δP − 2δ π − I∗{()} ≡ θmθ≥.
ηλ δP + 1 − 3δπ+I2

We next examine party 2’s compliance decision under integration. If he accepts the optimalorder xh∗ , his utility ishU2 (xh∗ | r1h∗ , r2h∗ ) = −I + n(−I | 0) + θ · 0 = −(1 + ηλ)I ≡ UDis.

If he rejects it, on the other hand,U2 ((δπ − I − δP, δP ) | r1h∗ , r2h∗ ) = δP + n (δP | 0) + θn (δπ − I − δP | π)′h
= (1 + η)δP − θηλ{π − (δπ − I − δP )} ≡ UDis.

40

Party 2 thus does not reject the order if
′

h
h
UDis
≥ UDis⇔θ≥(1 + η)δP + (1 + ηλ)I≡ θh∗ .
ηλ{π − (δπ − I − δP )}C.3 Immediate Agreement and Governance Structures∗ and θ ∗ leads to the following result:Comparing θmh
1+ηλ 2
π −η(λ−1)P (π+I)
∗ ≥ θ∗
2
 θm
≡ δ∗
if
δ
≥
1+ηλ
h
2 −η(λ−1)P 3 π−P
π
(2
)
2


 θ∗ < θ∗otherwise.
mh∗ ≥ θ ∗ does exist. We thus have the following proposition:
Since δ ∗ <1 holds, the case in which θmh

P ROPOSITION 3: When the parties care about discounting, integration achieves immediate∗ ) if and only if the following condition
agreement more easily than non-integration (θh∗ ≤ θmholds:]I,δ ≥ max δ ,π − 2P[∗

where
1+ηλ 2π − η(λ − 1)P (π + I)2δ ∗ ≡ 1+ηλ2

π 2 − η(λ − 1)P(3

2π − P).

This implies that when the cost of delay is not so large, integration achieves immediate agreement more easily than non-integration. When the parties care about discounting, party 2 faces
two costs from rejecting the offer/order: punishment for rejection (party 1’s shading) and the costof delay. As discussed in the main model, the punishment under integration is much severer thanthat under non-integration. This implies that the cost of delay has an insignificant effect on party
2’s utility compared to party 1’s shading under integration. Hence, if integration achieves fasteragreement than non-integration, the cost of delay must be small enough to have little effect on
the parties’ utility under either governance structure (i.e., δ is close enough to 1).
41Appendix D: Altruism
In this appendix, we examine the case in which the parties are altruistic. That is, each party i
considers party j’s gain and loss. (In the main model, party i does not care j’s gain.) In such acase, each party i’s utility is given by
Ui (y | ri , rj ) = yi + nii (yi | rii ) + θnij (yj | rjj )wherenij (yj | rjj ) = η(yj − rjj )if yj ≥ rjj ηλij (yj − rjj )if yj <rjj .

λij (>1) represents party i’s sensitivity to j’s loss and we assume that λii >λij and λ11 = λ22 forsimplicity. We further assume that θ ≤ (1 + ηλii )/ηλij , which corresponds to the assumptionθ ≤ (1 + ηλ)/ηλ in the main model. In this setting, θ can be considered each party’s level ofaltruism.
We can easily check that such a change in each party’s utility function does not change party
1’s optimal offer/order (i.e., she offers what her reference point specifies). Hence, we only need to
examine party 2’s acceptance/compliance decision given that party 1 offers xm = (π/2, π/2−I)
under non-integration and order xh = (π, −I) under integration.
Under non-integration, if party 2 accepts xm , then his utility is given by
m

U2 (x

π
| r1m , r2m ) = − I + n
2

(

π
π−I
−I |
2
2

)
+ θn

(π
2

|

π) π
ηλ22
= −I −
I.
2
2
2

Note that party 2’s reference point is r2m = {(π − I)/2, (π − I)/2}. If he rejects the offer, on theother hand, his utility is
)
(
(
π)
π−I
+ θn π − I − P |U2 ((π − I − P, P ) | r1m , r2m ) = P + n P |
2
2
(
)
{
}
π−I
π
= P − ηλ22
− P − θηλ21− (π − I − P ) .
2242Thus, we can determine that party 2 accepts the offer if the following condition holds:θ≥

1 + ηλ22
A
≡ θm
.
ηλ21

A corresponds to θ in our main model.
Note that θmm

We then analyze party 2’s compliance strategy under integration given that party 1’s order is
xh = r1h = (π, −I) and party 2’s reference point is r2h = (π − I, 0). If he accepts the order, hisutility is
U2 (xh | r1h , r2h ) = −I + n(−I | 0) + θn(π | π) = −(1 + ηλ22 )I.
If he rejects the order, on the other hand, his utility is given by
U2 ((π−I−P, P ) | r1h , r2h ) = P +n(P | 0)+θn(π−I−P | π) = (1+η)P −θηλ21 {π−(π−I−P )}.
Hence, party 2 accepts the order ifθ≥(1 + η)P + (1 + ηλ22 )I≡ θhA .
ηλ21 (P + I)

θhA corresponds to θh in our main model.
A >θ A . This implies that immediate settlement under nonWe can easily determine that θmhintegration requires party 2 to be more altruistic than immediate agreement under integration.
We thus find that our main message (i.e., integration can achieve immediate agreement moreeasily than non-integration) continues to emerge under the altruism case.

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