GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 348

Hierarchies Versus Committees: Communication
and Information Acquisition in Organizations

Junichiro Ishida

September 2014

GCOE Secretariat
Graduate School of Economics
OSAKA UNIVERSITY
1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Hierarchies Versus Committees: Communication
and Information Acquisition in Organizations∗
Junichiro Ishida†
ISER, Osaka University
September 22, 2014

Abstract
In most firms, if not all, workers are divided asymmetrically in terms of authority
and responsibility. In this paper, we view the asymmetric allocations of authority andresponsibility as essential features of hierarchy and examine why hierarchies often prevailin organizations from that perspective. A key departure is that we consider a case where
the authority relationship is defined only by the allocation of responsibility via contingent
contracts. Within this framework, we show that the contractual arrangement which
allocates responsibility asymmetrically often emerges as the optimal organizational form,
which gives rise to the chain of command pertaining to hierarchical organizations.

JEL Classification Codes: D03, D99.
Key Words: Authority; Responsibility; Contract; Cheap-talk communication; Informationacquisition.
∗
Correspondence to: Junichiro Ishida, Institute of Social and Economic Research, Osaka University, 6-1
Mihogaoka, Ibaraki, Osaka 567-0047, Japan. e-mail address: jishida@iser.osaka-u.ac.jp.
†
I thank an anonymous referee for many careful comments which substantially improve the exposition of
the manuscript. All remaining errors are my own. The financial support from Grant-in-Aid for Scientific
Research (C), JSPS, is gratefully acknowledged.

1Introduction

It is very rare, if ever, to find a firm where all of its workers are treated just equally. In mostfirm organizations, some workers, typically those higher up in the hierarchy, are conferredmore authority and hence carry an asymmetrically large weight in the decision-making process
than others. At the same time, those with more authority are also given more stringent
incentives and moreover held responsible for a wider range of outcomes, such as the firm’s
or their respective division’s overall performances. While the degree of centralization orworker empowerment differs across firms as well as over time, workers are by and large
divided asymmetrically in terms of both authority and responsibility (i.e., accountability foroutcomes). In this paper, we view these asymmetric allocations of authority and responsibility
as essential features of hierarchical organizations and examine why hierarchies often prevailin organizations from that perspective.
At a glance, the asymmetric allocation of responsibility seems to be a straightforward
consequence of that of authority because if a worker is entitled to make a decision, he shouldbe held accountable for any consequences brought by that decision. In this line of reasoning,
it is the allocation of authority which subsequently determines the allocation of responsibility,
so that the causation runs from authority to responsibility. What is implicit in this argument
is therefore that the principal can allocate (formal) authority at her own discretion. While
this presumption may be reasonable in some contexts, one can also think of a case where theprincipal cannot explicitly contract on decision rights. In this paper, as a key departure fromthe existing literature, we consider an environment where the principal has no direct control
over the allocation of authority, and the authority relationship is instead determined by theallocation of responsibility via contingent contracts.1 Since the presence of hierarchy is quite
ubiquitous in firm organizations, it seems worthwhile to explore the nature of hierarchy inan environment where, due to some technological or informational constraints, the principal
has no direct control over the allocation of authority.
To this end, we consider an organization which consists of a principal (the contract designer) and two agents. Each agent privately chooses a task to implement, which stochastically leads to some observable output. The productivity of each task is not known ex ante,
1

In the literature, it is often assumed that the principal allocates (formal) authority at her own discretion,e.g., by granting or restricting access to critical resources that are indispensable for production (Aghion andTirole, 1997; Rajan and Zingales, 2001; Dessein, 2002; Hart and Moore, 2005).

1and each agent must hence acquire information about which task is the more productive.
This information-acquisition stage involves two rounds. In the first round, each agent privately exerts effort to acquire information about the productivity of each task (or produce
an “idea”). This is followed by the second round where each agent sends a costless message
to share this information, if any, with the other agent. With no feasible way to allocate authority, however, no party can force an agent to take actions that are not in his best interest,and every decision to be made must be incentive-compatible under the agreed contracts. The
chain of command (i.e., who orders and who obeys) then arises endogenously as an optimal
response to the given structure of incentives.
The current framework admits several organizational forms, depending on how the structure of incentives is shaped by the set of contingent contracts. We say that a hierarchy emerges
when one agent (the superior) orders the other agent (the subordinate) what to do, and thesubordinate has an incentive to follow the order. Under this contractual arrangement, theflow of information is restricted to be unilateral, always from the superior to the subordinate,
and the superior is given a disproportionately large weight in the decision-making process
ex ante. As an alternative to this arrangement, the incentive contracts may be designed toplace no restriction over the flow of information. In this case, information flows from the informed party to the uninformed in an unspecified direction, and each agent is given an equal
weight ex ante as in a committee. With the addition of the benchmark case, we consider andcompare the following three organizational forms summarized as below.2
1. Independent Production (the benchmark): Each agent independently exerts effort toacquire the information without ever communicating with each other. No interactions
take place between the agents.
2. Committee (the symmetric contracts): Both of the agents are induced to exert effort
and then communicate with each other. Communication is bilateral where each agent
carries the same weight ex ante in the decision-making process.
3. Hierarchy (the asymmetric contracts): Only one of the agents, the superior, is induced
to exert effort while the other, the subordinate, is not. Communication is unilateral
where the superior orders the subordinate what to do.
2

While there are more feasible contractual arrangements in this setup, we can show that it suffices toconsider those three cases. See Appendix B for more detail.

2

We show that the optimal contractual arrangement is often asymmetric, where only one
agent is motivated to acquire the information, and Hierarchy thus emerges as the optimalorganization form under a wide range of circumstances.3 To derive this result, we focus on
the tradeoff between costly information acquisition and costless (cheap-talk) communication,
which stems from the fact that an incentive contract in this setup is subject to two constraints,
one for information acquisition (whether to exert effort to acquire information) and the otherfor truthful communication (whether to reveal truthfully the acquired information). The
problem is that these two constraints are naturally at odds with each other, because theconstraint for information acquisition calls for competition between the agents while that forcommunication calls for cooperation between them. The optimal contract must balance theseconcerns, which in turn determines how the information is acquired and disseminated in theorganization.
To illustrate the tradeoff, we start with the benchmark case of Independent Production
which makes no use of communication. The optimal contract under this arrangement generically takes the form of relative performance evaluation, where the agents are compensatedbased on the difference in the outputs. This is the most efficient way to provide incentives
if the principal’s only concern is to motivate them to exert effort. Independent Production
has a clear weakness, however, because the constraint for truthful communication cannot besatisfied under relative performance evaluation. With no information flowing between theagents, therefore, it may leave some of the existing knowledge unutilized: in this sense, thelevel of competition between the agents is often excessive under Independent Production,
which impedes cooperation that is equally critical for efficient production. Given that information is free to disseminate once it is acquired, it is clearly ex post optimal to share any
useful information between the agents. Since it is not known ex ante who actually ends up
with a good idea, this can be done most effectively by removing any restrictions on the flowof information.
Given this result, we now turn to Committee where both of the agents are induced toexert effort and no restriction whatsoever is placed on the extent of communication (bilateralcommunication). Under this arrangement, each agent carries the same weight in the decision3
The contrast between hierarchies and committees is also depicted in Sah and Stiglitz (1988) with a totallydifferent approach. They compare three different decision-making protocols – committees, hierarchies andpolyarchies – with its particular emphasis on the tradeoff between the type I and type II errors.

3

making process ex ante, and information flows from a party with an idea to a party without
it. A virtue of Committee is then evident: it can make the best use of the existing knowledge
within the organization by fully exploiting the benefit of costless communication. As it turns
out, though, this ex post optimal arrangement is not necessarily ex ante optimal, as it raises
the agency cost of inducing costly effort. The analysis identifies three channels through whichbilateral communication entails ex ante inefficiency, as summarized below.
Incentive provision: To facilitate communication, the agents must be held jointly accountable, which is a less efficient way to provide incentives.
Freeriding: When communication is informative, there arises an incentive to freeride on theother agent’s effort.
Task coordination: When communication is restricted, the agents can increase the chanceof coordinating their task choices only by acquiring the information. This effect is absent
when the agents can always coordinate via communication.
Due to these problems, Committee is often less profitable, especially when the agency
problem regarding information acquisition is sufficiently severe. This does not necessarily
mean, though, that we must give up the benefit of communication entirely; it rather meansthat going all the way from no communication to bilateral communication is often excessive.
We argue that there is a way to exploit the benefit of communication while keeping its cost
minimum. This can be done by the asymmetric allocation of responsibility where one agent,
the superior, is offered high-powered (team) incentives while the other, the subordinate, isoffered low-powered (individual) incentives. This asymmetric contract yields two beneficial
effects. First, Hierarchy reduces the total agency cost as it only needs to motivate one agent.
In an environment where information acquisition is costly while communication is free, thisis a thrifty way to acquire information as a group. Second, the asymmetric and concentrated
allocation of responsibility eliminates the freeriding incentive as the superior can no longer relyon the subordinate’s information. We show that this asymmetric contractual arrangement is
optimal for a wide range of circumstances, as it achieves the right balance of competition andcooperation. Under the asymmetric allocation of responsibility, the flow of information isrestricted to be unilateral, always from the superior to the subordinate, which endogenously
gives rise to the chain of command that is inherent in hierarchical organizations.
The results obtained in this paper suggest that whether Hierarchy or Committee is optimal

4

depends crucially on the severity of the agency problem in the information-acquisition stage.
Hierarchy, which allocates responsibility asymmetrically, outperforms Committee when costly
information acquisition is the main concern to be dealt with. We argue that this corresponds
to typical firm organizations where a relatively fixed group of members must confront withand find solutions for new problems on the day-to-day basis. In such a case, Hierarchy isoften optimal, lending support for the view that most firms are hierarchical. This stands
in sharp contrast to committees which typically consist of experts who are well informed in
the first place. In committees, members are in many cases selected for specific problems andinformation acquisition is hence rarely an issue. In such a case, there is no reason to treat
members asymmetrically, and Committee with the more symmetric allocation of authority
and responsibility emerges as the better option to cope with the problem at hand.
The paper is related to several stands of literature.4 The nature of authority we consider
here is closely related to the notion of real authority by Aghion and Tirole (1997) in thatthe authority relationship stems from one’s informational superiority over others. Aghion
and Tirole (1997) consider an incomplete-contracting environment where the principal canonly allocate decision rights and analyze how the allocation of formal authority affects theagents’ incentive to acquire information through the tradeoff between the loss of initiative andthe loss of incentive.5 There are two critical difference between their work and ours. First,
we consider a multi-agent situation with emphasis on the authority relationship between
the agents, rather than on that between the principal and the agent. Second, and more
importantly, we consider an environment where the principal cannot even allocate formal
authority: the structure of information is determined by the allocation of formal authority
in Aghion and Tirole (1997), whereas it is determined by the allocation of responsibility via
incentive contracts in the current analysis.6 We then focus on a different incentive problem
4
Needless to say, there is a vast literature on hierarchy. A large body of literature centers around the
Revelation Principle which implies that centralized contracting cannot be dominated by hierarchial contracting.
In the face of this fact, a substantial amount of attention has been paid to the cases where the Revelation
Principle fails to hold, e.g., due to costly communication/information processing or collusion among agents.
Some of the most notable are Radner (1993), Van Zandt (1999), Baliga and Sjostrom (1998), Bolton and
Dewatripont (1994), Laffont and Matimort (1998), Laffont et al. (2003). Mookherjee (2006) provides an
excellent survey from this mechanism design perspective.
5
See Choe and Ishiguro (2012) for a more recent example of this approach.
6
In this respect, the paper is also related to the emerging literature which explores the nature of interpersonal authority. Van den Steen (2010) considers a setting where two agents engage in a pair of related projects,
with decision externalities between the two projects. With differing priors, the agents can disagree about what
decision to make. In this setup, he shows that how the allocation of assets and income rights influences thenature of interpersonal authority. In an environment where the agent can disobey the principal’s order, Marino

5which stems from the tension between information acquisition and truthful communication.
Second, the current model builds on cheap-talk communication, initiated by Crawford
and Sobel (1982), which deals with the transmission of unverifiable soft information.7 There
are now many applications of this insightful idea, most notably Dessein (2002), and thispaper belongs to this strand as well.8 In most applications, however, the payoff structureis exogenously given, despite the fact that the degree of preference incongruence is almost
always the center of attention in cheap-talk models. Instead, we introduce incentive contracts
which allow us to endogenize the degree of preference incongruence. By writing a contract,
the principal can either facilitate or restrict communication between the agents. Of course,
since the principal can only observe each agent’s output and the incentive for informationacquisition cannot hence be separated out from that for communication, any contract inevitably affects the process of information acquisition, leading to a tradeoff which lies at thecore of the analysis.
Finally, the paper is also related to a growing literature on committees with endogenous
information. As often emphasized in the literature (Li, 2001; Li and Suen, 2009), one of theimportant aspects of the model is that the ex post efficient rule is not necessarily ex ante
efficient. The freeriding problem in a committee is pointed out by Li (2001) where eachmember must independently acquire information.9 In that environment, he shows that asuper-majority rule, the one that biases against the ex ante preferred option, can be used tomitigate the freeriding incentive. The current model provides yet another example of thissituation, illuminating the tradeoff between information acquisition and communication. A
point of departure is that we introduce incentive contracts into the model and suggest a
different solution to this problem. With the explicit consideration of incentive contracts, we
also show that information acquisition in a committee entails different types of inefficiency,
i.e., incentive provision and freeriding.10
et al. (2010) argue how the agent’s ability to disobey the principal limits the extent of centralization. Neither
work considers the moral hazard problem in information acquisition, however, as all the necessary information
for the agents is exogenously given. See Bolton and Dewatripont (2013) for a succinct survey on this issue.
7
There is also a strand of literature which deals with the disclosure of verifiable hard information. See
Grossman and Hart (1980), Milgrom (1981) and Caillaud and Tirole (2007) for this approach.
8
Also see Friebel and Raith (2010), Dessein et al. (2010) and Rantakari (2010) among others for applications
to organizational economics.
9
Persico (2004) considers a similar problem where costly information acquisition is followed by voting. The
optimal voting mechanism with costly information acquisition is also considered by Gerardi and Yariv (2007)
and Gershkov and Szentes (2009).
10
In a different setup, Gromb and Martimort (2007) also consider the case where the agent needs to be

6

2

Model

2.1

setup

Consider an organization in which a risk-neutral principal (e.g., a firm owner) hires two riskneutral agents (e.g., workers), each denoted by i ∈ {1, 2}. Each agent independently chooses
a task xi ∈ {L, R} to implement, which stochastically affects the output yi ∈ {0, 1}. Eachagent’s task choice is his private information, which cannot be observed by either the otheragent or the principal and is hence not contractible. This means that there is no way toforce an agent to take an action which is not in his best interest (no authority over the task
choice).
The output is either high (yi = 1) or low (yi = 0), depending on the state of nature
represented by (s, a) ∈ {L, R} × {G, B}. The state of nature is two-dimensional, where s
indicates the relative productivity of each task while a indicates the aggregate productivity
which captures a common productivity (or demand) shock. When a = G, the (aggregate)
state is “good” and the output is always high regardless of the task choice. When a = B, thestate is “bad” and the output is high if and only if the right task, i.e., xi = s, is implemented.
Letting p(xi , s, a) := prob{yi = 1 | xi , s, a}, we thus have(p(L, s, G) = p(R, s, G) = 1 for s = L, R,
p(L, L, B) = p(R, R, B) = 1 and p(L, R, B) = p(R, L, B) = 0.

2.2

Information acquisition

The state of nature is not directly observable. The prior distribution of the state is given by(prob{s = L} = prob{s = R} = 0.5,
prob{a = G} = λ and prob{a = B} = 1 − λ,where s and a are independent of each other. λ is one of the key parameters of the model,
which measures the salience of the common stochastic shock. We mostly focus on a casewhere λ is strictly positive but relatively small, so that information acquisition constitutes acritical aspect of the production process.
While the state of nature is not freely observable, each agent may observe the relative
motivated to acquire information and reveal it truthfully via contingent contracts. The main difference isthat, while we consider communication between the agents, they consider communication between each agent
and the principal and in particular examine the effect of potential collusion on the optimal form of organization.

7

productivity s by incurring some private cost.11 Let ŝi ∈ {L, R, ∅} denote the private signalof s observed by agent i. Each agent may fail to observe any relevant information with someprobability, and this event is denoted by ŝi = ∅. If ŝi 6= ∅, then the signal accurately reflects
the true state, i.e., ŝi = s. For expositional purposes, we say that an agent is “informed”
when ŝi 6= ∅ and “uninformed” when ŝi = ∅.
The probability that an agent becomes informed depends on how hard he works on acquiring the information. Define ei ∈ {0, 1} as the effort level chosen by agent i, where ei = 1
means that the agent chooses to collect evidence of his own. The probability of becoming
informed is then given byprob{ŝi 6= ∅ | ei } = prob{ŝi = s | ei } = rei , r ∈ (0, 1).
It should be noted that what we mean by information acquisition in this context is rather
broad, including not just the cost of literally gathering information (expertise) but also thatof processing and interpreting available evidence or generating ideas, insights and visions thatare indispensable when determining the course of action.
The cost of effort is given by c > 0. We assume that effort is sufficiently valuable for the
principal to exclude a trivial equilibrium where the agents are not induced to exert effort.
More precisely, we make the following assumption.
Assumption 1r≥2(1 + r)c.
r(1 − λ)As we will see later, this condition is sufficient to rule out the trivial equilibrium.

2.3

Contracts

The principal designs and offers a contract to each agent to maximize her expected profit.
We assume that each agent’s output is the only contractible variable in this environment.12y y

A feasible contract can thus be written as Wi := (wi11 , wi10 , wi01 , wi00 ) where wi i j , i 6= j,denotes the wage to be received by agent i contingent on the outputs yi and yj . We impose
11

Note that each agent has no incentive to acquire information about the aggregate state a, as long as heobserves a signal of the relative productivity s, because the knowledge of the aggregate state does not improve
his task choice.
12
To be more precise, we follow the recent literature, e.g., Aghion and Tirole (1996) and Dessein (2001),
by assuming that tasks (or states of nature) cannot be described and contracted upon ex ante, so that the
principal cannot use a standard mechanism to solicit the private information.

8

y y

a limited liability condition wi i j ≥ 0, so that any wage payment must be nonnegative. The
contracts offered are publicly observable, so that each can observe the other agent’s contract.
The nature of a contract is determined largely by how each agent’s compensation depends
on the other agent’s output. For expositional purposes, we use the following terminologies:• Independent performance evaluation (IPE): (wi11 , wi01 ) = (wi10 , wi00 );• Relative performance evaluation (RPE): (wi11 , wi01 ) ≤ (wi10 , wi00 );• Joint performance evaluation (JPE): (wi11 , wi01 ) ≥ (wi10 , wi00 ).

2.4

Communication and the task choice

Upon observing a signal, each agent communicates with each other to share the acquired information, if any, and chooses the task to implement. More precisely, each agent simultaneously
sends a message mi ∈ {L, R, ∅} to the other. The message is costless and unverifiable, so thismessage game belongs to the class of cheap talk. Given the message and his own observed
signal, each agent chooses his task xi ∈ {L, R}.

2.5

Preferences and the timing

Both the principal and the agents are risk-neutral, where the principal maximizes the expected
profit (the expected output minus the expected wage costs) while each agent maximizes the
expected wage minus the effort cost. The timing of the model is summarized as follows:
1. The state of nature (a, s) ∈ {G, B} × {L, R} is randomly drawn.
2. The principal offers a contract Wi to each agent.
3. Each agent determines the effort level ei ∈ {0, 1}.
4. Each agent observes a signal ŝi ∈ {L, R, ∅}.
5. Upon observing ŝi , each agent sends a message mi ∈ {L, R, ∅} to the other.
6. Upon observing ŝi and mj , j 6= i, each agent chooses the task xi ∈ {L, R}.
7. The outputs (y1 , y2 ) ∈ {0, 1}2 are realized.

9

3

The communication stage

3.1

Optimal task choice

In the communication stage, each agent sends a message mi conditional on the observed
signal. Let Mi (ŝi ) denote agent i’s message strategy. For the cases we consider, we focus on
fully revealing (truth-telling) strategies where Mi (ŝi ) = ŝi .13 To obtain conditions for truth
telling, however, we must first characterize the optimal task choice contingent on the message
and the observed signal, under the premise that each agent reports truthfully.
First, if ŝi 6= ∅, the state is known to be s = ŝi . Letting σj := prob{yj = 1 | ŝi , mj }, theagent chooses xi = ŝi , regardless of the message, if
σj wi11 + (1 − σj )wi10 ≥ σj wi01 + (1 − σj )wi00 .
This condition holds for any σj if wi11 ≥ wi01 and wi10 ≥ wi00 . Since this is generally satisfied
by any optimal contract as we will see shortly, communication virtually plays no role when
the agent is informed.
Communication may matter, on the other hand, when the agent is uninformed. Suppose
first that mj 6= ∅. In this case, the optimal task choice is to follow the other agent’s
recommendation if
wi11 ≥ wi01 ,which is again satisfied by any optimal contract. If mj = ∅, neither agent has any clue andhence no preference over either task. In this case, we allow the agents to coordinate any
way they can to achieve ex ante Pareto-efficient outcomes, if any, when communication istechnically feasible. We say that an agent has the incentive to coordinate (on the same task)
if
wi11 + wi00 ≥ wi10 + wi01 ,(1)

whereas an agent has the incentive to differentiate if this is not satisfied. If (1) is satisfied forboth of the agents, it is Pareto-efficient for them to coordinate their task choices (x1 = x2 ).
If it is satisfied for neither, it is then Pareto-efficient to differentiate (x1 6= x2 ). Finally, if
13There are some exceptional cases where it is not possible to achieve full separation. We do not consider
these cases because they are not optimal under the maintained assumptions. See Appendix B for more detail.

10

it is satisfied only for one of the agents, there is no Pareto-efficient outcome, and the agents
must randomize and choose each task with equal probability.14

3.2

Strategic information disclosure

We now turn to the communication stage and explore conditions for truth telling. Since aninformed agent cannot be influenced by any message, we can focus on the case where theother agent is uninformed and simply follows whatever is recommended in any truth-telling
equilibrium. We check under which an agent has an incentive to reveal truthfully on the basisthat xj = mi . Given that ŝj = mj = ∅, there are two cases we need to consider.
Case 1 (ŝi = ∅): The agent has no information and hence has no preference over the task
choice. If there exists a Pareto-efficient outcome (both agents have an incentive to coordinate
or differentiate), it is weakly optimal to report truthfully since the agent is totally indifferent
between any messages. This means that under any symmetric contract, an uninformed agent
has no incentive to lie.15
If one agent has the incentive to coordinate while the other has the incentive to differentiate, on the other hand, truth telling cannot be induced on the equilibrium path. To see this,
if an agent reports truthfully, the agents know that they have no relevant information. In
this case, they can never agree on who chooses which task and are hence forced to randomize
over the tasks. If the agent misrepresents and claims either mi = L or mi = R, however,he can induce the other agent to choose xj = mi , which allows the agent to coordinate ordifferentiate. No information can therefore be conveyed in this case.
Case 2 (ŝi 6= ∅): This is the case where communication becomes strategic. If the agent
reports truthfully, then the other agent yields the high output for sure using that information.
This may or may not be in his best interest, depending on the type of contract he faces. To
see this, suppose that ŝi = L without loss of generality. The agent has an incentive to lie
only when he would like the other agent to choose xj = R; the best way to achieve this is toclaim mi = R. Given this, the agent truthfully discloses his observation iff
wi11 ≥ wi10 ,14(2)This last case would not arise, however, under the three cases we consider.
A symmetric contract refers to a case where the same contract is offered to both agents. In this case, thepreferences of the two agents are aligned and there must be a Pareto-efficient outcome.
15

11

which we refer to as the condition for truth telling. If (2) does not hold, no message can betaken seriously by the other agent, and no information can hence be conveyed.

4

Optimal organization

4.1

Equilibrium with no communication: a benchmark

We start the analysis with a benchmark case where any form of communication is not feasible
between the agents, possibly for some technological reasons. Each agent thus chooses thetask independently without ever communicating with the other, as if there exists only one
agent. This also precludes the possibility of task coordination when both of the agents are
uninformed. For expositional purposes, we refer to this scheme as Independent Production.
This benchmark case is instrumental in illuminating the role of communication in the current
setup.
Under this scheme, an agent has no choice but to choose the task randomly when heis uninformed. The expected payoff as a function of the effort choices under this scheme,
denoted by πiI , is then obtained as(1 − λ)(wi11 + wi10 ) πiI (ei , ej ) = r 2 ei ej wi11 + rei (1 − rej ) λwi11 +2
11 + w 01 ) 
(1
−
λ)(w
i
i
+ rej (1 − rei ) λwi11 +2(1 − λ)(wi11 + wi10 + wi01 + wi00 ) − cei .
+ (1 − rei )(1 − rej ) λwi11 +4
Taking the other agent’s effort choice ej as given, each agent chooses to exert effort iff
πiI (1, ej ) ≥ πiI (0, ej ), which can be written as
rej

wi11 − wi01
w11 + wi10 − wi01 − wi00c
+ (1 − rej ) i≥.
24r(1 − λ)(3)Lemma 1 The optimal contract in the absence of communication is given by
wi10 =

4c, wi11 = wi01 = wi00 = 0.
r(1 − r)(1 − λ)Proof: See Appendix A.

As is well known, in the presence of common stochastic shocks, the optimal contract
generally takes the form of RPE, where an agent is compensated based on the difference in12the outputs, because it filters out common stochastic shocks.16 The expected profit under
this optimal contract is given by(1 − λ)(1 − r)(1 + r) 10(w1 + w210 )42(1 + r)c
= 2λ + (1 − λ)(1 + r) −.
r

ΠI = 2λ + (1 − λ)(1 + r) −Note that under Assumption 1, this is larger than the expected profit when the agents are
not induced to exert effort.

4.2

Decision making by Committee: bilateral communication

In the presence of common stochastic shocks, the optimal contract typically takes the formof RPE where the agents are compensated based on the difference in the outputs. One
drawback of this type of contract is that by having the agents compete with each other, it
necessarily impedes cooperation between them. In this particular context, even when one
agent is informed, there is no incentive to reveal truthfully his own observation under thistype of contract: the optimal contract in the absence of communication cannot satisfy thecondition for truth telling (2). The lack of truthful communication entails an efficiency loss
since information is typically non-rival and its value does not depend on the number of people
who use it. When the cost of communication is negligibly small (or zero as in this case), it
is clearly ex post efficient to share all the relevant information within the organization via
communication.
Here, we seek for an equilibrium where both of the agents exert effort to acquire theinformation and then truthfully report what is observed. We refer to this situation as decision
making by Committee, where both agents carry the same weight in the decision-making
process ex ante with no restriction on the flow of information (bilateral communication). An
apparent virtue of Committee is that it allows the information to flow from an informed
party to an uninformed party, making the best use of the existing knowledge within theorganization.
In order to facilitate communication between the agents, the condition for truth telling
becomes an additional constraint to be satisfied. Once (2) is satisfied, however, the condition
for information acquisition also needs to be modified because an uninformed agent may
now receive the information via communication. Suppose for now that the agents have the16

IPE, RPE and JPE are all equivalent when λ = 0; for any λ > 0, RPE is strictly better.

13

incentive to coordinate (which needs to be verified later). The expected payoff, denoted by
πiC , is then obtained as
πiC (ei , ej ) = (rei + rej (1 − rei ))wi11 + (1 − rei )(1 − rej )(1 + λ)wi11 + (1 − λ)wi00− cei .
2

The condition for information acquisition is given byr(1 − rej )(wi11 − wi00 ) ≥

2c
,
1−λ

(4)

while the condition for truth telling is given by (2). The optimal contract must also satisfy(1) so that the agents indeed have the incentive to coordinate.
Lemma 2 The optimal contract under Committee is given by
wi11 =

2c, wi10 = wi01 = wi00 = 0.
r(1 − r)(1 − λ)Proof: Given that each agent has an incentive to coordinate when uninformed, i.e., (1) issatisfied, the principal’s problem under Committee is formulated as
min
Wi



1−

(1 − λ)(1 − r)2  11 (1 − λ)(1 − r)2 00
wi +
wi ,
2
2

subject to (2), (4) and the limited liability constraint. It is clear from (4) and the limited
liability constraint that wi10 = wi01 = wi00 = 0. Then, from (4), we obtain wi11 , which caneasily be verified to satisfy (1) and (2).
Q.E.D.
The expected output is maximized under Committee as the output is low only when both
fail to acquire the information. This does not necessarily raise the principal’s profit, however,since facilitating communication has its own costs. There are three reasons for this. First, tofacilitate communication, the agents must be held jointly accountable (JPE),17 but JPE is
generically a less efficient way to provide incentives in the face of common stochastic shocks.
Second, when communication is informative, an uninformed agent can costlessly acquire theinformation via communication, and there hence arises an incentive to freeride on the other’s
information. Finally, in the absence of communication, the agents can increase the chance
17

Communicating truthfully in this context can be seen as a form of cooperation. It is now well known that
JPE is instrumental in fostering cooperation within an organization. See, e.g., Itoh (1981) and Che and Yoo(2001).

14

of coordinating their task choices by acquiring the information, which provides an additional
incentive. This effect is absent when communication is feasible because the agents can always
coordinate their actions via communication even when both of them are uninformed.
This indicates that the ex post efficient rule is not necessarily ex ante efficient as is oftenemphasized in the literature. The expected profit is
2 − (1 − λ)(1 − r)2 11(w1 + w211 )22(2 − (1 − λ)(1 − r)2 )c,= 2 − (1 − λ)(1 − r)2 −r(1 − r)(1 − λ)ΠC = 2 − (1 − λ)(1 − r)2 −As we will see below, Committee tends to be less profitable than Hierarchy when λ or r is
close to one, because the cost of adopting JPE is more salient when λ is relatively large, andthe freeriding incentive intensifies when r is large.

4.3

Decision making by Hierarchy: unilateral communication

As we have seen, it is apparently ex post efficient to facilitate communication between theagents when communication is costless as in the current setup. The problem is that it is not
ex ante efficient because communication raises the agency cost of inducing costly effort. In
the interest of finding a better way to exploit the benefit of communication, we now let theconditions for information acquisition and truth telling hold only for one agent, say agent 1,
so that information only flows from agent 1 to 2 but not the other way around. The chain ofcommand is now hierarchical in that one orders the other what to do, and the other always
has the incentive to follow the order.
Since agent 2 exerts no effort, we only need to look at agent 1’s incentives. Suppose for
now that both of the agents have the incentive to coordinate when uninformed. The expected
payoff, denoted by πiH , is then given by(1 + λ)wi11 + (1 − λ)wi01
2(1 + λ)wi11 + (1 − λ)wi00− cei .
+ (1 − rei )(1 − rej )2πiH (ei , ej ) = rei wi11 + rej (1 − rei )The agent exerts effort iff
wi11 − rejwi11 + wi01
w11 + wi002c
− (1 − rej ) i≥.
2
2
2r(1 − λ)We can then show the following.
15(5)

Lemma 3 The optimal contract under Hierarchy is
w111 =

2c, w110 = w101 = w100 = 0 and w211 = w210 = w201 = w200 = 0,r(1 − λ)which implements e1 = 1 and e2 = 0.
Proof of Lemma 3:

We again suppose that both of the agents have an incentive tocoordinate, i.e., (1) is satisfied. Since e2 = 0, it is evident that the optimal contract for agent
2 is a trivial one where w211 = w210 = w201 = w200 = 0. For agent 1, the principal’s problem
under Hierarchy is formulated as(1 − λ)(1 − r)  11 (1 − λ)(1 − r) 00
1−
min
w1 +
w1 ,
W1
2
2

subject to (2), (5) and the limited liability constraint. It follows from (5) and the limited
liability constraint that wi10 = wi01 = wi00 = 0. Then, from (5), we obtain w111 , which caneasily be verified to satisfy (1) and (2).
Q.E.D.
The expected profit under Hierarchy is given by(1 + r)(1 − λ)  11
w1
ΠH = 1 + r + λ(1 − r) − λ +2(1 + λ + r(1 − λ))c
= 1 + r + λ(1 − r) −.
r(1 − λ)Note that under Hierarchy, the allocation of responsibility is asymmetric in that agent 1 isgiven high-powered incentives and also held accountable for agent 2’s output (team incentives)
while agent 2 is given low-powered incentives and in principle held accountable only for
his own output (individual incentives).18 There are two virtues of Hierarchy in this setup.
First, under Hierarchy, only one agent needs to be motivated to exert effort. Although thisarrangement raises the probability that neither agent is informed compared to Committee,
it can still capture some benefit of costless communication. Second, it also eliminates thefreeriding incentive entirely, which occupies a substantial part of the cost of communication
under Committee. By allocating responsibility asymmetrically, agent 1 cannot rely on agent
2, which in turn raises agent 1’s motivation to exert effort.
18

In the current specification, agent 2 is actually given no incentives and held accountable for nothing, sothat the optimal contract is a special case of IPE. With a simple twist to the basic setup, however, the optimal
contract can be made IPE in the strict sense. Suppose that the production process requires costly individual
effort di ∈ {0, 1}, and the output is given by yi = p(xi , s, a)di so that the output is high iff the agent chooses
to exert effort for production. In this case, the optimal contract for agent 2 is IPE where the cost of effort iscompensated iff his own output is high.

16

4.4

Comparison

We have thus far examined three distinct schemes: (i) Independent Production with nocommunication, (ii) Committee and (iii) Hierarchy.19 We now compare these schemes andsee which organization form yields the highest expected profit.
When the outputs are positively correlated, RPE functions well by filtering out common
stochastic shocks. It is thus clear that Independent Production, which employs RPE, tends toemerge as the only profitable organizational form when λ is relatively large (while satisfying
Assumption 1). As λ decreases toward zero, on the other hand, the benefit of communication
outweighs the cost, and Hierarchy outperforms Independent Production.
Proposition 1 There exists a threshold
λ̄HI =

1+r,
3+r

such that Hierarchy outperforms Independent Production for λ̄HI ≥ λ.
Proof: It follows from above thatΠH − ΠI =1 + r − (3 + r)λc.
r(1 − λ)Solving ΠH − ΠI ≥ 0 for λ yields the result.
Q.E.D.
It becomes optimal to utilize communication in some way when λ is sufficiently small.
There are two possibilities as we have seen. One possibility is to have the agents communicate
only unilaterally in the fixed direction, as in the case of Hierarchy. When both agents exert
effort, however, unilateral communication is not ex post efficient because it is ex ante notclear who ends up with the useful information. The expected output is in general maximized
by letting both agents exert effort and communicate bilaterally. When this benefit outweighs
the higher agency cost, Committee becomes superior to Hierarchy.
Proposition 2 If
r 2 (1 − r)2 > (2(1 + r) − (1 − r)2 )c,
19

These three schemes do not exhaust all the possible contract forms; however, other forms are rarely optimalunder plausible assumptions. See Appendix B for this point.

17

there exists a threshold
CH

λ̄

=1+

(1 − r)c −p(1 − r)2 c2 + 8r 2 (1 + r)c,
2r 2 (1 − r)such that Committee outperforms Hierarchy for λ̄CH ≥ λ. Otherwise, Hierarchy always outperforms Committee.
Proof: It follows from above thatΠH − ΠC =−r 2 (1 − r)2 (1 − λ)2 − (1 − r)2 c(1 − λ) + 2(1 + r)c.
r(1 − r)(1 − λ)Note that this is strictly increasing in λ, so that ΠH − ΠC ≥ 0 is least likely to hold at λ = 0.
If
r 2 (1 − r)2 > (2(1 + r) − (1 − r)2 )c,there exists a threshold below which Committee outperforms Hierarchy; otherwise, Hierarchy
outperforms Committee for any λ. Hierarchy outperforms Committee if−r 2 (1 − r)2 (1 − λ)2 − (1 − r)2 c(1 − λ) + 2(1 + r)c ≥ 0,
which can be written as−(1 − r)c +p(1 − r)2 c2 + 8r 2 (1 + r)c≥ 1 − λ.
2r 2 (1 − r)
Q.E.D.

The proposition shows that for any given c, Hierarchy tends to dominate Committee whenr is close either to one or to the lowerbound implied by Assumption 1. There are two reasonsfor this. First, since the marginal increase in the output (from Hierarchy to Committee) isr(1 − r)(1 − λ), the benefit diminishes as r approaches either end. Second, as r approaches
one, the freeriding incentive intensifies and sharply increases the agency cost. Combinedwith Proposition 1, the result leads to a sufficient condition for Hierarchy to be the optimalorganizational form.
Corollary 1 Hierarchy is optimal if λ̄HI ≥ λ and r is sufficiently close to zero or one.
We now explore conditions under which Committee becomes optimal. While Hierarchy
surely dominates Independent Production for a sufficiently small λ, the same statement cannot be made for Committee.
18

Proposition 3 Ifr(1 − r)2 > 4c,
there exists a threshold
CI

λ̄

√
2c − 2 c2 + r 2 c,=1+
r 2 (1 − r)such that Committee outperforms Independent Production for λ̄CI ≥ λ. Otherwise, Independent Production always outperforms Committee.
Proof: It follows from above thatΠC − ΠI =4((1 − λ)(1 − r) − 1)c + r(1 − r)(1 − λ).
r(1 − r)(1 − λ)Note that this is strictly decreasing in λ, so that ΠC − ΠI < 0 is least likely to hold at λ = 0.
Ifr(1 − r)2 > 4c,
there exists a threshold below which Committee outperforms Independent Production; otherwise, Independent Production outperforms Committee for any λ. Committee outperforms
Independent Production if
r 2 (1 − r)2 (1 − λ)2 + 4(1 − λ)(1 − r)c − 4c ≥ 0,
which can be written as√−2c + 2 c2 + r 2 c.
1−λ≥r 2 (1 − r)
Q.E.D.
From propositions 2 and 3, we can now obtain a sufficient condition for Committee tobe optimal. Note that limc→0 λ̄CH = 1 and limc→0 λ̄CI = 1, which lead to the following
statement.
Corollary 2 Committee is optimal if c is sufficiently small.

19

In general, Committee works better when the cost of information acquisition is relatively
small, which is intuitive because the cost of bilateral communication comes from the increasein the agency cost. This means that if an organization does not need to motivate its members
to acquire information, Committee is often an efficient way to make decisions. After all, this iswhat we expect of a typical committee: in many cases, a committee consists of well informedexperts to begin with, and information acquisition is rarely an issue. In such a situation, it
is often less optimal to assign more weight on anyone’s opinion by restricting the information
flow; it thus makes more sense to treat its members more evenly.20

4.5

The first-best allocation: technology or incentives?

The current analysis shows that Hierarchy often emerges as the optimal contractual arrangement when information acquisition is sufficiently important. Aside from the incentive issues
we have discussed, however, there are also other technological factors which influence theoptimal number of information sources. One key factor is obviously r: when r is close to one,
there is no need to diversify information sources since letting one agent acquire informationis almost enough. Similarly, an increase in λ diminishes the value of information and hence
tends to favor Hierarchy. As it stands, therefore, it is not necessarily clear how importantthe incentive issues are in deriving our main results.
To single out the effects of those technological factors, we here examine the first-best
allocation when there is no information asymmetry, either in information acquisition andcommunication. In the absence of information asymmetry, the principal can effectively orderan agent to exert effort at a cost c. Moreover, any information that is obtained in the process
will be shared immediately without any strategic concerns. Let Πk , k = 0, 1, 2, denote theexpected profit, which also equals the total surplus, when k agents are induced to exert effort.
Straightforward computation then establishes
Π2 = 2 − (1 − λ)(1 − r)2 − 2c,Π1 = 2 − (1 − λ)(1 − r) − c,20

Obviously, the current setup does not apply directly to typical committees where the task choice and theoutcome are normally shared among the members. While the model needs some modifications to precisely
accommodate this aspect, it does not change the substance of our argument. All that matters in this context
is the willingness of each member to share his or hew own information: in the case of typical committees,
the members are effectively tied though an exogenously imposed team contract, which gives rise to the three
aforementioned costs in the information-acquisition stage.

20

Π0 = 1 + λ.
It is optimal to induce both of the agents to collect information (Committee) if(1 − λ)r(1 − r) ≥ c,(6)

while it is optimal to induce only one agent to do so (Hierarchy) if(1 − λ)r > c > (1 − λ)r(1 − r).

(7)

As we will see below, (6) is not particularly a stringent condition to be satisfied and holds aslong as c is reasonably small.
To conclude this section, we summarize our findings by two figures, each of which depicts
which organizational form becomes optimal in the (r, λ) space. In each case, the dotted line
represents (6) inside of which Committee is the first-best allocation.21 It is clear from thefigures that Committee is the optimal choice in the absence of information asymmetry except
for some extreme cases, suggesting that the incentive issues are the critical force behind
our main results. In the presence of information asymmetry, as we have seen, Independent
Production is optimal when λ is relatively large for the obvious reason. Our interest thus
lies in the case where λ is not too high. Figure 1 illustrates a situation where the cost of
information acquisition is relatively high and the agency problem is hence severer. In thiscase, Hierarchy is the optimal form of organization for a wide range of parameters. As the costof information acquisition declines, the range in which Committee becomes optimal enlarges,
as depicted in Figure 2.
[Figures 1 and 2]

5

Conclusion

This paper considers an environment where the principal can only allocate responsibility via
incentive contracts and asks why hierarchies prevail in organizations. The focus of attention
is placed on the tension between costly information acquisition and costless communication.
In this setting, we show that the optimal incentive scheme is often asymmetric, where one
21

In the figures, we do not indicate the region where no agent is induced to exert effort (Assumption 1 underinformation asymmetry and (7) under no information asymmetry) for expositional clarity, because the regionis negligibly small in either case when c is sufficiently small. These conditions for the trivial equilibrium hold
only when r is very close to zero.

21

agent is given high-powered team incentives while the other is given low-powered individual
incentives. Under Hierarchy, the flow of information is restricted to be unilateral and thisgives rise to the chain of command pertaining to hierarchial organizations. This asymmetricallocation of responsibility is the optimal way to acquire information and knowledge as agroup when the agency cost is sufficiently severe.

References
Aghion, Philippe and Tirole, Jean, 1997, Formal and Real Authority in Organizations, Journal of Political Economy, 105, 1-29.
Baliga, Sandeep and Sjostrom, Tomas, 1998, Decentralization and Collusion, Journal of
Economic Theory, 83, 196-232.
Bolton, Patrick and Dewatripont, Mathias, 1994, The Firm as a Communication Network,
Quarterly Journal of Economics, 109, 809-39.
Bolton, Patrick and Dewatripont, Mathias, 2013, Authority in Organizations: A Survey,
in Gibbons, Robert and Roberts, John, eds., Handbook of Oraganizational Economics,
342-72.
Caillaud, Bernard and Tirole, Jean, 2007, Consensus Building: How to Persuade a Group,
American Economic Review, 97, 1877-900.
Che, Yeon-Koo and Yoo, Seung-Weon, 2001, Optimal Incentives for Teams, American Economic Review, 91, 525-541.
Choe, Chongwoo and Ishiguro, Shingo, 2012, On the Optimality of Multi-ter Hierarchies:
Coordination and Motivation, Journal of Law, Economics, and Organization, 28, 486517.
Crawford, Vincent P. and Sobel, Joel, 1982, Strategic Information Transmission, Econometrica, 50, 1431-51.
Dessein, Wouter, 2002, Authority and Communication in Organizations, Review of Economic
Studies, 69, 811-38.
Dessein, Wouter; Garicano, Luis, and Gertner, Robert, 2010, Organizing for Synergies, American Economic Journal: Microeconomics, 4, 77-114.
22

Gerardi, Dino and Yariv, Leeat, 2008, Information Acquisition in Committees, Games andEconomic Behavior, 62, 436-59.
Gershkov, Alex and Szentes, Balazs, 2009, Optimal Voting Schemes with Costly Information
Acquisition, Journal of Economic Theory, 144, 36-68.
Gromb, Denis and Martimort, David, 2007, Collusion and the Organization of DelegatedExpertise, Journal of Economic Theory, 137, 271-99.
Grossman, Sanford J. and Hart, Oliver, 1980, Disclosure Laws and Takeover Bids, Journalof Finance, 35, 323-34.
Faure-Grimaud, Antoine; Laffont, Jean-Jacques, and Matimort, David, 2003, Collusion, Delegation and Supervision with Soft Information, Review of Economic Studies, 70, 253-79.
Friebel, Guido and Raith, Michael, 2010, Reosurce Allocation and Organizational Form,
American Economic Journal: Microeconomics, 2, 1-33.
Hart, Oliver and Moore, John, 2005, On the Desing of Hierarchies: Coordination versus
Specialization, Journal of Political Economy, 113, 675-702.
Itoh, Hideshi, 1991, Incentives to Help in Multi-Agent Situations, Econometrica, 59, 611-636.
Laffont, Jean-Jacques and Martimort, David, 1998, Collusion and Delegation, RAND Journalof Economics, 29, 280-305.
Li, Hao, 2001, A Theory of Conservatism, Journal of Political Economy, 109, 617-36.
Li, Hao and Suen, Wing, 2009, Decision-Making in Committees, Canadian Journal of Economics, 42, 359-92.
Marino, Anthony M.; Matsusaka, John G., and Zabojnik, Jan, 2010, Disobedience and Authority, Journal of Law, Economics, and Organization, 26, 427-59.
Milgrom, Paul R., 1981, Good News and Bad News: Representation Theorems and Applications, Bell Journal of Economics, 12, 380-91.
Mookherjee, Dilip, 2006, Decentralization, Hierarchies and Incentives: A Mechanism Design
Perspective, Journal of Economic Literature, 44, 367-90.
Persico, Nicola, 2004, Committee Design with Endogenous Information, Review of Economic
Studies, 71, 165-4.
23

Radner, Roy, 1993, The Organization of Decentralized Information Processing, Econometrica,
61, 1109-46.
Rajan, Raghuram G. and Zingales, Luigi, 2001, The Firm as a Dedicated Hierarchy: A Theoryof the Origins and Growth of Firms, Quarterly Journal of Economics, 116, 805-51.
Rantakari, Heikki, 2010, Organizational Design and Environmental Volatility, mimeo, University of Southern Califormnia.
Sah, Raaj Kumar and Stiglitz, Joseph E., 1988, Committees, Hierarchies and Polyarchies,
Economic Journal, 98, 451-70.
Van den Steen, Eric, 2010, Interpersonal Authority in a Theory of the Firm, American
Economic Review, 100, 466-90.
Van Zandt, Timothy, 1999, Real-Time Decentralized Information Processing as a Model ofOrganizations with Boundedly Rational Agents, Review of Economic Studies, 66, 633-58.

Appendix A: Proofs
Proof of Lemma 1:

Provided that it is optimal to implement ei = 1, the principal’s

problem in the absence of communication is defined asminWi

4λ + (1 − λ)(4r + (1 − r)2 ) 11 (1 − λ)(2r(1 − r) + (1 − r)2 ) 10
wi +(wi + wi01 )44(1 − λ)(1 − r)2 00
wi ,
+
4

subject to (3) and the limited liability constraint. It directly follows from (3) that wi01 =wi00 = 0 at the optimal solution. This leaves us two possibilities, either wi11 > wi10 = 0 (JPE)or wi10 > wi11 = 0 (RPE). A candidate contract under JPE, denoted by w̃i11 , isw̃i11 =4c.
r(1 + r)(1 − λ)Similarly, a candidate contract under RPE, denoted by w̃i10 , isw̃i10 =4c.
r(1 − r)(1 − λ)RPE yields higher profit than JPE if(1 − λ)(2r(1 − r) + (1 − r)2 ) 10
4λ + (1 − λ)(4r + (1 − r)2 ) 11
w̃i ≥
w̃i .
4
4
24

This can be written as
4λ + (1 − λ)(4r + (1 − r)2 )(1 − λ)(2r(1 − r) + (1 − r)2 )
≥
,
1+r
1−r
which is further simplified toλ(1 − r) ≥ 0.
This shows that RPE is generically better than JPE (the two are equivalent only when λ = 0).
Q.E.D.

Appendix B: Other Contractual Arrangements
In the analysis, we examine only three contractual arrangements, which apparently do not
exhaust all the possibilities. Note that there are two incentive compatibility constraints –one for information acquisition (hereafter IA) and the other for truth telling (TT). Since
the condition for truth telling matters only when the condition for information acquisition issatisfied, there are generically six possible contract forms as summarized below:
1. IA and TT are satisfied for both agents (Committee).
2. IA is satisfied for both agents but TT is satisfied for one agent.
3. IA is satisfied for both agents but TT is satisfied for neither.
4. IA and TT are satisfied for one agent (Hierarchy).
5. IA is satisfied for one agent but TT is satisfied for neither.
6. IA is satisfied for neither.
Cases 1 and 4 are already analyzed. We have also seen that it is optimal to let the agentsacquire the information in the absence of communication, which rules out cases 5 and 6. Thisimplies that we only need to consider cases 2 and 3.

Case 2In this case, both of the agents exert effort to acquire the information, but only one ofthem reports it truthfully. We refer to this situation as Partial Delegation, since the flowof information is unilateral as in the case of Hierarchy but the subordinate acts on his own
information whenever he has one. For the sake of the argument, suppose that TT is satisfied

25

for agent 1 but not for agent 2. To derive the optimal contract within this class, we need toconsider four distinct possibilities.
Case 2-1. Only agent 1 has the incentive to coordinate: In this case, fully separating
communication cannot be implemented because there is no incentive to report truthfully whenŝ1 = ∅. For communication to be meaningful, it is then necessary for agent 2 to follow agent
1’s message when he is uninformed. Given that ŝ2 = ∅, this condition can be written as
w11 + w200 
re1 w211 + (1 − re1 ) λw211 + (1 − λ) 22
w10 + w201 ,≥ re1 (λw211 + (1 − λ)w201 ) + (1 − re1 ) λw211 + (1 − λ) 22which is simplified to(1 + re1 )(w211 − w201 ) ≥ (1 − re1 )(w210 − w200 ).

(8)

The condition for truth telling for agent 1 is the same as before: the agent reports truthfully
iff w111 ≥ w110 .
Given that these conditions are satisfied, the expected payoff for agent 1 is obtained as(1 + λ)w111 + (1 − λ)w101
2(1 + λ)w111 + (1 − λ)w100− ce1 .
+ (1 − re1 )(1 − re2 )2

π1 (e1 , e2 ) = re1 w111 + re2 (1 − re1 )The agent exerts effort iff
w111 − re2 w101 − (1 − re2 )w100 ≥2c.
r(1 − λ)A candidate contract is
w111 =

2c, w10 = w101 = w100 = 0,r(1 − λ) 1

which also satisfies the condition for truth telling. Under this contract, the agent also has anincentive to coordinate.
Similarly, the expected payoff for agent 2 is obtained as(1 + λ)w211 + (1 − λ)w210
2(1 + λ)w111 + (1 − λ)w100+ (1 − re2 )(1 − re1 )− ce2 .
2π2 (e2 , e1 ) = re1 w211 + re2 (1 − re1 )26

The agent exerts effort iff(1 − re1 )(w210 − w200 ) ≥2c.
r(1 − λ)(9)We have also assume that the agent has an incentive to differentiate, which means thatw210 − w200 > w211 − w201 .

(10)

The optimal contract within this class must satisfy (8), (9) and (10). Since e1 = 1, all ofthese condition together imply
w210 − w200 > w211 − w201 ≥1 − r 102c
(w2 − w200 ) ≥.
1+r
r(1 + r)(1 − λ)A candidate contract is thus
w211 =

2c
2c, w10 =
, w101 = w100 = 0.
r(1 + r)(1 − λ) 2r(1 − r)(1 − λ)Under this contract, the agent has no incentive to report truthfully, as assumed.
We now show that this contract cannot be optimal. The expected profit under thisarrangement, denoted by ΠP , is(1 − r)(2 − r)(1 + λ) 2c(1 − r)(1 + λ) − r+
22r(1 − r)(1 − λ)2c2cr(1 − r)(1 − λ)(1 − r)(1 + λ) 
−
.
− r+
2
r(1 + r)(1 − λ)2r(1 − r)(1 − λ)ΠP = 2r + r(1 − r) +Let the expected profit under each arrangement be decomposed into the expected output
Y k and the expected wage cost W k , such that Πk = Y k − W k , k = H, C, P . Hierarchy

outperforms Partial Delegation if Y H − W H ≥ Y P − W P while Committee outperforms

Partial Delegation if Y C − W C ≥ Y P − W P . Since
YC−YP =YP−YH =r(1 − r)(1 − λ),2Partial Delegation cannot be optimal if 2W P ≥ W C + W H , which can be written as
4 − 2(1 − λ)(1 − r)2 1 + λ + r(1 − λ)4(2r + (1 − r)(1 + λ))+2≥+.
r(1 − r)(1 + r)(1 − λ)r(1 − r)(1 − λ)r(1 − λ)With some algebra obtain1≥(1 + r)(4 − 2(1 − λ)(1 − r)2 ) + (1 − r)(1 + r)(1 + λ) − 8r − 4(1 − r)(1 + λ).
r(1 − r)(1 + r)(1 − λ)27which is further simplified to1≥(1 + r)(3λ − 2r(1 − λ) − 1) − 4λ⇔ (1 + r)2 ≥ (4r + r 2 − 1)λ.
r(1 + r)(1 − λ)One can then easily verify that this condition holds for any λ ∈ [0, 1], which proves that
Delegated Hierarchy cannot be optimal in this case.
Case 2-2. Only agent 1 has the incentive to differentiate: Again, in this case, fully
separating communication cannot be implemented because there is no incentive to report
truthfully when ŝ1 = ∅. We thus need the same condition as above, i.e., it is necessary foragent 2 to follow agent 1’s message when he is uninformed. Given that ŝ2 = ∅, this condition
can be written as
w10 + w201 
re1 w211 + (1 − re1 ) λw211 + (1 − λ) 22

w11 + w200 ,≥ re1 (λw211 + (1 − λ)w201 ) + (1 − re1 ) λw211 + (1 − λ) 22which is simplified to(1 + re1 )(w211 − w201 ) ≥ (1 − re1 )(w200 − w210 ).

(11)

The condition for truth telling for agent 1 is the same as before: the agent reports truthfully
iff w111 ≥ w110 .
Given that these conditions are satisfied, the expected payoff for agent 1 is obtained as(1 + λ)w111 + (1 − λ)w101
2
112λw1 + (1 − λ)(w110 + w101 )+ (1 − re1 )(1 − re2 )− ce1 .
2

π1 (e1 , e2 ) = re1 w111 + re2 (1 − re1 )The agent exerts effort iff
re2 (w111 − w101 ) + (1 − re2 )(2w111 − w110 − w101 ) ≥2c.
r(1 − λ)Since w110 + w101 ≥ w111 + w100 (the incentive to differentiate), a necessary condition for this isre2 (w111 − w101 ) + (1 − re2 )(w111 − w100 ) ≥2c.
r(1 − λ)A candidate contract is
w111 = w110 =2c, w101 = w100 = 0,r(1 − λ)28

which also satisfies the condition for truth telling.
Similarly, the expected payoff for agent 2 is obtained as(1 + λ)w211 + (1 − λ)w2102112λw1 + (1 − λ)(w210 + w101 )+ (1 − re2 )(1 − re1 )− ce2 .
2π2 (e2 , e1 ) = re1 w211 + re2 (1 − re1 )The agent exerts effort iff(1 − re1 )(w211 − w201 ) ≥2c.
r(1 − λ)(12)

Since the condition for truth telling must not hold for agent 2, a candidate contract is
w211 = w210 =2c, w101 = w100 = 0.
r(1 − r)(1 − λ)These contracts are, however, clearly less profitable than the ones obtained in the previous
case, implying that Partial Delegation is not optimal in this case.
Case 2-3. Both agents have the incentive to coordinate: The condition for information acquisition is the same as in case 2-1. The condition for agent 1 is given by
w111 − re2 w101 − (1 − re2 )w100 ≥2c.
r(1 − λ)while that for agent 2 is
(1 − re1 )(w210 − w200 ) ≥2c.
r(1 − λ)Since full revelation is possible in this case, the incentive for agent 2 to follow agent 1’s
message is not necessary. Agent 2 must have the incentive to coordinate, however, and that
requiresw211 + w200 ≥ w210 + w201 .
Note that this restriction is more stringent than (8), so that the resulting profit must be lessthan that in case 2-1.
Case 2-4. Both agents the incentive to differentiate: The condition for informationacquisition is the same as in case 2-2. The condition for agent 1 is given byre2 (w111 − w101 ) + (1 − re2 )(2w111 − w110 − w101 ) ≥29

2c.
r(1 − λ)while that for agent 2 is
(1 − re1 )(w211 − w201 ) ≥2c.
r(1 − λ)Since full revelation is possible in this case, the incentive for agent 2 to follow agent 1’s
message is not necessary. Agent 1 must have the incentive to differentiate, however, and that
requiresw110 + w101 ≥ w111 + w100 .
Moreover, the condition for truth telling must not hold for agent 2. These additional requirements are the same as in case 2-2, leading to the same outcome.

Case 3This situation is almost identical to Independent Production, except that communication
is now feasible, which allows them to coordinate on the task choice while exchanging no
information about the state of nature. Suppose first that each agent has the incentive todifferentiate. We can then consider the following strategy for each agent.
• When ŝi 6= ∅, mi = L or mi = R with equal probability (a babbling message);• When ŝi = ∅, mi = ∅.
One can verify that neither agent has the incentive to deviate from this strategy. Under thisstrategy, the expected payoff, denoted by π̃iI , is
(1 − λ)(wi11 + wi10 ) π̃iI (ei , ej ) = r 2 ei ej wi11 + rei (1 − rej ) λwi11 +
2

11
01
(1 − λ)(wi + wi ) + rej (1 − rei ) λwi11 +2(1 − λ)(wi10 + wi01 ) − cei .
+ (1 − rei )(1 − rej ) λwi11 +2
The agent chooses to exert effort iffcwi11 − wi01≥.
2r(1 − λ)Since the agents must the incentive to differentiate, we must also havewi10 + wi01 ≥ wi11 + wi00 .
30

The optimal contract within this class is hence
wi11 = wi10 =2c, wi01 = wi00 = 0.
r(1 − λ)but this is clearly less efficient than Independent Production. To see this, note that the
expected output under this contract is exactly the same as that under Independent Production because any task coordination when both agents are uninformed does not increase theexpected output. Independent Production then dominates this if(r 2 + r(1 − r)(1 + λ) + (1 − r)2 λ +2c(1 + r)c(1 − r)(1 − λ))≥,2r(1 − λ)rwhich can be shown to hold.
Now suppose that both of the agents have the incentive to coordinate. The same strategy
considered above works, and under this strategy, the expected payoff is(1 − λ)(wi11 + wi10 ) 
11
λwi +
2
11
01
(1 − λ)(w + w ) π̃iI (ei , ej ) = r 2 ei ej wi11 + rei (1 − rej )ii+ rej (1 − rei ) λwi11 +2(1 − λ)(wi11 + wi00 ) − cei .
+ (1 − rei )(1 − rej ) λwi11 +2
The agent chooses to exert effort iff
rej

wi11 − wi01
w10 − wi00c
+ (1 − rej ) i≥.
22r(1 − λ)Since the agents must the incentive to coordinate, we must also satisfy (1). The principal’s
problem is then defined asminWi2r 2 + (1 − r 2 )(1 + λ) 11 r(1 − r)(1 − λ) 10
wi +(wi + wi01 )2
2(1 − λ)(1 − r)2 00
+
wi ,
2

subject to the incentive constraints. In the absence of (1), the optimal contract would havewi11 = 0. The optimal contract within this class is thus given by
wi11 = wi10 =2c, wi01 = wi00 = 0.
r(1 − λ)which yields exactly the same profit as the one derived above (for the case where both agents
have the incentive to differentiate).
31

0.5
Independent

Hierarchy
λCommittee

0
0

r

1

Figure 1: Optimal organization when the cost of information acquisition is high(c = 0.02)

32

0.5
Independent

Hierarchy

λCommittee

0
0

r

1

Figure 2: Optimal organization when the cost of information acquisition is low(c = 0.01)

33