Discussion Paper No. 751

WHY HIERARCHY?
COMMUNICATION AND INFORMATIONACQUISITION IN ORGANIZATIONS

Junichiro Ishida

August 2009

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Why Hierarchy? Communication and Information
Acquisition in Organizations
Junichiro Ishida
ISER, Osaka University
August 24, 2009

Abstract
In most firms, if not all, workers are divided asymmetrically in terms of authority andresponsibility. In this paper, we view the asymmetric allocations of authority and responsibility as essential features of hierarchy and examine why hierarchies often prevail inorganizations from that perspective. The focus of attention is on the tradeoff between
costly information acquisition and costless communication. When the agency problem
concerning information acquisition is sufficiently severe, 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.
This explains why hierarchies often prevail in firms since a relatively fixed group of members must confront with new problems and come up with solutions on the day-to-day
basis, and hence the agency problem is an issue to be reckoned with.

JEL Classification Codes: D03, D99.
Key Words: Authority; Responsibility; Contract; Communication; Cheap talk; 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.

1 Introduction
It is very rare, if ever, to find a firm where all of its workers are treated just equally. In mostcases, some workers, typically those higher up in the hierarchy, are conferred more authority
and hence carry an asymmetrically larger weight in the decision-making process than others.
At the same time, those with more authority are also given more stringent incentives andmoreover 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 or worker empowerment
differs across firms as well as over time, workers are by and large divided asymmetrically interms of both authority and responsibility. In this paper, we view these asymmetric allocationsof authority and responsibility as essential features of hierarchical organizations and examine
why hierarchies often prevail in organizations from that perspective.
At a glance, the asymmetric allocation of responsibility seems to be a straightforward
consequence of that of authority: if a worker is entitled to make a decision, he should beheld accountable for any consequences brought by that decision. In this line of reasoning, itis 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, e.g., by
granting or restricting access to critical resources, as often assumed in the literature (e.g.,
Aghion and Tirole, 1997; Rajan and Zingales, 2001; Dessein, 2002; Hart and Moore, 2005).
This may not always be the case, however, because there may not exist such critical resourcesthat are indispensable for production or because there may be no realistic way to control
access to those resources. Since the presence of hierarchy is quite ubiquitous in firm organizations, it seems worthwhile to explore the nature of hierarchy in an 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 with a principal (the contract designer) and
two agents. Each agent privately chooses a task to implement, which stochastically leads tosome observable output. The productivity of each task is not known ex ante, and each agent

1

must hence acquire information about which task is the most productive. This informationacquisition stage involves two rounds. In the first round, each agent privately exerts effort
to acquire information (or produce an “idea”) about the productivity of each task. Thisis followed by the second round where each agent sends a costless message to share thisinformation (idea), if any, with the other agent. The problem is that the principal cannot
observe each agent’s task choice nor how that decision is reached (who had the idea andwhose idea was adopted); the only way for the principal to control the agents is to allocate
responsibility via incentive contracts contingent on the outputs. With no feasible way toallocate authority, 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.
An incentive contract in this setup is subject to two constraints: one for informationacquisition (whether to exert effort to acquire information) and the other for truthful communication (whether to reveal truthfully the acquired information). The problem is thatthe constraint for information acquisition generally calls for competition between the agents
while that for communication inherently calls for cooperation between them. These two constraints are therefore at odds with each other, and the optimal contract must achieve justthe right balance between these two concerns. A hierarchy emerges when one agent (thesuperior) orders the other agent (the subordinate) what to do, and the subordinate has anincentive to follow the order. Under this contractual arrangement, the flow of information isrestricted to be unilateral, always from the superior to the subordinate, and the superior isgiven a disproportionately large weight in the decision-making process ex ante. As an alternative to this arrangement, the incentive contracts may be designed to place no restriction
over the flow of information. In this case, information flows from the informed party to theuninformed 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 and compare thefollowing three organizational forms summarized as below.1
1

While there are many other contractual arrangements in this setup, we can show that it suffices to consider2

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.
We then 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 optimal organization form. Our analysis centers around the tradeoff between costly informationacquisition and costless (cheap-talk) communication. To illustrate this, we start with thebenchmark 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 compensated based on the difference in the outputs. Thisis the most efficient way to provide incentives if the principal’s only concern is to motivatethem to exert effort. Independent Production has a clear weakness, however, because theconstraint for truthful communication cannot be satisfied under relative performance evaluation. With no information flowing between the agents, therefore, it may leave some of theexisting knowledge unutilized: in this sense, the level of competition between the agents isoften 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 flow of information.
those three cases. See Appendix B for more detail.

3

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 ex ante carries the same weight in thedecision-making process, 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 exploit the benefit of costless communication. As it turns
out, though, this ex post optimal arrangement is not ex ante optimal, as it raises the agency
cost of inducing costly effort. The analysis identifies three channels through which bilateralcommunication entails ex ante inefficiency.
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.
Coordination: In the absence of communication, the agents can increase the chance of coordinating their task choices by acquiring the information. This effect is absent because theagents 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, which places
no restriction on the extent of communication, is often excessive. We argue that there is a
way to exploit the benefit of communication while keeping its cost minimum. This can bedone by the asymmetric allocation of responsibility where one agent, the superior, is offered
high-powered (team) incentives while the other, the subordinate, is offered 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, this is a thrifty way
to acquire information as a group. Second, the asymmetric and concentrated allocation of4responsibility eliminates the freeriding incentive as the superior can no longer rely on thesubordinate’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 and cooperation. Under the asymmetric allocation of responsibility, the flow of information is restricted
to be unilateral, always from the superior to the subordinate, which endogenously gives riseto the chain of command pertaining to hierarchical organizations.
The results obtained in this paper suggest that whether Hierarchy or Committee is optimal depends crucially on the severity of the agency problem. Hierarchy, which allocates
responsibility asymmetrically, outperforms Committee when costly information acquisition is
the main concern. We argue that this corresponds to typical firm organizations where a relatively fixed group of members must confront with and find solutions for new problems on the
day-to-day basis. In such a case, Hierarchy is often optimal, lending a support for the viewthat most firms are hierarchical. This draws contrast to committees which typically consist ofexperts who are well informed in the first place. In committees, members are in many cases
selected for specific problems and information acquisition is hence rarely an issue. In sucha 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 withthe problem at hand.
The paper is related to several strands of literature. The paper is more closely related
to a growing literature on committees with endogenous information. As often emphasizedin the literature (Li, 2001; Li and Suen, 2009), one of the important aspects of the modelis 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 each member must independently acquire
information.2 In that environment, he shows that a super-majority rule, the one that biases
against the ex ante preferred option, can be used to mitigate the freeriding incentive. The
current model provides yet another example of this situation, illuminating the tradeoff between information acquisition and communication. A point of departure is that we introduce
2
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) andGershkov and Szentes (2009).

5

incentive contracts into the model and suggest a different solution to this problem.3 With theexplicit consideration of incentive contracts, we also show that information acquisition in acommittee entails different types of inefficiency – incentive provision and coordination.
Second, there is also a vast literature on hierarchy, too numerous to list them all. Amongthem, the paper is particularly related to works on the optimal allocation of authority. Aghion
and Tirole (1997) is close in spirit to ours, as they shed light on the impact of the allocationof authority on the incentive to acquire information with its focus on the distinction between
real and formal authority.4 As emphasized earlier, in Aghion and Tirole and others, the starting point of the analysis is the allocation of authority which can be made by the principal ather own discretion. They then analyze how this allocation affects the agents’ incentive to acquire information through the tradeoff between the loss of initiative and the loss of incentive.
Instead, we consider a situation where the principal can only allocate responsibility, which inturn determines the allocation of authority: that is, the allocation of authority is at the end
point of the analysis.5 We view our analysis as complementary to the existing literature, as it
approaches the same issue from the opposite angle.
Finally, the current model builds on cheap-talk communication, put forth by Crawford andSobel (1982). There are now many applications of this insightful idea, and this paper belongs
to this strand as well. In most applications, however, the payoff structure is exogenously
given, despite the fact that the degree of preference incongruence is almost always the centerof attention in cheap-talk models. Instead, we introduce incentive contracts which allow us toendogenize the degree of preference incongruence. By writing a contract, the principal caneither facilitate or restrict communication. Of course, since the principal can only observe
each agent’s output and the incentive for information acquisition cannot hence be separated
3

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 and polyarchies – with its particular emphasis on the tradeoff between the type I and type II errors.
4
Another approach to explore the link between hierarchy and knowledge acquisition is provided by Garicano(2000). There, the main focus is on the tradeoff between communication and knowledge acquisition costs withno regard to incentive issues.
5
It is not our intention to argue that firms do not allocate formal authority: they may or may not. Our point
is rather that for the allocation of formal authority to be meaningful, it must be incentive-compatible, at least
to some extent, for the subordinate to follow the superior’s order. Our specification thus represents an extreme
point of the spectrum while the conventional approach represents the other end.

6

out from that for communication, any contract inevitably affects the process of informationacquisition, leading to a tradeoff which lies at the core of the analysis.

2 Model
2.1 The setup
Consider an organization in which a risk-neutral principal (e.g., a firm owner) hires two
risk-neutral agents (e.g., employees), each denoted by i 2 f1; 2g. Each agent independently

chooses a task xi 2 fL; Rg to implement, which yields the output yi 2 f0; 1g. Each agent’s

task choice is his private information, which cannot be observed by either the other agent or
the principal. This means that there is no way to force an agent to take an action which is
not in his best interest.
The output is either high (yi = 1) or low (yi = 0), depending on the state of nature

represented by (s; a) 2 fL; Rg  fG; B g. The state of nature is two-dimensional, where s
indicates the relative productivity of each task while a the aggregate productivity. Whena = G, the (aggregate) state is “good” and the output is always high regardless of the task
choice. When a = B , the state 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) := probfyi = 1 j xi ; s; ag, we thus have8
< 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

8<:

probfs = Lg = probfs = Rg = 0:5;
probfa = Gg =  and probfa = B g = 1

;where s and a are independent of each other.  is one of the key parameters of the model,
which measures the salience of the common stochastic shock. We mostly focus on a casewhere  is strictly positive but relatively small.
While the state of nature is not freely observable, each agent may observe the relative
productivity s with some probability by incurring some private cost. Let s^i 2 fL; R; g denote7

the private signal of s. Each agent may fail to observe any relevant information with someprobability, and this event is denoted by si = . If s^i 6= , then the signal accurately reflects
the true state, i.e., s^i = s.6 For expositional purposes, we say that an agent is “informed”
when si 6=  and “uninformed” when si = .

The probability that an agent becomes informed depends on how hard he works on acquiring it: 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 or collecting information but
also that of processing and interpreting available evidence or generating ideas, insights andvisions. Define ei 2 f0; 1g as the effort level chosen by agent i, where ei = 1 means that theagent chooses to collect evidence of his own. The probability of becoming informed is thengiven byprobfs^i 6=  j eig = probfs^i = s j ei g = rei; r 2 (0; 1):
The cost of effort is given by > 0.

2.3 Contracts
The principal designs and offers a contract to each agent to maximize her expected profit. The
output yi is the only contractible variable in this environment. A feasible contract can thusyy

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 a limited liability condition

wiyi yj  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 );6This means that when an agent has some information about the state of nature, he knows it with precision.
We make this assumption to avoid a purely technical problem which arises when two imperfectly informed parties
communicate with each other. See Ishida and Shimizu (2009) on this problem.

8• 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 and chooses the task. More precisely, each agent simultaneously sends a message

mi 2 fL; R; g to the other: for clarity, we consider the message space which coincides withthe signal space. The message is costless and unverifiable, so this message game belongs to
the class of cheap talk. Given the message and his own observed signal, each agent thenchooses his task xi 2 fL; Rg.

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 asfollows:
1. The state of nature (a; s) 2 fG; B g  fL; Rg is randomly drawn.
2. The principal offers a contract Wi to each agent.
3. Each agent determines the effort level ei 2 f0; 1g.
4. Each agent observes a signal s^i 2 fL; R; g.
5. Upon observing s^i , each agent sends a message mi 2 fL; R; g to the other.
6. Upon observing s^i and mj , each agent chooses the task xi 2 fL; Rg.
7. The outputs (y1 ; y2 ) 2 f0; 1g2 are realized.

3 The Communication Stage
3.1 The Optimal Task Choice
In the communication stage, each agent sends a message mi conditional on the observed
signal. Let Mi (^si ) denote agent i’s message strategy. For the cases we consider, we focus on
9fully revealing (truth-telling) strategies where Mi (^si ) = s^i .7 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 s^i 6= , the state is known to be s = s^i . Letting j := probfyj = 1 j s^i ; mj g, theagent chooses xi = s^i , regardless of the message, if

j wi11 + (1j )wi10  j wi01 + (1j )wi00 :This condition holds for any j 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 it issatisfied only for one of the agents, there is no Pareto-efficient outcome, and the agents must
randomize and choose each task with equal probability.8
7
There are some exceptional cases where it is not possible to achieve full separation. We do not consider thesecases because they are not optimal under the maintained assumptions. See Appendix B for more detail.
8This last case would not arise, however, under the three cases we consider.

103.2 Strategic Information Disclosure
We now explore conditions under which an agent has an incentive to reveal truthfully. Since
an informed agent cannot be influenced by any message, we can focus on the case where theother agent is uninformed. Given that s^j = mj = , there are two cases we need to consider.
Case 1 (s^i = ): The agent has no information and hence has no preference over the task
choice. If there exists a Pareto-efficient outcome (both agents have the 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.
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 end up with no information. In this case, they cannever agree on who chooses which task and are hence forced to randomize over the tasks.
If the agent misrepresents and claim either mi = L or mi = R, however, he can induce theother agent to choose xj = mi , which allows the agent to coordinate or differentiate. No
information can therefore be conveyed in this case.
Case 2 (s^i 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 s^i = 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 to claim

mi = R. Given this, the agent truthfully discloses his observation iff
wi11  wi10 ;(2)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 (a babbling
equilibrium).

11

4 Optimal Organizations
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 iI , is then obtained as

iI (ei ; ej ) = r2 ei ej wi11 + rei (1rej ) wi11 +(1)(wi11 + wi10 ) 2)(wi11 + wi01 ) + rej (1 rei) wi11 + (1

+ (1 rei)(1 rej ) wi11 + (12)(wi11 + wi10 + wi01 + wi00 ) 

4

ei :

Taking the other agent’s effort choice ej as given, each agent chooses to exert effort iff

iI (1; ej )  iI (0; ej ), which can be written as
w11
rej i

2

wi01

+ (1

w11 + wi10rej ) i

4

wi01

wi00

 r(1

)

:

(3)

Lemma 1 The optimal contract in the absence of communication is given by

wi10 =

4r(1 r)(1); wi11 = wi01 = wi00 = 0:

P ROOF: See Appendix A.

As is well known, in the presence of common stochastic shocks, the optimal contract inthis case takes the form of RPE where an agent is compensated based on the difference in12the outputs. RPE is generically superior in inducing costly effort as it filters out common
stochastic shocks.9 The expected profit under this optimal contract is given byI = 2 + (1)(1 + r)= 2 + (1)(1 + r)

(1

)(1

4

r)(1 + r)

2(1 + r) :

r(1

8

r)(1

)

r

We assume that this is larger than the expected profit when the agents are not induced toexert effort. This is the case if+ r) :
I  1 +  , r  2(1r(1 )In what follows, we assume that is sufficiently small, so that this condition holds.

4.2 Decision Making by Committee: Bilateral Communication
In the presence of common stochastic shocks, the optimal contract typically takes the form of
RPE where the agents are compensated based on the difference in the outputs. One drawbackof 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 this type ofcontract: the optimal contract in the absence of communication cannot satisfy the condition
for truth telling (2). The lack of truthful communication entails an efficiency loss since information is typically a public good whose value does not depend on the number of people
who use it. When the cost of communication is negligibly small, it is clearly ex post efficient
to share all the relevant information within the organization.
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.
9

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

13

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 the
incentive to coordinate (which needs to be verified later). The expected payoff, denoted by

iC , is then obtained as
iC (ei ; ej ) = (rei + rej (1rei ))wi11 + (1rei)(1rej )(1 + )wi11 + (12)wi00ei :The condition for information acquisition is given byr(1wi00 ) rej )(wi11

1

2



;

(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 =

2r(1 r)(1); wi10 = wi01 = wi00 = 0:

P ROOF: Given that each agent have an incentive to coordinate when uninformed, the principal’s problem under Committee is formulated as

2 + (1
max
W
i

)(2

2

(1

r)2 )

wi11 +

(1

)(1

2

r)2

wi00 ;

subject to (4) and (2). It follows that wi10 = wi01 = wi00 = 0. Solving (4) then yields the
proposed contract, which can easily be verified to satisfy (1).
Q.E.D.
The expected output is maximized under Committee as the output is low only whenboth 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 thisFirst, to facilitate communication, the agents must be held jointly accountable (JPE), but
JPE is generically a less efficient way to provide incentives. Second, when communication14

is informative, there arises an incentive to freeride on the other’s information acquired via
costless communication. Finally, in the absence of communication, the agents can increase
the chance of coordinating their task choices by acquiring the information. This effect isabsent because the agents can always coordinate via communication.
This indicates that the ex post efficient rule is not necessarily ex ante efficient as is oftenemphasized in the literature. The expected profit isC = 2 (1

)(1

r)2

= 2 (1

)(1

r)2

2 (1

)(1

r)2

4
2
r(1 r)(1
2(2 (1 )(1 r)2 ) ;r(1 r)(1 ))Committee becomes increasingly less profitable as  or r gets larger: the cost of adopting JPE
is more salient when  is relatively large, and the freeriding incentive intensifies when r islarge.

4.3 Decision Making by Hierarchy: Unilateral Communication
As we have seen, it is apparently ex post efficient to facilitate communication between theagents because communication is free in the current setup. The problem is that it is not ex
ante efficient because communication raises the agency cost of inducing costly effort. Theremay be a better way to exploit the benefit of communication than the symmetric contract
obtained under Committee. The key is the nature of information: when communication
is informative, only one agent needs to be informed. To minimize the cost arising from
communication, we now let the conditions for information acquisition and truth telling holdfor only one agent, say agent 1, so that information only flows from agent 1 to 2 but not theother way around. The chain of command is now hierarchical in that one orders the otherwhat to do (note that the task choice is his private information).
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 expected15

payoff, denoted by iH , is then given by(1 + )wi11 + (1 )wi01
2(1+
)wi11 + (1 )wi00+ (1 rei)(1 rej )2

iH (ei ; ej ) = reiwi11 + rej (1

rei )

ei :

The agent exerts effort iff

w11 + wi01
rej i

wi11

w11 + wi00
rej ) i


(1

2

2

2
2r(1

)

:

(5)

We can then show the following.
Lemma 3 The optimal contract under Hierarchy is

w111 =2r(1); w110 = w101 = w100 = 0 and w211 = w210 = w201 = w200 = 0;

which implements e1 = 1 and e2 = 0.
P ROOF OF L EMMA 3:

We again suppose that both of the agents have an incentive to co-ordinate. 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 isformulated as

2 + (1 )(1 + r) w11 + (1
max
1
W
2

)(1

r)

00

w1 ;
2
subject to (5) and (2). It follows that wi10 = wi01 = wi00 = 0. Solving (5) then yields the
1

proposed contract, which can easily be verified to satisfy (1).
Q.E.D.
The expected profit under Hierarchy is given by(1 + r)(1 )  2
2r(1 )+ r(1 )) := 1 + r + (1 r) (1 + r(1)H = 1 + r + (1

r)



+

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
16

for his own output (individual incentives).10 There are two virtues of Hierarchy in this setup.
First, under Hierarchy, only one agent needs to be motivated to exert effort. Although thisraises the probability that neither agent is informed compared to Committee,11 this is anefficient way to exploit the fact that information transmission via communication is free.
Second, it also eliminates the freeriding incentive, which occupies a substantial part of thecost 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.

4.4 Comparison
We have thus far examined three distinct schemes: (i) Independent Production with no communication, (ii) Committee and (iii) Hierarchy.12 We now compare each of these schemes
and see which one yields the highest expected profit, especially when Hierarchy outperforms
the other organizational forms.
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, emerges
as the only profitable organizational form when  is arbitrarily close to one. As  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 HI =

1 + r;
3+r

HI  .
such that Hierarchy outperforms Independent Production for 
10

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 2 f0; 1g, 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 is compensated
iff his own output is high.
11
In fact, this potential cost is totally offset note that the expected output under Hierarchy is the same as that
under Independent Production.
12
These three schemes do not exhaust all the possible contract forms; however, other forms are rarely optimalunder plausible assumptions. See Appendix for this point.

17

P ROOF: It follows from above that

H I = 2(1 )(1 + r)r(1 (1+)  + r(1+ r) 2 := (1 r)(1(1 )
Solving H))I  0 for  yields the result.
Q.E.D.

When  is sufficiently small, communication works better to exploit the information which
may be dispersed within the organization. The question is then the direction of the information flow. One way 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 not clear who has the useful information.
By having both agents exert effort and communicate bilaterally, the expected output is in
general maximized under Committee. When this benefit outweighs the higher agency cost,
Committee becomes superior to Hierarchy.
Proposition 2 If

r2(1r)2 > (2(1 + r)

(1r)2 ) ;

there exists a threshold(1
 CH = 1 +r)p(1 r)2 2 + 8r2(1 + r) ;2r2(1 r) CH  . Otherwise, Hierarchy always outpersuch that Committee outperforms Hierarchy for 
forms Committee.
P ROOF: It follows from above that2
(1 r)(1 +  + r(1 ))H C = 2(2 (1 )(1 rr)(1) r)(1)))
= 4 (1 r(1r)(3r)(1 r(1r(1 r)(1 ):
)

18

r(1

r)(1

)

Note that this is strictly increasing in , so that H

r2(1C  0 is least likely to hold at  = 0. Ifr)2 > (2(1 + r)

(1r)2 ) ;

there exists a threshold below which Committee outperforms Hierarchy; otherwise, Hierarchy
outperforms Committee for any . Hierarchy outperforms Committee ifr2(1r)2 (1)2(1r)2 (1) + 2(1 + r)  0;

which can be written as

(1

r) +

p

(1 r)2 2 + 8r2(1 + r)  1
2r2(1 r):
Q.E.D.

The proposition shows that for any given , Hierarchy is superior to Committee when r is
close to either zero or one. There are two reasons for this. First, since the marginal increasein the output (from Hierarchy to Committee) is r (1r)(1), the benefit diminishes asr approaches either end. Second, as r approaches one, the freeriding incentive intensifies
and sharply increases the agency cost. Combined with Proposition 1, the result leads to a
sufficient condition for Hierarchy to be the optimal organizational form.

HI   and r is sufficiently close to zero or one.
Corollary 1 Hierarchy is optimal if 
We now explore conditions under which Committee becomes optimal. While Hierarchy
surely dominates Independent Production for a sufficiently small , the same statement cannot be made for Committee.
Proposition 3 Ifr(1r)2 > 4 ;there exists a threshold2
 CI = 1 +p

2 2 + r2 ;r2(1 r)CI  . Otherwise, Independent
such that Committee outperforms Independent Production for 
Production always outperforms Committee.
19

P ROOF: It follows from above thatC I = 2(1 )(1 r)(1r+(1r) r)(12(2 )(1 )(1r) 1)
= 4((1r(1 )(1+ r(1 r)(1 ):r)(1 )Note that this is strictly decreasing in , so that C

r(1

r)2 )

+ r(1

r)(1

)

I < 0 is least likely to hold at  = 0. Ifr)2 > 4 ;there exists a threshold below which Committee outperforms Independent Production; otherwise, Independent Production outperforms Committee for any . Committee outperforms
Independent Production if

r2 (1r)2 (1)2 + 4(1which can be written as

)(1

r)

4  0;p

2 2 + r2 :1   2 r+2(1r)
Q.E.D.
From propositions 2 and 3, we can now obtain a sufficient condition for Committee to be CH = 1, so that Committee outperforms Hierarchy
optimal. First, from proposition 2, lim !0 
for any . Second, from proposition 3,CI CIlim!0  = 0 := 1v(1 + r):r(1 r)The result implies that for any positive , Committee cannot be optimal if r is close to one.

CI
Corollary 2 Committee is optimal if 
0   and is sufficiently close to zero or one.
In general, Committee works better when the cost of information acquisition is relatively
small: this is intuitive because the cost of bilateral communication comes from the increase in
the agency cost. This means that if an organization does not need to motivate its members toacquire information, Committee is often an efficient way to make decisions. After all, this is20

what 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 isoften 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.

5 Conclusion
This paper asks why hierarchies prevail in organizations in an environment where the principal can only allocate responsibility via incentive contracts but not authority. The focus ofattention is placed on costly information acquisition and costless communication. In thissetting, we show that the optimal incentive scheme is often asymmetric, where one agent isgiven 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 this gives riseto the chain of command pertaining to hierarchial organizations. This asymmetric allocationof responsibility is the optimal way to acquire information and knowledge as a group when
the agency cost is sufficiently severe.

References
Aghion, Philippe and Tirole, Jean, 1997, Formal and Real Authority in Organizations, Journalof Political Economy, 105, 1-29.
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.
Dewatripont, Mathias and Tirole, Jean, 1999, Advocates, Journal of Political Economy, 107,
1-39.
Garicano, Luis, 2000, Hierarchies and the Organization of Knowledge in Production, Journalof Political Economy, 108, 874-904.

21

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, forthcoming in Journal of Economic Theory.
Hart, Oliver and Moore, John, 2005, On the Desing of Hierarchies: Coordination versus
Specialization, Journal of Political Economy, 113, 675-702.
Ishida, Junichiro and Shimizu, Takashi, 2009, Cheap Talk with an Informed Receiver, ISER
Discussion Paper No. 746, Osaka University.
Krishna, Vijay and Morgan, John, 2001, A Model of Expertise, Quarterly Journal of Economics,
116, 747-75.
Levy, Gilat, 2007, Decision Making in Committees: Transparency, Reputation and Voting
Rules, American Economic Review, 97, 150-68.
Li, Hao, 2001, A Theory of Conservatism, Journal of Political Economy, 109, 617-36.
Li, Hao and Suen, Wing, 2009, Decision-Making in Committees, forthcoming in Canadian
Journal of Economics.
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.
Sah, Raaj Kumar and Stiglitz, Joseph E., 1988, Committees, Hierarchies and Polyarchies,
Economic Journal, 98, 451-70.
Szalay, Dezsö, 2005, The Economics of Clear Advice and Extreme Options, Review of Economic
Studies, 72, 1173-98.

22

Appendix A: Proofs
P ROOF OF L EMMA 1: Provided that it is optimal to implement ei = 1, the principal’s problem
in the absence of communication is defined as

4 + (1 )(4r + (1 r)2) w11 + (1
min
i
W
4
r)2 00wi ;+ (1 )(14

)(2r(14ir) + (1r)2 )(wi10 + wi01)

subject to (3). It directly follows from (3) that wi01 = wi00 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 w
~i11, isw~i11 =

4 2rv :
r(1 + r)(1 )Similarly, a candidate contract under RPE, denoted by w
~i10, isw~i10 =

r(1

4

2rv :
r)(1 )RPE yields higher profit than JPE if

4 + (1)(4r + (1

4

r)2 )

(1

)(2r(1

r)2 )

 (1

)(2r(1(1r)  0:w~i11 4r) + (1r)2 )r) + (1rr)2 )w~i10 :

This can be written as

4 + (1)(4r + (1
1+r

1

;

which is further simplified toThis shows that RPE is generically better than JPE (the two are equivalent only when  = 0).
Q.E.D.

23

Appendix B: Other Contractual Arrangements
In the analysis, we examine only three contractual arrangements, which apparently do not
exhaust all the possibilities. Since there are two incentive conditions, one for informationacquisition (hereafter IA) and the other for truth telling (TT), there are more possible contract
forms. Since the condition for truth telling matters only when the condition for informationacquisition is satisfied, there are generically six possible contract forms.
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 of them
reports it truthfully. We refer to this situation as Delegated Hierarchy, since the flow of
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
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
when s^1 = . For communication to be meaningful, it is then necessary for agent 2 to follow
agent 1’s message when he is uninformed. Given that s^2 = , this condition can be written

24

as

re1w211 + (1re1 ) w211 + (1

 re1(w211 + (1)w201 ) + (1)

w211 + w200 2re1) w211 + (1)w210 + w201 ;

2which is simplified to(1 + re1)(w211

w201 )  (1re1 )(w210w200 ):(6)

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 + )w111 + (1 )w101
2(1+)w111 + (1 )w100+ (1 re1)(1 re2)21 (e1 ; e2 ) = re1w111 + re2 (1

re1)

e1 :

The agent exerts effort iff

w111

re2w101(1re2)w100 

2

r(1

)

:

A candidate contract is

w111 =

2 ; w10 = w01 = w00 = 0;1
1r(1 ) 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 + )w211 + (1 )w2102
1100+ (1 re2)(1 re1) (1 + )w1 +2 (1 )w1

2 (e2 ; e1 ) = re1w211 + re2 (1

re1)

e2 :

The agent exerts effort iff(1re1)(w210w200 ) 25

2 :r(1 )(7)

We have also assume that the agent has an incentive to differentiate, which means that

w210

w200 > w211

w201 :(8)

The optimal contract within this class must satisfy (6), (10) and (8). Since e1 = 1, all ofthese condition together imply

w210

w201 

w200 > w211

1 r (w10
1+r 2

w200 ) 2r(1 + r)(1):

A candidate contract is thus

w211 =

2r(1 + r)(1)

; w210 =

r(1

2

r)(1

)

; w101 = w100 = 0:

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 this arrangement, denoted by P , is+ ) 
2
P = 2r + r(1 r) + (1 r)(2 2 r)(1 + ) r + (1 r)(12
r(1 r)(1 )(1 r)(1 + )
2r(1 r)(1 )
2r+:
2r(1 + r)(1 )
2r(1 r)(1 )
Let the expected profit under each arrangement be decomposed into the expected output

Y k and the expected wage cost W k , such that k = Y koutperforms Partial Delegation if Y H
Delegation if Y C

W k , k = H; C; P . Hierarchy

W H  Y P W P while Committee outperforms Partial

WC  Y P

W P. Since

YC

YP =YP

YH =

r(1

r)(1

2

)

;

Partial Delegation cannot be optimal if 2W P  W C + W H , which can be written as

4(2r + (1 r)(1 + )) + 2  4 2(1 )(1 r)2 + 1 +  + r(1 ) :r(1 r)(1 + r)(1 )r(1 r)(1 )
r(1 )
With some algebra obtain

1  (1 + r)(4 2(1)(1r)2 ) + (1 r)(1 + r)(1 + )r(1 r)(1 + r)(1 )

26

8r 4(1r)(1 + ):which is further simplified to1  (1 + r)(3r(1 +2rr(1)(1 )) 1) 4 , (1 + r)2  (4r + r2 1):One can then easily verify that this condition holds for any  2 [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 s^1 = . 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 s^2 = , this condition
can be written as

re1w211 + (1re1 ) w211 + (1

 re1(w211 + (1))w201 ) + (1w210 + w201 2re1) w211 + (1)

w211 + w200 2;which is simplified to(1 + re1)(w211

w201 )  (1re1 )(w200w210 ):(9)

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 + )w111 + (1 )w101
22
w111 + (1 )(w110 + w101 )+ (1 re1)(1 re2)21 (e1 ; e2 ) = re1w111 + re2 (1

re1)

e1 :

The agent exerts effort iff

re2(w111

w101 ) + (1re2 )(2w111

w110

w101 ) 

2 :r(1 )

Since w110 + w101  w111 + w100 (the incentive to differentiate), a necessary condition for this isre2 (w111

w101 ) + (1re2 )(w11127

w100 ) 

2 :r(1 )

A candidate contract is

w111 = w110 =2 ; w01 = w00 = 0;
1r(1 ) 1

which also satisfies the condition for truth telling.
Similarly, the expected payoff for agent 2 is obtained as(1 + )w211 + (1 )w21022
w111 + (1 )(w210 + w101 )+ (1 re2)(1 re1)22 (e2 ; e1 ) = re1w211 + re2 (1

re1)

e2 :

The agent exerts effort iff(1

w201 ) re1)(w211

2 :r(1 )(10)

Since the condition for truth telling must not hold for agent 2, a candidate contract is

w211 = w210 =

r(1

2

r)(1

)

; w101 = w100 = 0:

These contracts are, however, clearly less profitable than the ones obtained in the previous
case, implying that Delegated Hierarchy is not optimal in this case.
Case 2-3. Both agents have the incentive to coordinate: The condition for informationacquisition is the same as in case 2-1. The condition for agent 1 is given by

w111

re2w101(1re2)w100 

2 :r(1 )

while that for agent 2 is(1

re1)(w210w200 ) 

2 :r(1 )

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 (6), so that the resulting profit must be lessthan that in case 2-1.
28

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 ) + (1re2 )(2w111

w101 ) 

w110

2

r(1

)

:

while that for agent 2 is

(1

w201 ) re1)(w211

2 :r(1 )

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 to differentiate. We can then consider the following strategy for each agent.
• When s^i 6= , mi = L or mi = R with equal probability (a babbling message);• When s^i = , mi = .
One can verify that neither agent has the incentive to deviate from this strategy. Under thisstrategy, the expected payoff, denoted by ~iI , is~iI (ei ; ej ) = r2 ei ej wi11 + rei (1rej ) wi11 ++ rej (1 rei) wi11 + (129)(wi11 + wi10 ) 2)(wi11 + wi01 ) + (1 rei)(1 rej ) wi11 + (1


(1

2

)(wi10 + wi01 ) 

2

ei :

The agent chooses to exert effort iff

wi11

2

wi01

 r(1

)

:

Since the agents must the incentive to differentiate, we must also havewi10 + wi01  wi11 + wi00 :The optimal contract within this class is hence

wi11 = wi10 =2 ; w01 = w00 = 0:ir(1 ) i

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 the expected output. Independent Production then dominates this if(r2 + r(1r)(1 + ) + (1r)2  +

(1

r)(1

)

2

) r(12 )  (1 +r r) ;which 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

~iI (ei ; ej ) = r2 ei ej wi11 + rei (1+ rej (1+ (1rei ) wi11 +rei )(1(1(1)( i + i ) rej ) wi11 +

w11

2



(1

w10
rej ) iwi00rej ) wi11 +)(wi11 + wi10 ) w01

2)(wi11 + wi00 ) 

2

ei :

The agent chooses to exert effort iff

w11
rej i

2

wi01

+ (1

2

 r(1

)

:

Since the agents must the incentive to coordinate, we must also satisfy (1). The principal’s
problem is then defined as

2r2 + (1 r2)(1 + ) w11 + r(1
min
i
W
2
r)2 00+ (1 )(1
wi ;
2
i

30

r)(1

2

)

(wi10 + wi01)

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 =2 ; w01 = w00 = 0:ir(1 ) i

which yields exactly the same profit as the one derived above (for the case where both agents
have the incentive to differentiate).

31