Centralized and Decentralized Contracts in a Moral Hazard Environment

CENTRALIZED AND DECENTRALIZED CONTRACTSIN A MORAL HAZARD ENVIRONMENT*

Ines Macho-Stadler{ and J. David Perez-Castrillo{

We study the optimal allocation of the contracting capacity in a moralhazard environment. Centralizing is superior when the principal is ableto establish all the contracts with the agents simultaneously and sheis able to monitor side contracting between the agents. Otherwise,decentralizing can be a superior strategy. We apply our results to a¢rm's decision on which outlets to franchise. They suggest thatfranchising is more likely to occur the further the store is fromheadquarters, the more isolated it is and in those activities where therisk is low. This conclusion is consistent with empirical studies.

i. introduction

The multiagent dimension of an organization makes the following twodecisions crucial for its e¤ciency. Firstly, the organization must decidewho will be responsible for each productive task. Secondly, it also has todecide who will be in charge of hiring (designing the contract of) eachparticipant. Assuming that the principal hires all the agents, HolmstrÎmand Milgrom [1991] analyze the optimal allocation of agents to di¡erenttasks depending on the possibilities for the principal to provide incentivesfor each task. Our paper contributes to the discussion of the comparativeadvantages of alternative hierarchical arrangements by analyzing thesecond aspect, that is the allocation of the contracting capacity, withinmoral hazard environments.

There are numerous situations where the allocation of the contractingcapacity is important. As a motivating example, the problem of whether to

ß Blackwell Publishers Ltd. 1998, 108 Cowley Road, Oxford OX4 1JF, UK, and 350 Main Street, Malden, MA 02148, USA.

489

THE JOURNAL OF INDUSTRIAL ECONOMICS 0022-1821Volume XLVI December 1998 No. 4

*We would like to thank Angel de la Fuente, Hugo Hopenhaym, Pau Olivella, twoanonymous referees and the editor Morten Hviid for helpful discussions and comments.Preliminary versions of this paper were presented at the 7 Jornadas de Econom|a Industrial,at the XI Meeting of ASSET, at the XVI Simposio de Analisis Economico, at the XI LatinAmerican Meeting of the Econometric Society, at the 2nd Meeting on Social Choice andWelfare and at seminars in Alicante, Madrid, Barcelona and Paris. We also acknowledge¢nancial support from the DGES under projects PB 92-0590 and PB96-1192 and theGeneralitat of Catalunya under project SGR96-75.{Authors' a¤liation: Ines Macho-Stadler, Departament d'Economia i d'Histo© ria

Econo© mica & CODE, Universitat Auto© noma de Barcelona, 08193 Bellaterra ^ Barcelona,SPAINemail: [email protected]{ J. David Perez-Castrillo, Departament d'Economia i d'Histo© ria Econo© mica & CODE,

Universitat Auto© noma de Barcelona, 08193 Bellaterra ^ Barcelona, SPAINemail: [email protected]

franchise or to establish divisions gives an idea of the possibilities of ouranalysis. A franchise agreement is a contractual arrangement between twoindependent parties, whereby the franchisee pays the franchisor for theright to sell the franchisor's product and to use his trademark. Somedecision rights, such as menu selection, building designs, etc. are usuallycentralized by the franchisor, while decision rights for hiring personnel,some local advertising, etc. are decentralized to the franchisee. Our theoryo¡ers an explanation for why some decision rights are decentralized.

Empirical papers (see, for example, Brickley and Dark, [1987], Norton,[1988], Brickley, Dark and Weisbach, [1991], and Lafontaine, [1992])provide support for the hypothesis that incentive issues are the drivingforce behind franchising. In particular, they highlight the fact that thelikelihood of franchising increases with the cost of monitoring employees.This seems to suggest that franchising is one solution to the problem ofproviding incentives for the store's manager. This conclusion is consistentwith agency theory, which shows that when employees are di¤cult tomonitor, they must be paid according to performance. But performance-related payments can be enforced inside the ¢rm as well through contracts.A franchising contract is more than a contingent payment mechanism.1

We relate the decision of whether to franchise to the moral hazardproblem faced by the company not only with respect to the manager's (orother employees') behavior, but also with respect to the behavior of theentire group of people working in the store.

Why is it the case that hiring decisions are decentralized to thefranchisee? Our results suggest that these decisions should be decentralizedwhenever it is not possible for the central company to monitor collusionamong employees in a store. It seems reasonable to assume that thiscollusion is easier to achieve the further the store is from the headquartersor the more isolated it is. It is indeed the case that the empirical analysesquoted above show that franchising appears more likely in more distantareas, in rural areas, and near freeways.2 Moreover, franchising is lessprevalent for companies where the initial investment cost per unit is high,which is also consistent with our result that decentralizing is more likelywhen the risk is low.

Our ¢ndings can also give some insight to the design of the optimalhierarchy for subcontractors of large ¢rms (see Section V), as is the casewith automobile manufacturers and textile or electronic ¢rms. Sub-contractors can be under the direct control of the buyer or the buyer can

1 For example, Lutz [1995] states that `there is therefore little reason to conclude on eithertheoretical or empirical grounds that the compensation o¡ered to employee managersnecessarily takes the form of a ¢xed fee; identifying franchising with share contracts isunconvincing' (p. 106).

2 Brickley and Dark [1987] and Brickley et al. [1991] ¢nd this last result surprising, whileit is consistent with our reasoning.

490 ines macho-stadler and j. david perez-castrillo

ß Blackwell Publishers Ltd. 1998.

deal only with some of the subcontractors and allow these to organizethe relations with the rest. Other examples where the allocation ofcontracting capacity is important are the relationship between the State,intermediaries and contractors, that of the owners of a ¢rm with itsmanagers and auditors and the one established between the centralmanagement and the di¡erent divisions of a ¢rm.

In order to present our results formally, consider a relationshipinvolving a principal and two agents. The principal can adopt either acentralized two-tier structure in which she hires both agents, or adecentralized three-tier structure in which she hires an agent who, in turn,employs the other one. We present our conclusions in two steps.

Suppose, ¢rst, that in centralized structures the principal o¡ers bothcontracts simultaneously. In this context, centralized structures aresuperior to decentralized ones. We identify exactly where the disadvantageof decentralized contracts lies: a decentralized structure is equivalent to acentralized structure where agents can reach monetary agreements onpayments that are contingent upon the outcome. In other words,decentralizing contracts is similar to allowing agent side-contracting,which implies e¤ciency losses.3

Assume now that the principal cannot design all the contractssimultaneously and cannot commit on the contracts that she will o¡er inwhat follows. Then, when the principal hires all the agents, but o¡erscontracts sequentially, the situation is equivalent to a centralized structurewith simultaneous contracts where coalitions between the principal andone agent are possible. That is, centralizing contracts are equivalent toallowing renegotiation between the principal and one of the agents. In thiscontext, either sequential centralization or decentralization can be optimal.Both imply an e¤ciency loss relative to the centralized organization withsimultaneous contracts.4 Hence, the optimal organizational structuredepends on which coalition would have a lower cost, which in turndepends on the agents' risk aversion and on the complementarity of theagents' tasks. In particular, decentralizing is never inferior to centralizingwhen the principal is not able to monitor (to forbid) side contractingbetween the agents.

Our analysis focuses on environments in which the main concern of theprincipal is to provide incentives to the agents for them to try hard, or to

3 For the sake of simplicity, the model considers the two-agent case. However, the resultsgeneralize to the case of more participants. In the n-agent case, decentralizing to Agent i thehiring of the set S of agents is equivalent to centralizing all the contracts in an environmentwhere the agents in S [ fig can reach monetary agreements.

4 This e¤ciency loss can be understood in terms of a moral hazard problem created by agroup. In sequential centralization the non-veri¢able behavior involves the principal and thesecond hired agent, while in a decentralized framework the non-veri¢able behavior of theagents creates a new dimension of moral hazard.

contracts in a moral hazard environment 491


take the right decisions. In other economic situations, the main purposeof the contracts is to elicit private information from the agents. Forexample, in regulatory situations where production costs are only knownby the ¢rm and not by the regulator, Myerson [1982] shows that, in theseadverse selection environments, any non-cooperative equilibrium outcomeof an arbitrary decentralized organization can be mimicked by acentralized one, where agents communicate their private informationdirectly to the principal without there being any interaction among them.This result is a generalization of the revelation principle and it impliesthat one can con¢ne one's attention to centralized organizations. Inaddition, Melumad, Mookherjee and Reichelstein [1995] show that bothorganizational structures are equivalent when, in the decentralizedstructure, the principal can make the payment to the intermediate agentcontingent on the contract set up between this agent and his/her partners.When this is not so, the centralized structure is strictly superior. Baronand Besanko [1992] analyze the optimal hierarchical structure in industrieswith several production phases, when the ¢rms have private informationrelating to their costs. They show that structures which concentrate alltasks on a single agent are superior. The advantage of centralization is dueto an e¤ciency argument: when the tasks are all carried out by a singleagent, the incentives to dishonestly reveal the costs of each of the phases isless since the fact that each announcement a¡ects the decision concerningthe other phase is taken into account. Finally, in a moral hazard modelwith limited liability, Baliga and SjÎstrÎm [1997] analyze when is itoptimal to delegate a contract from a given agent to another well informedagent.

The paper is organized as follows: in Section II we present the modeland the situation where, in a centralized structure, the principal o¡ers allthe contracts simultaneously. In Section III we analyze the decentralizedorganizations. In Section IV we deal with the situations in which theprincipal can only o¡er the contracts sequentially, not committing on thecontracts that she will o¡er to the next agent. In Section V, the comparisonbetween centralized and decentralized organizations is made, applyingthe results from the previous sections to the examples of the relationshipbetween a ¢rm and its subcontractors and the decision on franchising.Section VI concludes.

ii. the model and the benchmark.

Suppose that a principal is interested in hiring two agents, labelled 1 and2, to carry out two tasks. The monetary outcome of the agents' e¡ort isrepresented by a random variable x. For simplicity, we assume that x cantake N possible values, X � fx1; . . . ; xNg. Note that x may either representa pair of individual outcomes (in this case X � X1 �X2, where Xi



represents agent i's performance) or a joint outcome or the addition ofthe individual outcomes or a more complicated combination of the agents'performance.5 Let Pk�e1; e2� be the probability of observing the outcomexk conditioned on the e¡ort levels �e1; e2� 2P1�P2, where

Pi is the(possibly multidimensional) space of e¡orts for agent i. A contract foragent i, i � 1; 2, is a payment schedule wi�x� � wi � �wi

1; . . . ;wiN�.6 Agent i's

utility function is denoted by Ui�wi; ei�, and it is assumed to be increasingin the ¢rst argument and decreasing in the second.7 The agent'sexpected utility is given by EUi�wi; ei; e j� �PN

k�1 Pk�e1; e2�Ui�wik; e

i�. Agent i

accepts a contract if the expected utility it yields is larger than hisreservation utility Ui. The principal's utility function is denoted byV �x;w�. This function is increasing in the result and decreasing inthe agents' reward. The principal's expected utility is given byEV �x;w; e1; e2� �PN

k�1 Pk�e1; e2�V �xk;wk�. The assumptions include the casein which the principal maximizes the expected utility of her pro¢t, wherepro¢t is given by the di¡erence between the monetary outcome and thesum of the payments to the agents. It also applies to more generalsettings.

We will discuss the optimal allocation of the contracting capacity insuch a relationship.

De¢nition 1A centralized structure in this game is an organization in which Agents 1and 2 are hired directly by the principal. In a decentralized structure theprincipal hires one agent and lets him contract separately with the otheragent.

This de¢nition allows for two kinds of centralized structures. First, theprincipal can engage the agents simultaneously and second, she can engagethem sequentially. There are also two possible decentralized structuresdepending on the identity of the intermediary agent. This distinction ismeaningful since both agents can ful¢l di¡erent tasks, can have di¡erent adisutility cost or risk aversion and they also can have di¡erent outsideopportunities (summarized by the reservation utility).

We will use the centralized structure where the principal engages agentssimultaneously as a benchmark (this is the organizational structure usually

5 This model also takes into account the situations in which it is e¤cient from a technicalpoint of view that each agent puts some e¡ort for helping his colleague, as in HolmstrÎm andMilgrom [1990], Itoh [1991], or Macho-Stadler and Perez-Castrillo [1991], [1993].

6We do not consider more sophisticated schemes based on accusing reports and pleadingreplies (a© la Ma [1988]) that would take advantage of the connection between agents.

7 A concavity assumption is not necessary since we are not going to calculate the optimalcontracts but are going to compare the set of contracts satisfying the restrictions on di¡erentmaximization programs.



considered in the principal-multiagents literature). In this case, theprincipal simultaneously chooses the wage schemes, w1, w2 and, indirectly,the levels of e¡ort, e1, e2, that maximize her expected utility. She facestwo sets of constraints when designing the contracts: Participationconstraints which state that each agent's expected utility must be at leastequal to his reservation level; and Incentive Compatibility constraintswhich ensure that the agents have incentives to choose the e¡ort levelsdesired by the principal, given the payment mechanisms. Consequently,their contracts are the solution to program [PC�:

�PC�Max

�e1;e2;w1;w2�EV �x;w1 � w2; e1; e2�

s:t: EUi�wi; ei; e j� � Ui i; j � 1; 2; j 6� i;

ei 2 Arg maxa

EUi�wi; a; e j� i; j � 1; 2; j 6� i:

Note that the Incentive Compatibility constraints require the e¡ort levelsto be a Nash equilibrium of the e¡ort subgame played by the two agents.We assume, therefore, that each agent chooses his own e¡ort taking asgiven that of his colleague. This is the classical way of modelling asituation in which agents cannot choose e¡ort jointly, in a cooperativemanner. As we remark later, the absence of cooperation on e¡orts is not anecessary assumption.

In a relationship involving a principal and two agents, the only twopossible coalitional arrangements that can arise are the one between bothagents and the one between the principal and one of the agents.8 The ¢rstcoalitional arrangement is related to the opportunity for side-contractingbetween the agents that appears in many organizations. This opportunityis related to the presence of a personal relationship and reciprocity in thetreatment and can be based on monetary (bribes) or non-monetarycompensations (such as mutual help or a good atmosphere at the job). Thesecond one has more to do with the principal's ability to write all thecontracts simultaneously or with her capacity to commit on her futurebehavior when she is forced to engage the agents sequentially. Any of thesecoalitions can imply e¤ciency losses. The following de¢nition, adaptedfrom Tirole [1986], will be useful in identifying the advantages anddisadvantages of the di¡erent organizational structures:

De¢nition 2A coalition is a partnership of two participants, based on a side (cover)contract, signed after the main contracts but before the actions are taken.This contract speci¢es monetary transfers as a function of the veri¢able

8 Subgame perfection implies that there is no possible coalitional arrangement involvingthe principal and both agents.



outcome x. A coalition is formed by having an agent propose a sidecontract to the other agent, or a third party o¡ering the contract to theagents.9

Concerning the coalition that can be formed by the agents,HolmstrÎm and Milgrom [1990], Tirole [1992] and Itoh [1993], haveshown that the principal is never better o¡ when agents have thecapacity for obtaining side transfers. Monetary transfers are pro¢tablefor the agents (and costly for the principal) since they allow mutualinsurance, thereby inducing a distortion in the optimal arbitragebetween insurance and e¤ciency. Consequently, allowing for suchcoalitions can never be pro¢table. Concerning the coalitions between theprincipal and some agent, they are equivalent to a renegotiation of themain contracts before the actions are taken (or to a lack of commitmenton the side of the principal). In our framework, renegotiation can neverbe superior to commitment.10

iii. decentralized structure

In a decentralized structure the principal hires Agent 1 and lets himcontract separately with Agent 2. However, she predicts Agent 1'sproposed contract to Agent 2 when designing Agent 1's payment schedule.She knows that the contract Agent 1 o¡ers to Agent 2 must be optimalfor Agent 1. More precisely, let z�x� � z � �z1; . . . ; zN� denote thecontingent payment that Agent 1 receives from the principal andw2�x� � w2 � �w2

1; . . . ;w2N� the one Agent 2 receives from Agent 1.11 The

latter chooses this contract as well as his own e¡ort in order to solve�P�z��:

�P�z��

Max�e1;e2;w2�

EU1�zÿ w2; e1; e2�

s:t: EU2�w2; e2; e1� � U 2

e1 2 Arg maxa

EU1�zÿ w2; a; e2�e2 2 Arg max

aEU2�w2; a; e1�:

9 In our framework, there will not be any private information by the agents at the time theyform a coalition. This is the reason for the conclusions of our analysis to be the same whetherthe terms of the coalition are proposed by one of the agents or by a third party (for theadverse selection case, see for example Cremer [1996]).

10We do not consider the renegotiation that takes place after the actions have been taken.See Fudenberg and Tirole [1990].

11Note that the contract between the principal and the intermediate agent cannot dependon the contract signed between the agents afterwards. If such a `contract of contracts' couldbe signed, then the principal would have in fact the power to decide about both contracts.Therefore, a decentralized structure and a centralized structure would be equivalent.



This is a principal-agent program that determines the action of Agent 1(here he becomes `principal' with respect to Agent 2) and the contracto¡ered to Agent 2. Note that we have a two-sided moral hazard problem:Agent 1 hires Agent 2 and, at the same time, decides about his own e¡ortlevel in the relationship. Since this decision is not veri¢able, we ¢nd amoral hazard problem for Agent 1 (the principal in this program) thatadds to the moral hazard problem for Agent 2 (the agent).

Given the solution of the game between the two agents (by backwardinduction), the principal solves program �PD�:

�PD�Max�e1;e2;z;w2�

EV �x; z; e1; e2�

s:t: EU1�zÿ w2; e1; e2� � U 1

�e1; e2;w2� solves the program �P�z��:The principal chooses the contract o¡ered to Agent 1 subject to the

Participation and the Incentive Compatibility constraints. The Partici-pation constraint has the usual form. The Incentive Compatibilityconstraint includes, in addition to Agent 1's e¡ort, the contract that Agent1 o¡ers to Agent 2.

To compare the di¡erent programs, it is convenient to make thefollowing assumption:

Assumption 1The utility functions are such that the Participation constraints of bothagents are binding.

In particular, Assumption 1 holds if the utility functions are additivelyseparable on payment and e¡ort (the most usual assumption in moralhazard models) or if objective functions are ìn con£ict' (the Paretofrontier is decreasing).12

Proposition 1Under Assumption 1, in a moral hazard framework the following twosituations yield the same set of equilibria:

(i) a decentralized structure,(ii) a centralized structure where agents can collude.

ProofIn the Appendix it is shown that after some manipulations �PD� can bewritten as �PC� plus an additional constraint, that can be read as thepossibility for the agents to reach monetary agreements. Q.E.D.

12 Assumption 1 is useful because it allows us to derive quite clear-cut results. Most of theresults can be adapted to situations where it does not hold.



The fact that both agents' Participation constraints are binding issu¤cient to prove Proposition 1: independently of the way monetaryagreements between agents are reached (i.e., independently of the way thecoalition is formed), a decentralized structure is equivalent to a centralizedstructure in which these monetary agreements are possible. Note that in acentralized structure where agents can collude, the principal designscontracts such that there is no possibility for the agents' coalition to gain,and this is independent of the party in charge of the design of the sidecontract.

Of course, since decentralizing is equivalent to centralizing withadditional constraints, we have immediately:

Corollary 1Under Assumption 1, centralized organizations where participants cannotcollude are at least as e¤cient as decentralized ones.

Corollary 1 states that decentralization can never improve the outcomeof centralization. Given the equivalence established in Proposition 1, wecan measure exactly the loss in e¤ciency of decentralization with respectto centralization: decentralizing is as harmful as allowing agents' monetaryagreements. Moreover, Proposition 1 tells us when it is rational todecentralize from the principal's point of view. Decentralized structuresare equivalent to centralized ones in games where monetary agreementshave no value for the agents, or where these monetary agreements will bereached in any case. For example:

Corollary 2Under Assumption 1:

(a) If the principal cannot avoid agents' side-contracting, then theoutcome is the same should the principal delegate Agent 2's contractor not.

(b) A decentralized and a centralized structure where participantscannot collude are equivalent in any of the two following situations:(b1) agents are risk neutral;(b2) agents are identical, and the optimal contract assigns the same

payment in each contingency for both agents.

ProofIn Case (a) we have proven that a decentralized structure is equivalent toa centralized structure where the principal cannot avoid agents' sidecontracting. Moreover, it is easy to check that the possibility of agents'side contracting does not add any constraint to the decentralized program(as agents contract directly). Therefore, in this case decentralizing is



equivalent to centralizing. In neither of Cases (b1) or (b2) can an agents'coalition obtain positive pro¢ts, since either insurance plays no role orthere is no room for mutual insurance, and then from Proposition 1, bothorganizations are equivalent. Q.E.D.

When the optimal decentralized contract is di¡erent from the optimalcentralized contract, we can infer something on how to compare them.As we know, the objective of a coalition of the agents is to insure eachother. Hence, with monetary agreements we expect agents' paymentschemes to be more correlated than without collusion. This argument andProposition 1, suggest that a decentralized organization will tend toadopt more correlated payment schemes than a centralized one.

Moreover, identifying the nature of the disadvantage of decentralizationleads to another conclusion.

Corollary 3Under Assumption 1, if decentralization is enforced, the principal isindi¡erent about the identity of the agent to whom she delegates thecontract.

ProofImmediate from Proposition 1 and from the fact that the optimalcontract in a centralized structure where agents can collude is the sameindependently of who is the agent (or the party) responsible for thedesign of the side contract. Q.E.D.

This result is interesting in itself. Even if the agents are heterogeneous,the principal makes the same pro¢t independently of whoever ¢lls theintermediate level of the hierarchy. The meaning of this result is thefollowing: If the principal decides to decentralize or if she is forced to doit, then the existence of moral hazard problems does not matter in thechoice of the best intermediate agent. The optimal intermediate agent isdetermined independently from the existence of informational asymmetriesregarding agents' behavior.13 Moreover both the contract betweenprincipal and intermediate agent and the ¢nal payment schemes of theagents (once the second contract is set) are independent of the identity ofthe intermediate agent.

Let us make two comments on the generality of the results. Theframework considered in this Section is quite general with respect to theprincipal and agents' utility functions or the production technology. There

13Note that we are not claiming that the allocation of agents to tasks is indi¡erent but that,given the tasks agents are responsible for, who is in charge of hiring his colleague isirrelevant.



are, however, two assumptions whose role is important and must bediscussed: the nature of the game played by the agents and the number ofparticipants.

We prove Proposition 1 using the Nash assumption in the agents'Incentive Compatibility constraint. In fact, the result of Proposition 1 doesnot depend on this assumption. As long as the agents' behavior is assumedto be the same in both organizational structures, Proposition 1 holds.For example, if agents collude on their e¡ort levels and the nature of thiscollusion is the same in both organizational structures, Proposition 1holds. The same happens if one agent chooses his e¡ort before the otheragent, thus acting as the Stackelberg leader in the e¡orts' choice game.

Concerning the number of agents, our result can be generalized to morethan two agents. For these situations the following two structures areequivalent: (a) a decentralized three tier organization in which theprincipal delegates to one agent the contracts of the rest of agents, and (b)a centralized one in which monetary agreements involving all the agentscan be reached. Of course, as the number of agents increases, morecomplex organizational arrangements exist. We can also apply our resultto them. For example, consider a relationship involving one principal andthree agents. Take a four tier organization in which the principal delegatesto Agent 1 the other two contracts and Agent 1 in turn delegates toAgent 2 the contract with Agent 3. This hierarchy is equivalent to a threetier organization in which Agent 1 decides the Agents 2 and 3's contractsand in which monetary agreements between Agents 2 and 3 can bereached. Consequently, Corollaries 1 to 3 (and all the discussion in thisSection) remain valid for organizations involving more than two agents.

Finally, Proposition 1 allows us to make a comment on HolmstrÎm's[1982] seminal paper on moral hazard in teams. Imagine the organizationformed only by Agents 1 and 2 (a team, in HolmstrÎm's terminology).HolmstrÎm [1982] proves that the role of the principal is to break thebudget constraint of the team (in a game in which agents can no longerreach monetary agreements). This residual claimant argument can beunderstood in two steps. Firstly, the principal is useful since she acts as theresidual claimant for the whole relationship. This role can be performedeither through a centralized structure or through a contract signed withany of the agents (Proposition 1). In this sense, if agents have the ability toreach monetary agreements, adding a principal at the top of the team isequivalent to including her as the residual claimant of one of the agents.Secondly, when the principal can monitor any monetary agreement, thenshe can ful¢l the residual claimant role for each agent respectively andobtain a superior outcome (Corollary 1).

By now we have established the comparison between centralizedstructures with simultaneous contracting and decentralized organizations.Let us consider now the last possible case, the two-tier hierarchy where the



principal contracts with the agents sequentially (and she cannot commiton the way the whole relationship will be run).

iv. centralized structure when agents are engaged sequentially

Suppose now that, even though all contracts are designed by the principal,she signs them sequentially and without commitment. In thesecircumstances, is centralization still the superior choice?

In a centralized organization with sequential contracting, the principal¢rst signs the contract with Agent 1 and then makes an o¡er to Agent 2.Notice that this second contract determines not only Agent 2's incentives,but also, through the choice of e2, it sets Agent 1's incentives and expectedutility.14 The principal chooses Agent 2's contract in order to solve �P�w1��:

�P�w1��

Max�e1;e2;w2�

EV �x;w1 � w2; e1; e2�

s:t: EU1�w2; e2; e1� � U 2

e1 2 Arg maxa

EU1�w1; a; e2�e2 2 Arg max

aEU2�w2; a; e1�:

��

The principal designs the contract for Agent 1 taking into accountthat the contract for Agent 2 will depend on it, that is, she solves theprogram �PC0 �:

�PC0 �

Max�e1;e2;w1;w2�

EV �x;w1 � w2; e1; e2�

s:t: EU1�w1; e1; e2� � U 1

e1 2 Arg maxa

EU1�w1; a; e2��e1; e2;w2� solves the program �P�w1��:

��

In Proposition 2, we present the comparison between �PC0 � and thebenchmark, that is, a centralized structure with simultaneous contracts.

Proposition 2Under Assumption 1, in a moral hazard framework, the following twosituations yield the same set of equilibria:

(i) a centralized structure with sequential contracting (¢rst Agent 1'scontract, then Agent 2's).

(ii) a centralized structure (with simultaneous contracting) where theprincipal and Agent 2 can collude.

14We assume that Agent 1 cannot break the contract once signed. If he could do so, andthe contract between the principal and Agent 2 was veri¢able and not renegotiable, then thesequentiality of the contracts would not imply any ine¤ciency.



Proof�PC0 � includes two Incentive Compatibility constraints for Agent 1: ��and ��. The second one, however, is redundant since it is implied bythe ¢rst one. Therefore, the program �PC0 � can be understood asdescribing a relationship between a principal and two agents in which acoalition between the principal and Agent 2 is possible, the principalmaking a take-it-or-leave-it o¡er to Agent 2. Note however that, underAssumption 1, the solution to program �P�w1�� is the same if we weremaximizing Agent 2's expected utility EU2�:� subject to the constraintthat EV �x;w1 � w2; e1; e2� � EV �x;w1 � w2; e1; e2�. That is, �PC0 � also char-acterizes the optimal contract when a coalition is possible in whichAgent 2 can make a take-it-or-leave-it o¡er to the principal. The sameis true if a third party can o¡er a contract to the principal and to Agent2. Therefore, �PC0 � de¢nes the optimal renegotiation-proof (vis-a© -visAgent 2) simultaneous centralized contracts. Q.E.D.

The following corollary follows easily from Proposition 2:

Corollary 4Under Assumption 1, if collusion between the principal and Agent 2cannot be avoided, then a centralized structure with sequential contractingwhere Agent 1 is hired ¢rst is equivalent to a centralized structure withsimultaneous contracting.

The sequentiality of contracting in a centralized structure, therefore,implies an e¤ciency loss with respect to centralized contracts which areentered simultaneously. This is so because the optimal contracts in a simul-taneous centralized organization are not necessarily renegotiation-proof. Ina renegotiation of Agent 2's contract the principal could lower Agent 1'sexpected utility through the distortion of Agent 2's contract. Proposition 3gives precise conditions under which this intuition is true. It is stated undertwo additional assumptions, classical in the multi-agent literature.

Assumption 2The e¡ort ei takes on a value in R�, for i � 1; 2. The functions Ui�wi; ei�,V �x;w�, and Pk�e1; e2� are C1 in their arguments, for i � 1; 2 andk � 1; . . . ;N.

Assumption 3(i) The ¢rst-order approach applies, and (ii) the solution �e1c; e2c;w1c;w2c�to �PC� is characterized by the First-Order Conditions of its Lagrangean.15

15 For example, Itoh [1991] states su¤cient conditions for Assumption 3 to hold in multi-agent situations where each agent allocates his e¡ort to various production activities.



Proposition 3Under Assumptions 1 to 3, the contract �e1c; e2c;w1c;w2c� solution to �PC�is also the solution to �PC0 � if and only if:

@EU1

@e2�e1c; e2c;w1c;w2c� � 0:

ProofSee the Appendix. Q.E.D.

The optimal contract in a simultaneous centralized organization isrenegotiation-proof (with respect to the contract between the principal andAgent 2), if and only if Agent 2's e¡ort does not a¡ect Agent 1's expectedutility, evaluated at the optimal contract. This is so because in the solutionto �PC� the principal takes into account all the cross-in£uences betweenagents, while in �PC0 � she does not worry about Agent 1's utility, since thisAgent is already bound by a contract. The e¡ort e2 does not enter directlyin EU1. However, it enters into the probability of reaching the di¡erentoutcomes, Pk�e1; e2�. Therefore, the level of e2 in£uences EU1 as long as itchanges the probability that Agent 1 gets a higher or lower salary becauseof the changes in the probability of the occurrence of the di¡erentoutcomes.

The element that plays an important role in the determination of thee¤ciency loss in �PC0 � with respect to �PC� is the relationship (thecomplementarity or the substitutability in the output production) betweenthe e¡orts of the agents. To explain this, consider the following situation.Imagine each agent is a worker in charge of a certain job. The set of resultsX is in this case the Cartesian product of two sets X1 and X2 (seeMookherjee [1984] and Macho-Stadler and Perez-Castrillo [1993] for ananalysis of the optimal contracts in this situation). Consider ¢rst the casein which each agent's e¡ort does not in£uence the outcome of hiscolleague's job (or, more generally, that an agent's outcome does not addinformation concerning the other agent's e¡ort). In this case, it is optimalto pay each agent only in relation to his own performance. That is, thesalary of Agent i only depends on the results in Xi. In this case, increasing(or decreasing) Agent 2's e¡ort does not change Agent 1's expected utility.Therefore, the condition in Proposition 3 holds, and the optimal contractin a simultaneous centralized organization is renegotiation-proof, i.e. it isalso optimal in a sequential centralized organization.

In many other cases, however, an agent's e¡ort not only determines hisoutcome, but also strongly in£uences the colleague's performance. Forexample, it can be the case that an increase in Agent i 's e¡ort increases thelikelihood of a good outcome for Agent j 's. For these situations, theoptimal solution to �PC� establishes that each agent's pay should be a



function of the results of both X1 and X2. The better the result in Xi, thebetter will both agents be paid (when an increase in Agent i 's e¡ortdecreases the likelihood of Agent j 's performance being good, then anagent's pay should be directly related to his own performance, butinversely to his colleague's). Therefore, the condition in Proposition 3 doesnot hold: a change in Agent 2's e¡ort modi¢es the probability of the resultsin both X1 and X2 and consequently also the expected utility of Agent 1.The preceding case is not the only one in which the sequentiality of the

contracts introduces distortions. For example, in joint productionprocesses the same phenomena appear. In these production processes,every agent is paid as a function of the joint set of outcomes and an agent'se¡ort in£uences both his own wage and the colleagues'. Indeed, the moreinterrelated the agents' e¡orts are (i.e. the higher in absolute value@EU1=@e2 is), the higher the loss in e¤ciency introduced when contractingis sequential.

It must be noted that in the case of centralized structures with sequentialcontracts we cannot obtain a result which is parallel to Corollary 3. In thiscontext, it matters which agent signs the ¢rst contract, because thecoalition between the principal and one of the agents can be more harmfulthan that between the principal and the other agent. In order to make thisclear, imagine a relationship in which Agent 1's decision in£uencesAgent 2's task, but the reverse does not hold (for example, becauseAgent 1's decision concerns the cost of each unit of Agent 2' productivee¡ort). Then, hiring Agent 1 ¢rst will lead to the same outcome as acentralized structure with simultaneous contracts, whereas if Agent 2 isengaged ¢rst, the outcome will be strictly inferior. Given that the principalis the residual claimant of the relationship, the previous discussion givesus another conclusion: if the principal engages two agents and cannotengage them simultaneously, she will engage ¢rst the agent against whomthe coalition between the principal and the other agent implies a lowerdamage.

v. some applications to the subcontracting or franchising decision

The previous analysis allows us to discuss the relative advantages ofcentralized and decentralized structures in an organization which is subjectto moral hazard. The question of whether centralized sequential con-tracting is preferable to a decentralized structure on e¤ciency groundsreduces to the analysis of, ¢rstly, which coalitions can be avoided and,secondly, which coalition would imply the lower cost in a centralizedorganization with simultaneous contracting: one between the agents, orone between an agent and the principal. Let us take the examples of therelationship between a ¢rm and its subcontractors and the decision on



franchising (which we already discussed in the introduction) to illustratepotential applications and predictions of our results.16

Subcontractors can be organized in a single tier, all of them under thedirect control of the buyer or in a multiple tier structure in which thebuyer deals directly with some of the (¢rst-tier) subcontractors who inturn control second-tier contractors.17 The ¢rst message of our paper isthat if the ¢rm is able to establish all the contracts with its sub-contractors simultaneously and it can commit to not renegotiate them,centralizing is never inferior to decentralizing. Moreover, if the ¢rm isable to control side contracting among its subcontractors, centralizing isgenerally strictly superior. However, it seems that it would be di¤cult fora large ¢rm with a large number of subcontractors to ful¢l the twopreceding conditions.

When it is not possible for the ¢rm to sign all the agreementssimultaneously, the choice of the optimal hierarchy of subcontractorsinvolves a trade-o¡. Let us consider a situation in which no coalitionbetween subcontractors or between the ¢rm and any subcontractor, islikely. Then, our second message is that we should expect decentralizedcontracts in situations where potential side contracting between thesubcontractors would have not implied an important e¤ciency loss. Thisshould be the case when the environment is not very risky, the subcontrac-tors are not very risk averse or the environments in which the subcontrac-tors work are very correlated (so there is no room for mutual insurance).The empirical implication is that the bigger the subcontractors, the morebuyers they have or the more similar the uncertainty they face, the morewe should see decentralized hierarchies.

Also, when a ¢rm requests that the subcontractors perform closelyrelated tasks, decentralizing is its optimal strategy. The reason is thatwhen the tasks are closely related, the modi¢cation of one contracta¡ects the e¡ort each other subcontractor has to o¡er or the expectedpayment he receives. Therefore, we should expect decentralization for

16We only concentrate on the incentive provision aspect. Obviously, other approaches(e.g. transaction costs, bounded rationality, incomplete contracting, and specialization gains)also provide important contributions for the analysis of alternative internal structures (seeKeren and Levhari [1989], Marschak and Reichelstein [1990], and Sah and Stiglitz [1986], tocite a handful of the relevant works). In the example of subcontractors, decentralizing allowsthe ¢rm to lower the costs of acquiring and processing information when the boundedrationality of the buyer and the subcontractors makes communication without costs or noisesimpossible (see Melumad, Mookherjee, and Reichelstein [1995]).

17Many production processes, such as car manufacturers or builders, share this structureof subcontractors. Japanese car manufacturers are good examples of decentralized networksof subcontractors. Aoki [1988] reports that a Japanese prime manufacturer (possibly Toyota)had in 1977 direct relations with 122 ¢rst-tier suppliers and indirect relations with 5,437second-tier suppliers and 41,703 third-tier suppliers. On the other hand, US car manu-facturers use a very centralized structure of contracts. For instance, in 1986 GM dealt directlywith 35,000 suppliers (see Asanuma [1992]).



subcontractors ful¢lling a related task, while centralization of thecontracts should be the usual pattern when the subcontractors performunrelated tasks.

Thirdly, when the ¢rm is not able to monitor (to forbid) side contractingbetween subcontractors, decentralizing is never inferior to centralizing.Side contracting between subcontractors is easier to implement when theyenter often into a relationship with each other. This suggests a directrelationship between the frequency of the interaction between subcontrac-tors (working either for this ¢rm or for other ¢rms) and the degree ofdecentralization. It is indeed the case that Japanese car manufacturers,which establish more stable relationships with their subcontractors thando American car manufacturers, are more decentralized.

Fourthly, if coalitions between the ¢rm and one subcontractor cannotbe avoided, then centralizing is never inferior to decentralizing. Therefore,we should not expect to see decentralization in those relationshipsinvolving one subcontractor which is closely related to the ¢rm. This is thecase, for example, if the ¢rm owns a large part of the shares of thesubcontractor or if the ¢rm and this subcontractor are linked by othercontracts.

Finally, in a moral hazard environment in which all the coalitions arepossible, then all the possible organizational structures are equivalent.This means that in the economic situations where any subset of partnershas the opportunity to collude, from the incentive provision perspective,the e¤ciency of the relationship is independent of the organizationalstructure.

As we have pointed out in the introduction, it is possible to extend theprevious conclusions of the subcontractors example to franchising and theempirical analyses quoted there are consistent with our theoretical¢ndings. Moreover, our analysis can also shed some light on the empiricalphenomenon of individual franchisees and the franchisor, owning not justone but several units of the chain.

vi. conclusion

The study of the choice of organizational structures is fundamental tounderstanding the ¢rm's e¤ciency. Depending on the characteristics of therelationship involved, some structures can be highly e¤cient, whilethe same organizational structure can be signi¢cantly de¢cient whenerroneously adopted in an adverse environment.

We show that there is a clear relationship between, on the one hand,the relative advantages of centralizing and decentralizing contract designand, on the other hand, the study of the negative e¡ects of the di¡erentcoalitions which may arise in an organization. Any decision about organiz-



ational design determines the room that individuals and groups have foradopting opportunistic behavior. Understanding these e¡ects is important.For example, in a centralized structure of subcontractors each of themmay fear that any new contract (or any modi¢cation of existing contracts)makes his task more di¤cult or lowers his expected pay-o¡. Decentralizingmay alleviate this problem.

Let us stress some practical guidelines to organizational design whichare implied by our results. Which are the circumstances that push towarddecentralizing? First of all, decentralizing is optimal when it is not possible(or it is very expensive) to monitor coalitions between agents while it iseasy to avoid coalitions between the principal and any agent. Therefore,the distance between the places where the work is done and where theprincipal is situated, for example, should be positively related to the degreeof decentralization. Secondly, in those situations where coalitions of anytype can be avoided, decentralizing involves the same cost as allowingcoalitions between agents. Therefore, the degree of decentralization shouldbe positively related to the risk neutrality of the agents (i.e., to their sizeor to the number of other buyers, when the relationship concerns acontractor with his subcontractors). Thirdly, centralized sequential con-tracts without a commitment on the whole sequence of contracts are veryharmful when the output of the agents is joint work or when the agentswork in separated tasks but are subject to very correlated risks. Therefore,we should ¢nd an indirect relationship between the degree of decentraliza-tion and the possibility of obtaining individual and uncorrelated measuresof agents' e¡orts.

The preceding arguments can also be applied to the discussion on theadvantages and disadvantages of vertical integration, if by integration wemean a procedure allowing the buyer to gain control over all the contractsinside the other ¢rm.18 Centralizing can be interpreted as integratingvertically. Hence, a non-integrated structure is superior under thosecircumstances under which decentralizing is preferred.

As Williamson [1989] states, one of the main purposes of studyinginternal organization is to better understand the comparative e¤ciency ofinternal governance processes for attenuating opportunism. The mainmessage of this paper is that decentralizing contracts allows the avoidanceof opportunistic behavior stemming from alliances between the principaland agents, while centralizing contracts avoids opportunistic behaviorcoming from agents' coalitions.

ACCEPTED FEBRUARY 1998

18 Several situations are classi¢ed under the term vertical integration (see, Porter [1991]).



appendix

Proof of proposition 1:In order to compare �PD� with the program of a centralized organization, we usethe following notation. We separate the payment scheme z into two schedules, w1

and w2 with z � w1 � w2. We can interpret this as the principal paying z contingenton the result and `suggesting' to Agent 1 the way in which he can share this amountwith Agent 2. Obviously this is just a suggestion, since w2 is decided by Agent 1.�PD� can then be written as:

�PD�Max

�e1;e2;w1;w2�EV �x;w1 � w2; e1; e2�

s:t: EU1�w1; e1; e2� � U 1

�e1; e2;w2� solves the program �P�w1 � w2��PC1�

where �P�w1 � w2�� is:

�P�w1 � w2��

Max�e1;e2;w2�

EU1�w1 � w2 ÿ w2; e1; e2�

s:t: EU2�w2; e2; e1� � U 2

e1 2 Arg maxa

EU1�w1 � w2 ÿ w2; a; e2�e2 2 Arg max

aEU2�w2; a; e1�:

�PD� requires Agent 1's Participation constraint �PC1� to be ful¢lled at �e1; e2;w1�.Note that this vector is the solution to �P�w1 � w2��. Let us denote �PD�� as theprogram in which Agent 1's Participation constraint is considered as a constraintin Agent 1's maximization program, that is,

�PD��Max

�e1;e2;w1;w2�EV �x;w1 � w2; e1; e2�

s:t: �e1; e2;w2� solves the program �P��w1 � w2��;where:

�P��w1 � w2��

Max�e1;e2;w2�

EU�w1 � w2 ÿ w2; e1; e2�

s:t: EU1�w1 � w2 ÿ w2; e1; e2� � U 1

EU2�w2; e2; e1� � U 2

e1 2 Arg maxa

EU1�w1 � w2 ÿ w2; a; e2�e2 2 Arg max

aEU2�w2; a; e1�:

�PC1��

Lemma 1. �PD� and �PD�� are equivalent.

Proof. Denote B and B� the set of feasible contracts in �PD� and �PD�� respectively,i.e.

B � f�e1; e2;w1;w2�nEU1�w1; e1; e2� � U 1; and �e1; e2;w2� 2 Argmax �P�w1 � w2��g;B� � f�e1; e2;w1;w2�=�e1; e2;w2� 2 Argmax �P��w1 � w2��g:



We show that B � B�, which implies that the two programs are equivalent.Firstly, take �e1; e2;w1;w2� 2 B, that is, �e1; e2;w2� 2 Argmax �P�w1 � w2�� and thecontract satis¢es �PC1�. Therefore, it also ful¢ls �PC1�� in program �P��w1 � w2��.Notice that [P��w1 � w2�� coincides with �P�w1 � w2�� but with the additionalconstraint �PC1��. If a solution to �P�w1 � w2�� satis¢es �PC1��, it is also a solutionto �P��w1� w2��. Hence, �e1; e2;w2�2Argmax �P��w1 � w2��, and �e1; e2;w1;w2�2B�.Secondly, take �e1; e2;w1;w2� 2 B�, i.e. �e1; e2;w2� 2 Argmax �P��w1 � w2��.

In particular, �e1; e2;w2� ful¢ls �PC1�� in �P��w1 � w2��, which implies that�e1; e2;w2� ful¢ls �PC1�. Now, suppose by contradiction that �e1; e2;w2� 62Argmax �P�w1 � w2��. That means that there is �e10 ; e20 ;w20 � satisfying theconstraints in �P�w1 � w2�� and such that EU1�w1 � w2 ÿ w20 ; e1

0; e20 � >

EU1�w1; e1; e2� � U 1. Then �e10 ; e20 ;w20 � does ful¢l �PC1��, so it satis¢es everyconstraint in �P��w1 � w2��. This contradicts that �e1; e2;w2� maximizes�P��w1 � w2��. Therefore, we have proven that �e1; e2;w2� ful¢ls �PC1� and that�e1; e2;w2� 2 Argmax �P�w1 � w2��, i.e. �e1; e2;w1;w2� 2 B. Q.E.D.

Using the notation w1 � w1 � w2 ÿ w2, we can rewrite �PD�� as follows:Max

�e1;e2;w1;w2�EV �x;w1 � w2; e1; e2�

s:t: �e1; e2;w1;w2� solves the program �Q�

where �Q� is the program:

�Q�

Max�e1;e2;w1;w2�

EU1�w1; e1; e2�

s:t: EUi�wi; ei; e j� � Ui i; j � 1; 2; j 6� i

ei 2 Arg maxa

EUi�wi; a; e j � i; j � 1; 2; j 6� i

w1 � w2 � w1 � w2:

This program corresponds to a centralized structure in which the principaldesigns the two contracts. However, once she has made her o¡ers, Agent 1 canpropose to Agent 2 a monetary agreement contingent on the outcomes. This isre£ected in the fact that Agent 1 maximizes his utility under the constraint that, ineach contingency the sum of the salaries has to be equal to the total amount o¡eredby the principal, taking into account the two incentive constraints. The principalo¡ers coalition-proof contracts, that is, contracts such that Agent 1 cannotimprove his utility (and guarantee Agent 2 his reservation utility level) through acoalition.Under Assumption 1, the Participation constraints of both agents are binding.

This implies that the solution to program �Q� is independent of the objectivefunction being EU1, EU2 or any combination of both functions. This means thatthe solution of the program is the same if we have Agent 2 proposing a sidecontract to Agent 1 or if a third party o¡ers the contract to the agents thatparticipate in the coalition. The only elements that characterize the solution to �Q�are the constraints, not the objective function of the program. Q.E.D.



Proof of Proposition 3:Denote Y c � �e1c; e2c;w1c;w2c� an interior solution to �PC�. Because the ¢rst-orderapproach is assumed to hold, the Incentive Compatibility constraints in �PC� can bewritten as: @EUi=@ei�e1; e2;w1;w2� � 0.The contract Y c is also a solution to �PC0 � if and only if �e1c; e2c;w2c� is a solution

to �P�w1c��. Notice that programs �P�w1c�� and �PC� coincide but for the Agent 1'sParticipation constraint. Program �PC� is subject to this constraint, while �P�w1c�� isnot. Moreover, as Y c is solution to �PC�, it is also true that �e1c; e2c;w2c� is asolution to �PC� once w1 is set at its optimal level w1c. Therefore, �e1c; e2c;w2c� is asolution to �P�w1c�� if and only if Agent 1's Participation constraint does not matterin �PC� once w1c is ¢xed. If we denote the Lagrangean multipliers of the Agent i 'sParticipation and Incentive Compatibility constraints as li and mi respectively, theFOCs of �PC� with respect to e1; e2;w2

1; . . . ;w2k; . . . ;w2

N, which are satis¢ed in theoptimal vector �e1c; e2c;w2c�, are:

@EV

@e1�Y c� � l1

@EU1

@e1�Y c� � l2

@EU2

@e1�Y c� � m1

@2EU1

�@e1�2 �Yc� � m2

@2EU2

@e2@e1�Y c� � 0;

@EV

@e2�Y c� � l1

@EU1

@e2�Y c� � l2

@EU2

@e2�Y c� � m1

@2EU1

@e1@e2�Y c� � m2

@2EU2

�@e2�2 �Yc� � 0;

@EV

@w2k

�Y c� � l1@EU1

@w2k

�Y c� � l2@EU2

@w2k

�Y c� � m1@2EU1

@e1@w2k

�Y c� � m2@2EU2

@e2@w2k

�Y c� � 0;

for j � 1; . . . ;N. Under assumption 1, l1 > 0. Moreover, the FOCs of �P�w1c��coincide with the FOCs of �PC�, except that the ¢rst do no include the terms with l1

(since �P�w1c�� is not subject to Agent 1's Participation constraint). Notice that,¢rstly, @EU1=@e1 �Y c� � 0 because it is precisely the Agent 1's IncentiveCompatibility constraint, and secondly, @EU1=@w2

k �Y c� � 0 for k � 1; . . . ;N, sinceAgent 1's utility function does not depend on Agent 2's wages. Therefore,�e1c; e2c;w2c� is also the solution to �P�w1c�� if and only if the term that multiples l1

in the FOC with respect to e2 is zero, that is, @EU1=@e2 �Y c� � 0. Q.E.D.

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Centralized and Decentralized Contracts in a Moral Hazard Environment