1、Multi-Contracting Mechanism Design1David MartimortAbstractMulti-contracting practices prevail in many organizations be they public (govern-ments) or private (markets). This article surveys the literature on common agency,a major example of such multi-contracting settings. I first highlight some spec
2、ificfeatures of common agency games that distinguish them from centralized contract-ing. Then, I review the tools needed to describe allocations which are implementableas common agency equilibria. Economic examples are used to characterize equilib-ria under both complete and asymmetric information.
3、Particular focus is put onthe multiplicity problem and the (interim) efficiency properties of those equilibria.The comparison of those equilibria with the outcomes achieved under centralizedcontracting allows us to assess the transaction costs of multi-contracting. I alsoargue that, in some specific
4、 contexts, common agency may implement the optimaloutcome that would be achieved under centralized contracting if collusion betweenagents were an issue. More generally, common agency might outperform centralizedcontracting when either collusion or limited commitment matters.Keywords: Multi-Principal
5、s, Common Agency, Mechanism Design, Transaction Costs.1 IntroductionIncentive Theory is by now a mature field that has deeply changed our view of organiza-tions and markets over the last thirty years or so. In the conceptual framework proposedearly on by Hurwicz (1972) and largely inspired by the pl
6、anification literature, the wholeeconomy is ruled by a single (or complete) grand-contract. Within this framework, de-centralized information and strategic behavior by informed agents at the periphery of theorganization can easily be handled by means of simple incentive constraints that fullydescrib
7、e the set of feasible allocations available under asymmetric information. Onceequipped with the Revelation Principle,2 modelers are able to describe the feasible set1I benefitted of many discussions on the topic of this lecture and on related issues with several coau-thors, among which Antoine Faure
8、-Grimaud, Marc Ivaldi, Fahad Khalil, and Humberto Moreira. Specialthanks of course to Lars Stole whose collaboration has shaped much of my views on multi-contractingmechanism design. Vianney Dequiedt, Denis Gromb, Jerome Pouyet, Wilfried Sand-Zantman and AggeySemenov kindly provided comments on an e
9、arlier version. I was lucky to discuss many of the ideas de-veloped below with Jean-Jacques Laffont. Many thanks to Thomas Palfrey for his useful discussion atthe 2005 World Congress of the Econometric Society and to Torsten Persson for his comments.2Gibbard (1973), Green and Laffont (1977), Dasgupt
10、a, Hammond and Maskin (1978) and Myerson(1979).1and assess the performance of an organization with a given objective function. The anal-ysis can then proceed to determine the properties of the optimal contract chosen by aplanner running this organization. Finally, one may also investigate the mechan
11、isms thatcan be used to implement this outcome in practice.This modelling framework is useful to understand how simple organizations and mar-kets evolve in isolation from any external influence. Economists agree to recognize thata convenient set of modelling tools and theorems is now available to de
12、scribe the simplecontractual relationship between a buyer and a seller or between a regulator and regu-lated firms. We are also confident that the theory of auctions is a well-established bodyof literature which explains in details one of the most basic resource allocation problem.Despite these succ
13、esses, Incentive Theory has repeatedly being subject to criticismscoming from various horizons. The first line of criticisms is external to the field and can bebest summarized by the view held by some sociologists who argue that Incentive “Theoryassumes that social life is only a serie of contracts”
14、.3 In my view, the discomfort of othersocial scientists towards Incentive Theory stems in part from the fact that it most ofteneither focuses on the microeconomic bilateral relationship within a single principal-agentpair taken in isolation or, at the other extreme, it embraces the whole economy wit
15、hin asingle grand-contract. By taking these two polar views, Incentive Theory fails to providean intermediate perspective on the interactions between organizations and markets whichare the focus of organizational theorists coming from other fields of social sciences.The second line of criticisms is
16、internal to economic theory. It comes from our skep-ticism towards the grand-contracting approach which puts excessive emphasis on thecompleteness of the contract. Indeed, one of the most basic assumptions underlying theRevelation Principle is what Palfrey (1992) coined as the control assumption. Th
17、is as-sumption stipulates that the planner can control all communications that agents of theorganization can undertake. When such control is not feasible, the economy can no longerbe ruled by a single mechanism but by complex interactions among multiple mechanismdesigners. In this context, contracts
18、 are necessarily incomplete in the sense that theycannot prevent an agent from contracting with other principals. Any departure fromthe outcome that could have been achieved under centralized contracting can then beassociated to this incompleteness. The difference between the outcomes with and with-
19、out centralized contracting gives us a measure of the corresponding transaction costs.3This is a quote from one of the leading organizational theorists, Perrow (1986, Chapter 7, p. 224).2Such analysis is a first step towards some comparative analysis showing how differentcontractual and organization
20、al forms might reduce those transaction costs.This survey covers a body of literature which has studied interactions among mecha-nism designers with an emphasis on common agency, a major example of multi-contracting.Under common agency, several principals contract with a common agent to influence hi
21、sdecision-making. This setting is relevant to discuss the organization of the firm as anexus of contracts linking its management with various stakeholders be they shareholders,lenders, regulators, customers and suppliers. It also helps understanding the organiza-tion of the government as a collectio
22、n of legislative committees, bureaus and regulatoryagencies which do not necessarily cooperate. Section 2 provides more examples.Ideally, a complete survey of multi-contracting should also cover hierarchical contract-ing, competition between hierarchies and collusion within organizations. Space cons
23、traintsmean that I will only incidentally touch on those issues in passing. I will also focus on ad-verse selection and put aside moral hazard issues despite their importance. Nevertheless,common agency already offers a nice overview of some of the theoretical inquiries thatthe analysis of multi-con
24、tracting environments requires. Those inquiries can be classifiedas follows. On the positive side, one can take as given the existence of multi-contracting structures4and ask the following questions. What is the set of mechanisms available to competingprincipals? Which allocations are implementable
25、as contract equilibria? How much wel-fare is lost absent centralized contracting? Do we get a measure of the transaction costsassociated with multi-contracting? In a more normative perspective, and given that multi-contracting prevails both withinand across organizations, one may look for some ratio
26、nale behind those structures. Sincecentralized contracting internalizes the contractual externalities that arise under multi-contracting, the difficulty consists then in proving the latters optimality or, at least, itsgood performances in specific contractual environments which are necessarily const
27、rainedin some way to limit the benefits of centralized contracting.Much of the research in the field has focused on the first issues. These efforts arecovered in Sections 3 to 5 below. Much less effort has been devoted to the more normative4For instance, competing regulatory agencies may receive the
28、ir mandates at different points in time orfrom different governments and the allocation of powers among them is a consequence of either historyor geography. Anti-trust policies may also preclude centralized contracting between competing retailersand their common manufacturer.3issues which are addres
29、sed in Section 6. Section 7 briefly concludes and proposes alleysfor further research.2 Examples and Modelling IssuesI shall start by presenting a few examples of common agency models. In any such model,several principals Pi (i 1,.,n) want to influence a decision taken on their behalf bya common age
30、nt A. My goal here is to briefly highlight some of the basic issues arisingin such modelling. Example 1: Regulation. Consider the regulation of a public utility by n distinct reg-ulators (principals). For instance, one agency may be an economic regulator concerned byconsumers surplus. Another one ma
31、y be an environmental regulator controlling pollution.Regulators have specific objective functions given byVi = Si(q)ti, i 1,.,n, (1)where q is the firms output. This output may be multidimensional and of the formq = (q1,.,qn) where qi might itself be an array of activities controlled by regulator P
32、i.The surplus function Si() is strictly concave in q, and captures the (algebraic) benefit ofthe firms activity from regulator Pis point of view. ti is a regulatory transfer paid to thefirm by Pi. The firms profit can be written as:U =nsummationdisplayi=1ti C(q) (2)where C(q) is a cost function, whi
33、ch is increasing and convex. The efficiency parameter is drawn from a cumulative distribution F() on the interval = , with an atomlessand everywhere positive density f(). Depending on the informational environment underscrutiny, the parameter might either be private information for the firm or not.
34、Thisinformation structure is common knowledge.The reader familiar with the regulation literature will have recognized an extensionof the framework developed by Baron and Myerson (1982). The only difference is thefragmented nature of regulatory control which is shared among several government units.I
35、 will be silent on the definition of social welfare underlying the regulators objectives.Social welfare might be defined as the sum of these objectives if regulators have clear and4separable objectives. However, regulatory agencies could also have overlapping missions.5In any case, it is useful to c
36、onsider an hypothetical setting where all principals are mergedinto a single entity with the objective function summationtextni=1 Vi.Under complete information, efficiency requires to maximize the joint-payoff of thegrand-coalition made of all principals and the agent. The first-best output q() sati
37、sfies:nsummationdisplayi=1Sprimei(q() = Cprime(q(). (3)For future references, it is also useful to describe the cooperative solution achievedunder asymmetric information had all principals merged as one. The techniques to derivethis second-best (or interim efficient in the sense of Holmstrom and Mye
38、rson (1983)solution are by now standard.6 The cooperative outcome qC() satisfies:nsummationdisplayi=1Sprimei(qC() =parenleftbigg + F()f()parenrightbiggCprime(qC(). (4)Under asymmetric information, the efficiency parameter is replaced by a virtual effi-ciency parameter + F()f() that takes into accoun
39、t the fact that the agents informationrent is costly from the merged entitys viewpoint. Example 2: Lobbying. Several lobbying groups (principals) want to influence adecision-maker (the common agent) who chooses the level of a public good or, moregenerally, a policy variable (a regulated price, an im
40、port tariff, or a number of permits).These principals non-cooperatively offer contributions to influence the agents choice.Their objective functions are given by (1). The agents utility function is again as in(2) where C(q) should now be viewed as the opportunity cost of choosing a quantity qof publ
41、ic good.7 Contrary to Example 1 where regulatory contracts are mandatory, theagent can now reject a subset of the contributions. Example 3: Vertical Contracting. Two competing retailers P1 and P2 (the princi-pals) compete on a final market. They produce the final good with a one-to-one Leontiefftech
42、nology using a common input produced by a manufacturer (the common agent). Theagents reservation payoff is, for simplicity, normalized to zero. The retailers and manu-facturers profit functions are respectively given by:Vi = P(qi +qi)qi ti, i = 1,2, and U = t1 +t2 C(q1 +q2)5An extreme case would be
43、when social welfare maximization is replicated among the different agencies.Then, we have S1() = . = Sn().6See Laffont and Martimort (2002, Chapter 3) for instance.7This may include the welfare of unorganized groups which are not active lobbyists.5where the inverse demand function satisfies Pprime 0
44、, Cprimeprime 0). The manufacturermay either accept both offers, none or only one.An efficient outcome maximizes now the profit of the vertically and horizontally in-tegrated structure. The (symmetric) efficient production vector q() = q1() = q2() isthe monopoly outcome defined as:2Pprime(2q()q() +P
45、(2q() = Cprime(2q(). (5)A Few Issues: In all those examples, inefficient contractual outcomes may arise becauseof some underlying frictions in contracting. Those frictions may be due to arbitrary re-strictions of the space of contracts. They may also stem from asymmetric information andthe associate
46、d screening costs incurred by the principals in such contexts. A major diffi-culty of the common agency literature is precisely to understand the new frictions, if any,which are due to the principals non-cooperative behavior. This analysis requires a care-ful study of the contracting possibilities a
47、vailable to the principals. Different contractingpossibilities may either alleviate or exacerbate frictions depending on the context. Whenlooking at those contracting possibilities, common agency introduces some new featuresthat are not present under centralized contracting and that need to be caref
48、ully studied: Under centralized contracting, the agent has no other option than refusing the contractoffered by the merged entity. This participation decision is most often modelled by intro-ducing an exogenously given reservation payoff for the agent. Under common agency, theagent may either be for
49、ced to accept all contracts at once or may be able to play someprincipals against others by threatening to accept only a subset of the offers he receives.We will talk about intrinsic common agency in the former case and delegated commonagency in the latter.8 Intrinsic common agency arises in Example 1. Delegated commonagency occurs instead in Examples 2 and 3. Examples 1 and 3 also highlight another important feature of common agency. As wesplit control among different principals, we might also c
