Single-peakedness and coalition-proofness

We prove that multidimensional generalized median voter schemes are coalition-proof. Received: 16 July 1998 / Accepted 23 March 1999     

A characterization of the existenceof optimal dominant strategy mechanisms

This paper provides two theorems which characterize the domains of valuation functions for which there exist Pareto efficient and truth dominant strategy mechanisms (balanced Groves mechanisms). Theorem 1 characterizes the existence of balanced Groves mechanisms for a general class of valuation functions. Theorem 2 provides new balance-permitting domains of valuation functions by reducing the problem of solving partial differential equations to the problem of solving a polynomial function. It shows that a balanced Groves mechanism exists if and only if each valuation function in the family under consideration can be obtained by solving a polynomial function with order less than , where n is the number of individuals. Received: 5 January 1997 / Accepted: 25 May 1999     

Multiprincipals multiagents incentive design

This paper studies a simple setting in which the contractual arrangements which determine the incentives for agents are not designed by a single central planner, but are themselves the outcome of a game among multiple noncooperatively acting principals. The notion of an Epsilon Contracting Equilibrium is introduced to predict the outcome of the contract-design game among principals. Symmetric pure strategy Epsilon Contracting Equlibria may not exist in perfectly symmetric environments. In a symmetric Epsilon Contracting Equilibrium in mixed strategies coordination failure may lead to a suboptimal institutional network in which the agents “cheat” their principals. Received: 14 June 1995 / Accepted: 09 August 1999     

Constitutional implementation

We consider the problem of implementing a social choice correspondence H in Nash equilibrium when the constitution of the society is given by an effectivity function E. It is assumed that the effectivity function of , is a sub-correspondence of E. We found necessary and efficient conditions for a game form to implement H (in Nash equilibria), and to satisfy, at the same time, that , the effectivity function of , is a sub-correspondence of (which guarantees that is compatible with E). We also find sufficient conditions for the coincidence of the set of winning coalitions of and , and for . All our results are sharp as is shown by suitable examples. Received: 15 December 2000 / Accepted: 3 September 2001     

On efficient trading mechanisms between one seller and n buyers

Myerson and Satterthwaite (1983) prove that if one seller and one buyer have independent private valuations for an indivisible object then no individually rational and incentive compatible trading mechanism can guarantee ex post efficiency when gains from trade are uncertain. Makowski and Mezzetti (1993) show that this is not the case when there are at least two buyers. In the latter context, if the highest possible seller's valuation is not too large, we provide an ex post efficient mechanism in which the mechanism designer and the agents are not required to know the probability distribution for the seller's valuation. Received: February 18, 1998 / Accepted: September 10, 1999     

A study of proportionality and robustness in economies with a commonly owned technology

Abstract. Studying one-input one-output economies, we say that an allocation is proportional if the input-output ratio is identical among agents and if each agent maximizes her welfare given this ratio. We propose three equity axioms based on this definition, and we use them to compare the main solutions to this simple equity problem. We also combine efficiency, robustness axioms and our proportionality axioms to characterize two solutions. Received: 11 June 1997 / Accepted: 26 May 2000     

Achieving the first best in sequencing problems

Abstract. In a sequencing problem with linear time cost, Suijs (1996) proved that it is possible to achieve first best. By first best we mean that one can find mechanisms that satisfy efficiency of decision, dominant strategy incentive compatibility and budget balancedness. In this paper we show that among a more general and natural class of sequencing problems, sequencing problems with linear cost is the only class for which first best can be achieved. Received: 2 December 1999/Accepted: 9 May 2001     

Sprumont's characterization of the uniform rule when all single-peaked preferences are admissible

Sprumont (1991) has established that the only allocation rule for the division problem that is strategy-proof, efficient, and anonymous is the uniform rule when the domain is the set of all possible profiles of continuous single-peaked preferences. Sprumont's characterization of the uniform rule is shown to hold on any larger domain of single-peaked preferences. Received: 15 December 1998 / Accepted: 12 April 1999     

On the generalized principal-agent problem: Decomposition and existence results

This paper addresses the class of generalized agency problems: situations in which adverse selection and moral hazard are jointly present. We present a decomposition of the principal's optimization problem under the first-order approach that sheds light on the interactions between the two types of private information, and also significantly improves tractability. We use the decomposition to (1) provide examples of closed form solutions of the optimal contract, and (2) analyze the existence of optimal contracts. We also show that the first-order approach is valid in generalized agency problems if the production technology satisfies the linear distribution function condition (LDFC) in actions and types. For more general production technologies the Mirrlees-Rogerson sufficient conditions need to be extended to include restrictions on the form of the optimal contract. Received: 11 August 1997 / 26 September 1999     

Natural and double implementation of public ownership solutions in differentiable production economies

This paper examines the implementation of two public ownership solutions in convex production economies with differentiable production functions. The two public ownership solutions we focus on are the proportional and equal benefit solutions. Two “natural” mechanisms which doubly implement the proportional and equal benefit solutions respectively in Nash and strong Nash equilibria are proposed without assuming free disposal. Received: 7 May 1996 / Accepted: 1 December 1998     

Stable matchings and the small core in Nash equilibrium in the college admissions problem

Both rematching proof and strong equilibrium outcomes are stable with respect to the true preferences in the marriage problem. We show that not all rematching proof or strong equilibrium outcomes are stable in the college admissions problem. But we show that both rematching proof and strong equilibrium outcomes in truncations at the match point are all stable in the college admissions problem. Further, all true stable matchings can be achieved in both rematching proof and strong equilibrium in truncations at the match point. We show that any Nash equilibrium in truncations admits one and only one matching, stable or not. Therefore, the core at a Nash equilibrium in truncations must be small. But examples exist such that the set of stable matchings with respect to a Nash equilibrium may contain more than one matching. Nevertheless, each Nash equilibrium can only admit at most one true stable matching. If, indeed, there is a true stable matching at a Nash equilibrium, then the only possible equilibrium outcome will be the true stable matching, no matter how different are players' equilibrium strategies from the true preferences and how many other unstable matchings are there at that Nash equilibrium. Thus, we show that a necessary and sufficient condition for the stable matching rule to be implemented in a subset of Nash equilibria by the direct revelation game induced by a stable mechanism is that every Nash equilibrium profile in that subset admits one and only one true stable matching. Received: 30 December 1998 / Accepted: 12 October 2001 This paper is a revision of the paper “Manipulation and Stability in a College Admissions Problem” circulated since 1994. I thank Rich McLean, Abraham Neyman, Mark Satterthwaite, Sang-Chul Suh, and Tetsuji Yamada for helpful discussions. I thank the associate editor and the two anonymous referees for their helpful comments that have greatly improved the paper. I am grateful to the Kellogg G.S.M. at the Northwestern University for the hospitality for my visit. Any errors are mine.     

Abstention and political competition

The classical literature on spatial majority voting postulates that all citizens vote. The Median Voter Theorem (MVT) then obtains when parties have perfect information on voter behavior and are either office-seekers (“Downsian”) or ideological. This paper introduces abstention, a simple yet realistic modification. We show that the main features of the MVT survive to a large extent but subject to some qualifications. First, the winning policy does not bear any necessary relation to the median voter. Second, there exist examples in which the candidates choose different positions at equilibrium. Third, equilibrium may fail to exist or be unique. Finally, the equilibria of the model with office-motivated parties may differ from the ones where parties are ideological. Received: 18 September 1999 / Accepted: 31 January 2000     

Implementation of multi-agent incentive contracts with the principal's renegotiation offer

The purpose of this paper is to explore a mechanism for supporting desired equilibrium actions in a one-principal, multi-agent model when the principal makes a renegotiation offer. We show that there exists a mechanism in which the principal's most preferred mixed strategy is always supported. Received: 30 May 1997 / Accepted: 10 October 1998     

Multiproject team assignments

We consider expected profit maximizing mechanisms for a principal who has to allocate a group of agents among a number of projects, assuming that the principal has incomplete information about each agent's ability type, and the agents follow the Bayes-Nash or the dominant strategy equilibrium behavior. We find that while expected profit maximizing mechanisms are similar to the optimal auction (Myerson, 1981), the incentive compatibility constraints are much more restrictive. Interestingly, these constraints are satisfied if each agent's characteristics change in a consistent manner not only with types, but also from project to project. Received: 30 April 1997 / Accepted: 22 December 1998     

Solutions for cooperative games with r alternatives

We consider games with n players and r alternatives. In these games each player must choose one and only one alternative, reaching an ordered partition of the set of players. An extension of the Shapley value to this framework is studied. Received: 1 November 1997 / Accepted: 24 January 1999     

Stable and efficient bargaining networks

Abstract. We examine a bargaining game among players connected by a network, where successively potential partners negotiate over terms of a project. For any network structure and ordering of selection of bargaining partners, there is a unique subgame perfect equilibrium outcome which coincides with the standard Rubinstein split. Based on this, we derive expected payoffs for players as a function of the network. We the characterize the pairwise stable and efficient bargaining networks. These two sets do not always coincide and in many situations pairwise stable networks are over-connected. Received: 10 April 2001 / Accepted: 17 January 2002 I am indebted to Matthew Jackson for suggesting this paper. I also thank Bernard Caillaud, Sanjeev Goyal, and the seminar participants at Universidad de Alicante, Universidad Carlos III de Madrid, CEMFI (Madrid), Universitat Autònoma de Barcelona, Erasmus University of Rotterdam, Universitat Pompeu Fabra (Barcelona) and CERAS (Paris) for helpful comments. This paper was written while at Universitat Pompeu Fabra and CERAS. Financial support from the Spanish Ministry of Education through research grant DGESIC PB96-0302, and from the Ecole Nationale des Ponts et Chaussées, Paris is gratefully acknowledged. All errors are of course mine.     

Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation

We characterize full implementation of social choice sets in mixed-strategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It is shown that, in economic environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure. For implementing a social choice function, the case of two-agents is also covered by these conditions and mixed Bayesian monotonicity reduces to Bayesian monotonicity. Following parallel steps, mixed virtual implementation is shown to be equivalent to mixed virtual monotonicity, incentive compatibility and closure. The key condition, mixed virtual monotonicity, is argued to be very weak. In particular, it is weaker than Abreu–Matsushima’s measurability, thereby implying that: (1) virtual implementation in mixed Bayesian equilibrium is more permissive than virtual implementation in iteratively undominated strategies, and (2) non-regular mechanisms are essential for the implementation of rules in that gap.     

Proportionally adjusted marginal pricing method to share joint costs

We consider the cost sharing problem with divisible demands of heterogeneous goods. We propose a cost sharing method called Proportionally Adjusted Marginal Pricing (PAMP) method. PAMP is a nonadditive (in the cost function) extension of average cost pricing. We introduce an axiom called Local Independence (LI) and use LI together with Continuity, Proportionality, and Scale Invariance to characterize PAMP. Received: 23 March 2001 / Accepted: 16 November 2001 I thank Yves Sprumont, Hervé Moulin, and Ahmet Alkan for discussions, comments and suggestions. Thanks also go to the associate editor and the referees, whose comments and suggestions greatly improve the paper.     

Uniform allocation and reallocation revisited

Thomson (1995a) proved that the uniform allocation rule is the only allocation rule for allocation economies with single-peaked preferences that satisfies Pareto efficiency, no-envy,one-sided population-monotonicity, and replication-invariance on a restricted domain of single-peaked preferences. We prove that this result also holds on the unrestricted domain of single-peaked preferences. Next, replacing one-sided population-monotonicity by one-sided replacement-domination yields another characterization of the uniform allocation rule, Thomson (1997a). We show how this result can be extended to the more general framework of reallocation economies with individual endowments and single-peaked preferences. Following Thomson (1995b) we present allocation and reallocation economies in a unified framework of open economies. Received: 20 February 1999 / Accepted: 15 February 2000     

Regulation in a political economy: explaining limited commitment and the ratchet effect

Abstract. This paper shows that in a political economy with repeated elections governments that possess full commitment behave as if their commitment is limited. Two different endogenous versions of the ratchet effect obtain: If contracts of previous governments tie newly elected governments, governments are unable to resist renegotiation. If previous contracts do not bind new governments and taxation has a crowding–out effect, a ratchet effect occurs that is similar, but not identical to the standard ratchet effect that is due to intertemporal non–commitment. Social welfare may be higher in the latter case, when the governing party is allowed to use bonds. Received: March 14, 2000