Pablo Amorós

The Scholarship Assignment Problem

Abstract There are n graduate students and n faculty members. Each student will be assigned a scholarship by the joint faculty. The socially optimal outcome is that the best student should get the most prestigious scholarship, the second-best student should get the second most prestigious scholarship, and so on. The socially optimal outcome is common knowledge among all faculty members. Each professor wants one particular student to get the most prestigious scholarship and wants the remaining scholarships to be assigned according to the socially optimal outcome. We consider the problem of finding a mechanism such that in equilibrium, all scholarships are assigned according to the socially optimal outcome. Journal of Economic Literature Classification Numbers: D70, D78.

Single-peaked preferences with several commodities

Abstract. We consider the problem of allocating m commodities among n agents with single-peaked preferences. When m≥2 and n=2 any strategy-proof and efficient solution is dictatorial. We propose an extension of the Uniform Rule that (in the two-agents case) is the only one that satisfies strategy-proofness, envy-freeness, and a weak requirement related to efficiency. Alternatively, the envy-freeness property may be replaced by weak-anonymity.

NASH IMPLEMENTATION AND UNCERTAIN RENEGOTIATION

This paper studies Nash implementation when the outcomes of the mechanism can be renegotiated among the agents but the planner does not know the renegotiation function that they will use. We characterize the social objectives that can be implemented in Nash equilibrium when the same mechanism must work for every admissible renegotiation function. The constrained Walrasian correspondence, the core correspondence, and the Pareto-efficient and envy-free correspondence satisfy the necessary and sufficient conditions for this form of implementation if and only if freedisposal of the commodities is allowed. The uniform rule, on the other hand, is not Nash implementable for some admissible renegotiations functions.

Eliciting socially optimal rankings from unfair jurors

A jury must provide a ranking of contestants (students applying for scholarships or Ph.D. programs, gymnasts in a competition, etc.). There exists a true ranking which is common knowledge among the jurors, but is not verifiable. The socially optimal rule is that the contestants be ranked according to the true ranking. The jurors are partial and, for example, may have friends (contestants that they would like to benefit) and enemies (contestants that they would like to prejudice). We study necessary and sufficient conditions on the jury under which the socially optimal rule is implementable. These conditions incorporate strong informational requirements, particularly with respect to mechanism designer.

Efficiency and income redistribution in the single-peaked preferences model with several commodities

Abstract We consider the problem of allocating m infinitely divisible commodities among agents with single-peaked preferences. We propose a variation on the Mas–Colell’s Walrasian solution with slacks to characterize the efficient allocations. Our solution allows us to associate with each efficient allocation an income redistribution. We prove that the original solution proposed by Mas–Colell is the efficient selection which requires an income redistribution where the maximum payoff and the maximum subsidy are smallest. This generalizes a derivation of the Uniform Rule by Schummer and Thomson.

Subgame perfect implementation of the deserving winner of a competition with natural mechanisms

A jury has to decide the winner of a competition among a group of contestants. All members of the jury know who the deserving winner is, but this contestant is unknown to the planner. The social optimum is that the jury selects the deserving winner. Each individual juror may be biased in favor (friend) or against (enemy) some contestant, and therefore her goal does not necessarily coincide with the social objective. We analyze the problem of designing extensive form mechanisms that give the jurors the right incentives to always choose the deserving winner when the solution concept is subgame perfect equilibrium. We restrict the class of mechanisms considered to those which satisfy two conditions: (1) the jurors take turns to announce the contestant they think should win the competition, and (2) telling the truth is always part of a profile equilibrium strategies. A necessary but not sufficient condition for these mechanisms to exist is that, for each possible pair of contestants, there is at least one juror who is impartial with respect to them. If, in addition, the planner knows the friend or the enemy of at least one juror, the existence of these mechanisms is guaranteed in the three contestants case.

IMPLEMENTATION OF OPTIMAL CONTRACTS UNDER ADVERSE SELECTION

Abstract. This paper studies a 2-agent, 2-type principal-multiagent model of adverse selection under the assumption that the agents each have complete information. We construct a mechanism implementing the first-best contracts in Nash equilibrium that: satisfies a condition related to individual rationality, is renegotiation-proof, has a small-sized message space, achieves unique implementation and satisfies undomination of Nash equilibrium strategies. Moreover, we prove that other requirements which relate to individual rationality (different from the one satisfied by our mechanism) are not compatible with implementation of the first-best contracts.