A general impossibility result on strategy-proof social choice hyperfunctions

A social choice hyperfunction picks a non-empty set of alternatives at each admissible preference profile over sets of alternatives. We analyze the manipulability of social choice hyperfunctions. We identify a domain D^λ of lexicographic orderings which exhibits an impossibility of the Gibbard–Satterthwaite type. Moreover, this impossibility is inherited by all well-known superdomains of D^λ. As most of the standard extension axioms induce superdomains of D^λ while social choice correspondences are particular social choice hyperfunctions, we are able to generalize many impossibility results in the literature.     

Group incentive compatibility for matching with contracts

Hatfield and Milgrom [Hatfield, John William, Milgrom, Paul R., 2005. Matching with contracts. Amer. Econ. Rev. 95, 913–935] present a unified model of matching with contracts, which includes the standard two-sided matching and some package auction models as special cases. They show that the doctor-optimal stable mechanism is strategy-proof for doctors if hospitals' preferences satisfy substitutes and the law of aggregate demand. We show that the doctor-optimal stable mechanism is group strategy-proof for doctors under these same conditions. That is, no group of doctors can make each of its members strictly better off by jointly misreporting their preferences. We derive as a corollary of this result that no individually rational allocation is preferred by all the doctors to the doctor-optimal stable allocation.     

Differentiable strategy-proof mechanisms for private and public goods in domains that are not necessarily large or quasi-linear

In this paper, we develop a differentiable approach to deal with incentives in a, possibly small, subset of a general domain of preferences in economies with one public and one private good. We show that, for two agents, there is no mechanism which is efficient, strategy-proof and where consumption of both goods is positive for all agents. For the case of two or more agents the same result occurs when nondictatorship is replaced by Individual Rationality. We are very grateful to Atila Abdulkadiroglu, Carmen Beviá, Xavier Calsamiglia, Marco Celentani, Bernardo Moreno, Antonio Romero-Medina, William Thomson, Walter Trockel, an associate editor, three anonymous referees and participants at seminars at Universities of Alicante, Autónoma de Barcelona and Rochester and the Spanish Economic Association meeting in Sevilla for very helpful comments and suggestions.     

Consistent House Allocation

In practice we often face the problem of assigning indivisible objects (e.g., schools, housing, jobs, offices) to agents (e.g., students, homeless, workers, professors) when monetary compensations are not possible. We show that a rule that satisfies consistency, strategy-proofness, and efficiency must be an efficient generalized priority rule; i.e., it must adapt to an acyclic priority structure, except – maybe – for up to three agents in each object’s priority ordering. We are grateful to the Editor and an anonymous referee for helpful comments and suggestions. L. Ehlers acknowledges financial support from the SSHRC (Canada)     

Implementing egalitarian-equivalent allocation of indivisible goods on restricted domains

Summary. We study the problem of allocating several units of homogeneous indivisible goods when monetary compensations are possible. First, we show that there is no strategy-proof, budget balanced, and egalitarian-equivalent mechanism even on extremely restricted preference domains. Next, we present two characterizations of strategy-proof and decision-efficient mechanisms that satisfy a stronger version of egalitarian-equivalence on preference domains bounded above. These characterizations tell us a trade-off between strategy-proofness and Pareto efficiency, and a relationship with strategy-proof and envy-free mechanisms. Finally, we prove that no egalitarian-equivalent mechanism is Nash implementable even on extremely restricted preference domains.Received: 22 April 2002, Revised: 17 February 2003, JEL Classification Numbers: C72, D63, D71, D82.I am very grateful to Naoki Yoshihara for useful discussions and suggestions that motivate me to study this subject. I would also like to thank Kotaro Suzumura, Koichi Tadenuma, Yoshikatsu Tatamitani, and the editor and two anonymous referees of this journal for helpful comments.     

Strategy-proof risk sharing

We consider risk sharing problems with a single good and a finite number of states. Agents have a common prior and their preferences are represented in the expected utility form and are risk averse. We study efficient and individually rational risk sharing rules satisfying strategy-proofness, the requirement that no one can ever benefit by misrepresenting his preference. When aggregate certainty holds, we show that “fixed price selections” from Walrasian correspondence are the only rules satisfying efficiency, individual rationality, and strategy-proofness. However, when aggregate uncertainty holds, we show that there exists no rule satisfying the three requirements. Moreover, in the two agents case, we show that dictatorial rules are the only efficient and strategy-proof rules. Dropping the common prior assumption in the model, we show that this assumption is necessary and sufficient for the existence of rules satisfying the three main requirements in the two agents and aggregate certainty case.     

Secure implementability under Pareto-efficient rules in linear production economies with classical preferences

This paper studies secure implementability (Saijo et al. (2007) “Secure Implementation,” Theoretical Economics 2, pp.203–229) in linear production economies with classical preferences. Although secure implementability is in general stronger than the combination of strategy-proofness and non-bossiness (Satterthwaite and Sonnenschein (1981) “Strategy-Proof Allocation Mechanisms at Differentiable Points,” Review of Economic Studies 48, pp.587–597), this paper shows that both properties are equivalent under Pareto-efficient rules in the economies. In addition, this paper characterizes securely implementable and Pareto-efficient rules in the economies when the number of agents is two.     

Vickrey allocation rule with income effect

We consider situations in which a society tries to efficiently allocate several homogeneous and indivisible goods among agents. Each agent receives at most one unit of the good. In this paper, we establish that on domains that include nonquasi-linear preferences—preferences exhibiting income effects—an allocation rule that satisfies Pareto-efficiency, strategy-proofness, individual rationality, and nonnegative payment uniquely exists, which is the Vickrey allocation rule. H. Saitoh is a JSPS Research Fellow.     

Weakly fair allocations and strategy-proofness

This paper investigates the problem of allocating two types of indivisible objects among a group of agents when a priority-order must be respected and only restricted monetary transfers are allowed. Since the existence of a fair (as in envy-free) allocation is not generally guaranteed, due to the restrictions on the money transfers, the concept of fairness is weakened, and a new concept of fairness is introduced. This concept is called weak fairness. This paper defines an allocation rule that implements weakly fair allocations and demonstrates that it is coalitionally strategy-proof. In fact, under a mild regulatory condition and quasi-linear utility functions, it is demonstrated that this is the only coalitionally strategy-proof allocation rule that implements a weakly fair allocation. We would like to thank two anonymous referees, the participants at the Society for the Advancement of Economic Theory Conference (Greece, 2007) and the participants at the Association for Public Economic Theory Meeting (Nashville, USA, 2007) for valuable comments. The authors would also like to acknowledge financial support from The Jan Wallander and Tom Hedelius Foundation.     

The coordinate-wise core for multiple-type housing markets is second-best incentive compatible

We consider the generalization of Shapley and Scarf’s (1974) [Shapley, L., Scarf’s, H., 1974. On cores and indivisibility. Journal of Mathematical Economics 1, 23–37.] model of trading indivisible objects (houses) to so-called multiple-type housing markets. We show that the prominent solution for these markets, the coordinate-wise core rule, is second-best incentive compatible.