Shigehiro Serizawa

Efficient strategy-proof exchange and minimum consumption guarantees

For exchange economies with classical economic preferences, it is shown that any strategy-proof social choice function that selects Pareto optimal outcomes cannot guarantee everyone a consumption bundle bounded away from the origin. This result demonstrates that there is a fundamental conflict between efficiency and distributional goals in exchange economies if the social choice rule is required to be strategy-proof.

Pairwise Strategy-Proofness and Self-Enforcing Manipulation

Abstract“Strategy-proofness” is one of the axioms that are most frequently used in the recent literature on social choice theory. It requires that by misrepresenting his preferences, no agent can manipulate the outcome of the social choice rule in his favor. The stronger requirement of “group strategy-proofness” is also often employed to obtain clear characterization results of social choice rules. Group strategy-proofness requires that no group of agents can manipulate the outcome in their favors. In this paper, we advocate “effective pairwise strategy-proofness.” It is the requirement that the social choice rule should be immune to unilateral manipulation and “self-enforcing” pairwise manipulation in the sense that no agent of a pair has the incentive to betray his partner. We apply the axiom of effective pairwise strategy-proofness to three types of economies: public good economy, pure exchange economy, and allotment economy. Although effective pairwise strategy-proofness is seemingly a much weaker axiom than group strategy-proofness, effective pairwise strategy-proofness characterizes social choice rules that are analyzed by using different axioms in the literature.

Strategy-proof and individually rational social choice functions for public good economies

SummaryWe consider the problem of choosing an allocation in an economy in which there are one private good and one public good. Our purpose is to identify the class of procedures of choosing an allocation which satisfy “strategy-proofness,” “individual rationality”, “no exploitation” and “non-bossiness”. Any such procedure is a scheme of “semi-convex cost sharing” determined by “the minimum demand principle”.

Characterizing the Vickrey Combinatorial Auction by Induction

This note studies the allocation of heterogeneous commodities to agents whose private values for combinations of these commodities are monotonic by inclusion. This setting can accommodate the presence of complementarity and substitutability among the heterogeneous commodities. By using induction logic, we provide an elementary proof of Holmstroms (1919) characterization of the Vickrey combinatorial auction as the unique efficient, strategy-proof, and individually rational allocation rule. Our proof method can also be applied to domains to which his proof cannot be.

A characterization of the uniform rule with several commodities and agents

We consider a problem of allocating infinitely divisible commodities among a group of agents. More specifically, there are several commodities to be allocated and agents have continuous, strictly convex, and separable preferences. We establish that a rule satisfies strategy-proofness, unanimity, weak symmetry, and nonbossiness if and only if it is the uniform rule. This result extends to the class of continuous, strictly convex, and multidimensional single-peaked preferences.

Maximal Domain for Strategy-Proof Rules in Allotment Economies

We consider the problem of allocating an amount of a perfectly divisible good among a group of n agents. We study how large a preference domain can be to allow for the existence of strategy-proof, symmetric, and efficient allocation rules when the amount of the good is a variable. This question is qualified by an additional requirement that a domain should include a minimally rich domain. We first characterize the uniform rule (Bennasy, 1982) as the unique strategy-proof, symmetric, and efficient rule on a minimally rich domain when the amount of the good is fixed. Then, exploiting this characterization, we establish the following: There is a unique maximal domain that includes a minimally rich domain and allows for the existence of strategy-proof, symmetric, and efficient rules when the amount of good is a variable. It is the single-plateaued domain.

An impossibility theorem for matching problems

This paper studies the possibility of strategy-proof rules yielding satisfactory solutions to matching problems. Alcalde and Barberá (Econ Theory 4:417–435, 1994) and Sönmez (Econ Des 1:365–380, 1994) show that efficient and individually rational matching rules are manipulable. We pursue the possibility of strategy-proof matching rules by relaxing efficiency to the weaker condition of respect for unanimity. First, we prove that a strategy-proof rule exists that is individually rational and respects unanimity. However, this rule is unreasonable in the sense that mutually best pairs of agents are matched on only rare occasions. In order to explore the possibility of better matching rules, we introduce a natural condition of “respect for 2-unanimity.” Respect for 2-unanimity states that a mutually best pair of agents should be matched, and an agent wishing to being unmatched should be unmatched. Our second result is negative. Secondly, we prove that no strategy-proof rule exists that respects 2-unanimity. This result implies Roth (Math Oper Res 7:617–628, 1962; J Econ Theory 36:277–288, 1985) showing that stable rules are manipulable.

Coalitionally strategy-proof rules in allotment economies with homogeneous indivisible goods

We consider the allotment problem of homogeneous indivisible goods among agents with single-peaked and risk-averse von Neumann-Morgenstern expected utility functions. We establish that a rule satisfies coalitional strategy-proofness, same-sideness, and strong symmetry if and only if it is the uniform probabilistic rule. By constructing an example, we show that if same-sideness is replaced by respect for unanimity, this statement does not hold even with the additional requirements of no-envy, anonymity, at most binary, peaks-onlyness and continuity.

A maximal domain for strategy-proof and no-vetoer rules in the multi-object choice model

Following “Barberà et al. (1991, Econometrica 59:595–609)”, we study rules (or social choice functions) through which agents select a subset from a set of objects. We investigate domains on which there exist nontrivial strategy-proof rules. We establish that the set of separable preferences is a maximal domain for the existence of rules satisfying strategy-proofness and no-vetoer.

Strategy-Proof and Anonymous Allocation Rules of Indivisible Goods: A New Characterization of Vickrey Allocation Rule

We consider situations where a society allocates a finite units of an indivisible good among agents, and each agent receives at most one unit of the good. For example, imagine that a government allocates a fixed number of licences to private firms, or imagine that a government distributes equally divided lands to households. We show that the Vickrey allocation rule is the unique allocation rule satisfying strategy-proofness, anonymity and individual rationality.