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

Summary. Serizawa [3] characterized the set of strategy-proof, individually rational, no exploitative, and non-bossy social choice functions in economies with pure public goods. He left an open question whether non-bossiness is necessary for his characterization. We will prove that non-bossiness is implied by the other three axioms in his characterization. Received: October 17, 1997; revised version: January 19, 1998     

A geometric proof of Gibbard's random dictatorship theorem

Summary Gibbard has shown that a social choice function is strategy-proof if and only if it is a convex combination of dictatorships and pair-wise social choice functions. I use geometric techniques to prove the corollary that every strategy-proof and sovereign social choice function is a random dictatorship.I thank Kim Border for several useful discussions and many insightful comments.     

Subgame-perfect implementation of bargaining solutions

We study house allocation problems introduced by L. Shapley and H. Scarf (1974, J. Math. Econ.1, 23–28). We prove that a mechanism (a social choice function) is individually rational, anonymous, strategy-proof, and nonbossy (but not necessarily Pareto efficient) if and only if it is either the core mechanism or the no-trade mechanism, where the no-trade mechanism is the one that selects the initial allocation for each profile of preferences. This result confirms the intuition that even if we are willing to accept inefficiency, there exists no interesting strategy-proof mechanism other than the core mechanism. Journal of Economic Literature Classification Numbers: C71, C78, D71, D78, D89.     

Decomposable Strategy-Proof Social Choice Functions

This article shows that a social choice function defined on a domain of separable preferences which satisfies a relatively weak domain-richness condition on a product set of alternatives is (i) strategy-proof and only depends on the tops of the individual preferences if and only if (ii) the range of the social choice function is a product set and the social choice function can be decomposed into the product of one-dimensional, strategy-proof, nontop-insensitive social choice functions.
JEL Classification Number: D71.     

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.     

Market games with differential information and infinite dimensional commodity spaces: The core

Summary We provide an alternative proof of the existence of core allocations in exchange economies with differential information and infinite dimensional commodity spaces. We also identify a critical feature of information sharing rules that ensures nonemptiness of the core. In essence, the only condition we require on the sharing rules is that profitable insider trading be prohibited. In the absence of insider trading, balancedness is guaranteed and core nonemptiness follows.I thank Dan Arce, Erik Balder, Myrna Wooders, and Nicholas Yannelis for helpful comments. This paper is a greatly revised version of my paper entitled. A Variational Problem Arising in Market Games with Differential Information, written in August of 1991.     

On the nature of equilibria in a Downsian model with candidate valence

We analyze mechanisms that are used to allocate dormitory rooms to students at college campuses. Students consist of newcoming freshmen, who do not currently occupy any rooms, and more senior students each of whom occupies a room from the previous year. In addition to the rooms already occupied by the existing tenants, there are vacated rooms by the graduating class. Students have strict preferences over dormitory rooms. Each student shall be assigned a dormitory room in an environment where monetary transfers are not allowed. An existing tenant can move to another room as a result of the assignment. We show that you request my house–I get your turn mechanisms are the only mechanisms that are Pareto-efficient, individually rational, strategy-proof, weakly neutral, and consistent.     

Egalitarian division under Leontief Preferences

We consider the problem of fairly dividing $l$ divisible goods among $n$ agents with the generalized Leontief preferences. We propose and characterize the class of generalized egalitarian rules which satisfy efficiency, group strategy-proofness, anonymity, resource monotonicity, population monotonicity, envy-freeness and consistency. On the Leontief domain, our rules generalize the egalitarian-equivalent rules with reference bundles. We also extend our rules to agent-specific and endowment-specific egalitarian rules. The former is a larger class of rules satisfying all the previous properties except anonymity and envy-freeness. The latter is a class of efficient, group strategy-proof, anonymous and individually rational rules when the resources are assumed to be privately owned.     

Information revelation in a market with pairwise meetings: the one sided information case

Summary We study a market with pairwise meetings of agents and with a one sided information asymmetry regarding the state of the world, which may be low or high. We characterize the set of equilibria of the model, and study its behavior as the market becomes approximately frictionless. For any one sided information economy there is an equilibrium where trade occurs at the right price (an ex-post individually rational price). Moreover, there is an open set of economies where in all the equilibria trade occurs at the right price.We thank Douglas Gale, Jerry Green, Sergiu Hart, Andreu Mas-Colell, Eric Maskin, Thomas Sjöström, and Kathy Spier for their comments. We are grateful to a referee for correcting a mistake in an earlier draft and for providing extremely helpful suggestions. The financial support of the Fulbright — MEC program (R. Serrano) and the Sloan Foundation (O. Yosha) is acknowledged.     

Inefficiency of Strategy-Proof Rules for Pure Exchange Economies

In his pioneering article, (in “Decision and Organization” (C. B. McGuire and R. Radner, Eds.), pp. 297-336, North-Holland, Amsterdam, 1972) Hurwicz establishes that there is no strategy-proof, Pareto-efficient, and individually rational rule for pure exchange economies with two agents and two goods, provided that the domain includes a sufficiently wide class of classical preferences. In this article, we extend his result to pure exchange economies with any finite number of agents and goods. We establish that (i) there is no strategy-proof, Pareto-efficient, and individually rational rule on the class of classical, homothetic, and smooth preferences; and (ii) there is no strategy-proof, Pareto-efficient, and symmetric rule on the same class of preferences. Journal of Economic Literature Classification Numbers: D78, D71, C72.     

Remarks concerning concave utility functions on finite sets

Summary. A direct construction of concave utility functions representing convex preferences on finite sets is presented. An alternative construction in which at first directions of supergradients (prices) are found, and then utility levels and lengths of those supergradients are computed, is exhibited as well. The concept of a least concave utility function is problematic in this context.Received: 28 November 2002, Revised: 28 June 2004, JEL Classification Numbers: D11, C60.I am indebted to an anonymous referee, Marcel K. Richter and Kam-Chau Wong, for many valuable remarks and suggestions.     

Second-best efficiency of allocation rules: strategy-proofness and single-peaked preferences with multiple commodities

We study strategy-proof allocation rules in economies with perfectly divisible multiple commodities and single-peaked preferences. In this setup, it is known that the incompatibility among strategy-proofness, Pareto efficiency and non-dictatorship arises in contrast with the Sprumont (Econometrica 59:509–519, 1991) one commodity model. We first investigate the existence problem of strategy-proof and second-best efficient rules, where a strategy-proof rule is second-best efficient if it is not Pareto-dominated by any other strategy-proof rules. We show that there exists an egalitarian rational (consequently, non-dictatorial) strategy-proof rule satisfying second-best efficiency. Second, we give a new characterization of the generalized uniform rule with the second-best efficiency in two-agent case.     

Risk-Aversion in Constitutional Choice: Reply to Kyriacou

In his comment on my article on the possibility of discriminatory and non-consensual decsionmaking under Buchanan's veil of uncertainty (Müller 1998) Andreas Kyriacou proposes to take the players to be quasi-risk averse in order to secure fair and unanimous results at the constitutional level. As analytical tools of incorporating this premise into my model he not only suggests to assume that the individuals weigh losses higher than gains but also to take them as being rational maximiners. In this reply to his comment it is argued that both these points are inadequate to weaken my case against the veil's ability to guarantee unanimity and fairness of constitutional decisionmaking in view of a post-constitutional prisioners dilemma.     

On multiple equilibria and the rational expectations hypothesis

Summary This paper analyzes through a simple two-period model the fact that, if some agents hold inside money intertemporally, the second-period normalization matters. Thus, there are several equilibria of the second-period economy, indexed by the level of inflation. A concept of equilibrium acknowledging this fact, and requiring that agents put some weight on any of the possible second-period equilibrium price vectors is developed. Such an equilibrium is shown to exist, and is illustrated by an example.This a revised version of chapter three of my Ph.D. dissertation. I would like to thank David Cass, Atsushi Kajii, George Mailath and Shinichi Suda for helpful discussions and comments. Thanks are also due to Jean-Michel Grandmont who pointed out mistakes in a previous version. All remaining mistakes are of course my own. Financial support from a CARESS scholarship at the University of Pennsylvania is gratefully acknowledged.     

Random dictatorship domains

A domain of preference orderings is a random dictatorship domain if every strategy-proof random social choice function satisfying unanimity defined on the domain is a random dictatorship. Gibbard (1977) showed that the universal domain is a random dictatorship domain. We ask whether an arbitrary dictatorial domain is a random dictatorship domain and show that the answer is negative by constructing dictatorial domains that admit anonymous, unanimous, strategy-proof random social choice functions which are not random dictatorships. Our result applies to the constrained voting model. Lastly, we show that substantial strengthenings of linked domains (a class of dictatorial domains introduced in Aswal et al., 2003) are needed to restore random dictatorship and such strengthenings are “almost necessary”.     

Implementation of college admission rules

Summary We consider both Nash and strong Nash implementation of various matching rules for college admissions problems. We show that all such rules are supersolutions of the stable rule. Among these rules the lower bound stable rule is implementable in both senses. The upper bound Pareto and individually rational rule is strong Nash implementable yet it is not Nash implementable. Two corollaries of interest are the stable rule is the minimal (Nash or strong Nash) implementable solution that is Pareto optimal and individually rational, and the stable rule is the minimal (Nash or strong Nash) implementable extension of any of its subsolutions.We wish to thank Professor William Thomson for his efforts in supervision as well as his useful suggestions. We are grateful to the participants in his reading class, workshops at Bilkent University, University of Rochester, and in particular Jeffrey Banks, Stephen Ching, Bhaskar Dutta, Rangarajan Sundaram and an anonymous referee for their helpful comments.     

On the complexity of repeated principal agent games

Summary We examine an infinitely repeated principal agent game without discounting (Radner [1985]), in which the agent may engage in multiple projects. We focus on linear strategies that summarize each history into a linear function of public outcomes, and select an action according to a single threshold rule. We claim that linear strategies significantly simplify the computation needed to make strategic decisions following each history. Despite the simplicity of linear strategies, we can virtually recover the folk theorem. For any individually rational payoff vector in the interior of the set of feasible expected payoff vectors, there exists a pair of linear strategies that form a Nash equilibrium supporting the target payoff. The equilibrium strategies and the equilibrium payoff vectors form a globally stable solution (Smale [1980]).I would like to thank Andrew Atkeson and the anonymous referee for helpful comments. John Curran and Hao Li provided excellent research assistance. Financial support from the National Science Foundation, the Alfred P. Sloan Foundation and the Division of Social Sciences at the University of Chicago is gratefully acknowledged.     

Fully endogenous mechanism selection on finite outcome sets

Summary This paper defines a choice process over social outcomes in which agents choose the institutional rules ormechanisms themselves without outside interference. Truly endogenizing the mechanism selection process in this way, however, involves facing an infinite regress problem in which outcomes are chosen by games which are themselves chosen by games, ad infinitum. This paper allows the possibility of such an infinite regress which we callfully endogenous mechanism selection.We introduce the notion ofFree Choice which restricts the class of mechanisms in the regress to those which prevent agents from being locked in to an equilibrium outcome by the actions of others. Under this condition, the infinite regress is shown to get truncated with the number of selection iterations endogenously determined. It turns out that the outcomes resulting from a Free Choice-constrained regress are (Weakly) Pareto optimal; in particular, these outcomes solve a weighted Rawlsian Maxmin criterion. We also show that these outcomes are invariant to the equilibrium concept used to evaluate games in the regress.This paper is based on the author's dissertation from the University of Minnesota (November, 1989).I am very grateful for the guidance, advice, and encouragement from my advisor, Marcel K. Richter, and for the many helpful suggestions from David Levine. I have also benefited from conversations with Nabil Al-Najjar, Gerhard Glomm, Leonid Hurwicz, James Jordan, Ramon Marimon, Andrew McClennan, Ariel Rubinstein, and William Thomson.     

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

Summary We 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.I wish to thank Professors Salvador Barbera, Matthew Jackson, Herve Moulin and William Thomson for their helpful suggestions and two anonymous referees for their detailed comments. Conversations with Professors Hideo Konishi, Shinji Oseto Ken-ichi Shimomura and Stephen Ching were helpful. This work is supported by the Japan Economic Research Foundation and Research Grants PB89-0294 and PB89-0075 from the Direcion General de Investigacion Cientifica y Tecnica, Spanish Ministry of Education.     

Secure implementation experiments: Do strategy-proof mechanisms really work?

Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept used in social choice theory. Saijo, Sjöström and Yamato [Saijo, T., Sjöström, T., Yamato, T., 2003. Secure implementation: Strategy-proof mechanisms reconsidered. Working paper 4-03-1. Department of Economics, Pennsylvania State University] argue that this concept has serious drawbacks. In particular, many strategy-proof mechanisms have a continuum of Nash equilibria, including equilibria other than dominant strategy equilibria. For only a subset of strategy-proof mechanisms do the set of Nash equilibria and the set of dominant strategy equilibria coincide. For example, this double coincidence occurs in the Groves mechanism when preferences are single-peaked. We report experiments using two strategy-proof mechanisms. One of them has a large number of Nash equilibria, but the other has a unique Nash equilibrium. We found clear differences in the rate of dominant strategy play between the two.