Nash implementation of Lindahl allocations

We define a class of Nash based mechanisms that implement Lindahl allocations in standard public good economies. As those that first proved Nash implementation of Lindahl allocations, defined by Hurwicz (1979) and Walker (1981), the mechanisms provided here are continuous, feasible, and independent of agents' characteristics. In economies with two agents (e.g., bilateral monopolies, duopolies, principal-agent models), our mechanisms are also applicable, in contrast to the well-behaved mechanisms in the literature, and they satisfy favourable stability properties.     

Games with capacity manipulation: incentives and Nash equilibria

Studying the interactions between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and sufficient condition that guarantees the stability of a Nash equilibrium and the strategy-proofness of truthful capacity revelation under the hospital-optimal and intern-optimal stable rules. We then introduce generalized games of manipulation in which hospitals move first and state their capacities, and interns are subsequently assigned to hospitals using a sequential mechanism. In this setting, we first consider stable revelation mechanisms and introduce conditions guaranteeing the stability of the outcome. Next, we prove that every stable non-revelation mechanism leads to unstable allocations, unless restrictions on the preferences of the agents are introduced.     

Existence and Nash implementation of efficient sharing rules for a commonly owned technology

Suppose that a group of individuals owns collectively a technology which produces a consumption good by means of a (possibly heterogeneous) input. A sharing rule associates input contributions with a vector of consumptions that are technologically feasible. We show that the set of allocations obtained by any continuous sharing rule contains Pareto efficient allocations. We also present a mechanism that implements in Nash equilibrium the Pareto efficient allocations contained in an arbitrary sharing rule. Received: 29 June 1998/Accepted: 15 November 2000     

Implementation with renegotiation when preferences and feasible sets are state dependent

In this paper, we present a model of implementation where infeasible allocations are converted into feasible ones through a process of renegotiation that is represented by a reversion function. We describe the maximal set of Social Choice Correspondences that can be implemented in Nash Equilibrium in a class of reversion functions that punish agents for infeasibilities. This is used to study the implementation of the Walrasian Correspondence and several axiomatic solutions to problems of bargaining and taxation.     

The possibility of efficient provision of a public good in voluntary participation games

In this study, we provide the conditions for efficient provision of a public good in a participation game in which a non-negative integer number of units of the public good can be provided. In the case in which at most one unit of the public good can be provided, we provide refinements of Nash equilibria at which agents choose only a Nash equilibrium with an efficient allocation and provide sufficient conditions for cost-sharing rules that guarantee the existence of a Nash equilibrium with an efficient allocation. In the case of a multi-unit public good, we provide a necessary and sufficient condition for the existence of a Nash equilibrium with an efficient allocation and prove that Nash equilibria are less likely to support efficient allocations if the participation of many agents is needed for efficient provision of the public good in the case of identical agents. I would like to thank Koichi Tadenuma, Yukihiro Nishimura, Toshiyuki Fujita, John Weymark, Tatsuyoshi Saijo, Takehiko Yamato, Toshiji Miyakawa, Motohiro Sato, Takashi Shimizu, Nobue Suzuki, and Dirk T. G. Rübbelke for helpful comments and suggestions. I also thank the anonymous referees for detailed comments and suggestions. This research was supported by the Japanese Economic Research Foundation and the Grand-in-Aid for Young Scientists (Start-up) from the Japan Society for the Promotion of Science. Any remaining errors are my own.     

The ordinal egalitarian bargaining solution for finite choice sets

Rubinstein et al. (Econometrica 60:1171–1186, 1992) introduced the Ordinal Nash Bargaining Solution. They prove that Pareto optimality, ordinal invariance, ordinal symmetry, and IIA characterize this solution. A feature of their work is that attention is restricted to a domain of social choice problems with an infinite set of basic allocations. We introduce an alternative approach to solving finite social choice problems using a new notion called the Ordinal Egalitarian (OE) bargaining solution. This suggests the middle ranked allocation (or a lottery over the two middle ranked allocations) of the Pareto set as an outcome. We show that the OE solution is characterized by weak credible optimality, ordinal symmetry and independence of redundant alternatives. We conclude by arguing that what allows us to make progress on this problem is that with finite choice sets, the counting metric is a natural and fully ordinal way to measure gains and losses to agents seeking to solve bargaining problems.     

Implementation of the Walrasian correspondence without continuous,convex, and ordered preferences

This paper consideres the problem of designing better mechanisms whose Nash allocations coincide with constrained Walrasian allocations for non-neoclassical economies under the minimal possible assumptions. We show that no assumprions on preferences are needed for feasible and continuous implementation of the constrained Walraisan correspondence. Further, under the monotonicity assumption, we present a mechanism that is completely feasible and continuous. Hence, no continuity and convexity assumptions on preferences are required, and preferences may be nontotal or nontransitive. Thus, this paper gives a somewhat positive answer to the question raised in the literature by showing that, even for non-neoclassical economies, there are incentive-compatible, privacy preserving, and well-behaved mechanisms which yield Pareto-efficient and individually rational allocations at Nash equilibria.I wish to thank J. S. Chipman, J. Jordan, M. Richter, H. Weinberger, the editor, and two anonymous referees for useful comments and suggestions. I am particularly thankful to L. Hurwicz who stimulated my interest in this problem and provided detailed comments and suggestions.     

A voluntary participation game through a unit-by-unit cost share mechanism of a non-excludable public good

The strategic analysis of voluntary participation in the public good provision has shown two distinct results. First, when the provision of public goods is binary, there are Nash equilibria supporting efficient allocations, and these are Strong Nash equilibria of the game. On the other hand, a model of a continuous public good (Saijo–Yamato, J Econ Theory 84:227–242, 1999) showed that the participation of all agents is not an equilibrium in many situations. This article considers the provision of a discrete and multi-unit public good, and examines a unit-by-unit participation game. Namely, people are asked to participate in each unit of public good provision, and those who chose to participate share the marginal cost of public good. In this game of public good provision, there are subgame-perfect equilibria that are Pareto efficient. We also use the refinement concepts to eliminate inefficient subgame-perfect equilibria and also to characterize the efficient subgame-perfect equilibria.     

Natural implementation in public goods economies

In this paper, we identify necessary and sufficient conditions for social choice correspondences to be Nash implemented by “natural” mechanisms in economies with arbitrary numbers of private and public goods. We find that when there exist only one public good and an arbitrary number of private goods, the Lindahl correspondence is implementable by a natural quantity mechanism in which each agent announces his own consumption bundle of private goods and input vectors for public goods. However, regardless of the numbers of private and public goods, the Pareto correspondence is not implementable even by any natural price ⁿ -quantity mechanism in which each agent reports a price vector of private goods and all agents’ personalized price vectors of public goods, in addition to his own consumption bundle of private goods and input vectors for public goods.     

Generic efficiency and collusion-proofness in exchange economies

The purpose of this paper is to study the kind of efficient allocations that can be achieved in exchange economies with asymmetric information, by means of a decentralized mechanism robust to coalitional, strategic deviations. To this end, we define a new strategic equilibrium concept – called strong collusion-proof contract – designed to characterize stable communication agreements in games with differential information against non-binding, self-enforcing and incentive compatible deviations by coalitions. We then construct a strategic market mechanism which, for quasi-linear economies, is such that its strong collusion-proof contracts generically induce the incentive compatible interim efficient allocations. Moreover, we show that these allocations can be achieved by strong collusion-proof contracts. We show that the internally consistent extension of the strong collusion-proof contracts generically yields the same set of efficient allocations. Received: 22 January 2001/Accepted: 15 April 2002 RID="*" ID="*"  This author was working at CORE when this paper was written. We wish to thank Claude d'Aspremont, David Martimort, Jean-Fran?ois Mertens and Heracles Polemarchakis for helpful comments on an earlier version. The usual disclaimer applies.     

Spoilers,blocking coalitions,and the core

This paper surveys non-cooperative implementations of the core which tell an intuitive story of coalition formation. Under the core solution concept, if a blocking coalition exists those agents abandon the current allocation without regard for the consequences to players outside the blocking coalition. Yet in certain circumstances, these players have an incentive to prevent formation of any blocking coalition; a game analyzed in Lagunoff (Games Econ Behav 7:54–61, 1994) is vulnerable to such circumstances. To obtain all core allocations and only core allocations, a mechanism must either restrict the actions of non-members of a proposed coalition, or ensure that non-members are unharmed by the departure of the coalition. These requirements illustrate the core’s nonchalance toward agents not in blocking coalitions. The author gives special thanks to Beth Allen and Andy McLennan for their direction, and gratefully acknowledges valuable discussions with Roger Lagunoff, Hugo Sonnenschein, John Ledyard, Myrna Wooders, Nuray Akin, as well as comments from participants at the 2004 Spring Midwest Economic Theory and the Society for Economic Design conferences and from anonymous referees. All errors remain my own. Partial funding came from National Science Foundation grants DMI-0070257 and DMI-0217974.     

VOLUNTARY CONTRIBUTION GAMES: EFFICIENT PRIVATE PROVISION OF PUBLIC GOODS

This paper reports on a series of laboratory experiments designed to evaluate a mechanism for the voluntary provision of public good. The public good is provided if the total contributions meet or exceed a threshold and all contributions are returned if the public good is not provided. The members of the group all know the threshold, the incomes, and the valuations assigned the public good by all other members. The results support the prediction that this mechanism will yield Pareto efficient outcomes and suggest that economic agents adopt strategies which form equilibria satisfying certain refinements to the Nash equilibrium.     

Anonymous implementation of the Lindahl correspondence: possibility and impossibility results

This paper deals with the existence of anonymous mechanisms to realize the Lindahl correspondence. We consider, in turn, constant and decreasing returns to scale technologies for producing public goods. In each case, we provide a continuous (but not smooth) and weakly balanced mechanism, which meets the two conditions. We then remark that they satisfy a property (see property NC), which is related to, but in fact stronger than anonymity. Finally, we prove that if a mechanism has this property, if it is weakly balanced and implements the Lindahl correspondence, then it cannot be differentiable around Nash equilibria.     

Collusion, renegotiation and implementation

We study the implementation problem for exchange economies when agents can renegotiate the outcome assigned by the planner and can collude. We focus on the use of sequential mechanisms and present a simple sufficient condition for implementation with renegotiation in strong perfect equilibrium. We present an application to optimal risk sharing, showing that the possibility of collusion and renegotiation does not in general prevent the implementation of efficient allocations. Received: 27 August 1997/Accepted: 29 October 1998     

Money-metric utilitarianism

We discuss a method of ranking allocations in economic environments which applies when we do not know the names or preferences of individual agents. We require that two allocations can be ranked with the knowledge only of agents present, their aggregate bundles, and community indifference sets—a condition we refer to as aggregate independence. We also postulate a basic Pareto and continuity property, and a property stating that when two disjoint economies and allocations are put together, the ranking in the large economy should be consistent with the rankings in the two smaller economies (reinforcement). We show that a ranking method satisfies these axioms if and only if there is a probability measure over the strictly positive prices for which the rule ranks allocations on the basis of the random-price money-metric utilitarian rule. This is a rule which computes the money-metric utility for each agent at each price, sums these, and then takes an expectation according to the probability measure.     

Monotonicity implies generalized strategy-proofness for correspondences

We show that Maskin monotone social choice correspondences on sufficiently rich domains satisfy a generalized strategy-proofness property, thus generalizing Muller and Satterthwaite’s (1977) theorem to correspondences. The result is interpreted as a possibility theorem on the dominant-strategy implementability of monotone SCCs via set-valued mechanisms for agents who are completely ignorant about the finally selected outcome. Alternatively, the result yields a partial characterization of the restrictions entailed by Nash implementability of correspondences. Received: 3 November 1997/Accepted: 26 April 1999     

Stable coalition governments: the case of three political parties

We explore to what extent we can propose fixed negotiation rules and simple mechanisms (or protocols) that guarantee that political parties can form stable coalition governments. We analyze the case in which three parties can hold office in the form of two-party coalitions. We define a family of weighted rules that select political agreements as a function of the bliss points of the parties and electoral results (Gamson’s law and equal share among others are included). We show that every weighted rule yields a stable coalition. We use implementation theory to design a protocol (in the form of a mechanism) that guarantees that a stable coalition will govern. We find that no dominant solvable mechanism can be used for this purpose, but there is a simultaneous unanimity mechanism that implements it in Nash and strong Nash equilibrium. Finally, we analyze the case of a larger number of political parties.     

The equity-efficiency trade-off reconsidered

Envy-free and Pareto optimal allocations never exist in large economies with production, if there is enough variation with respect to preferences and innate abilities of the agents. If distributional equity is given priority only second best envy-free allocations may be considered. Those allocations are characterised in finite and continuum economies. In continuum economies envy-free allocations are type-egalitarian, i.e. agents with the same preferences but different abilities obtain the same consumption-labour bundle. Regarding implementation envy-free allocations can only be implemented by a tax depending on labour and income.I would like to thank two anonymous referees and the editor in charge of this paper for very helpful comments.     

Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization

The concept of coalition proof Nash equilibrium was introduced by Bernheim et al. [5]. In the present paper, we consider the representation problem for coalition proof Nash equilibrium: For a given effectivity function, describing the power structure or the system of rights of coalitions in society, it is investigated whether there is a game form which gives rise to this effectivity function and which is such that for any preference assignment, there is a coalition proof Nash equilibrium.  It is shown that the effectivity functions which can be represented in coalition proof Nash equilibrium are exactly those which satisfy the well-known properties of maximality and superadditivity. As a corollary of the result, we obtain necessary conditions for implementation of a social choice correspondence in coalition proof Nash equilibrium which can be formulated in terms of the associated effectivity function. Received: 24 June 1999/Accepted: 20 September 2000