Maskin's Theorem with limited veto power

We weaken the no-veto power condition of Maskin [Maskin, E.,1999. Nash equilibrium and welfare optimality. Rev. Econ. Stud. 66, 23–38] to limited veto power, and prove that any monotonic social choice rule is Nash implementable if it satisfies this weaker condition. The result is obtained by using the canonical Maskin mechanism without modification. An immediate corollary is that the weak core is Nash implementable in any coalitional game environment. An example is given to show that the strong core need not be implementable, even when it is monotonic.     

A characterization of social choice correspondences that implement the core of simple games

In a coalitional voting game, an alternative is said to be in the core when no majority is willing to replace it with another alternative. A social choice correspondence is a mapping which associates any profile of voters’ preferences with a non-empty subset of the set of alternatives, which is understood as the set of selected outcomes. We characterize the social choice correspondences which always select the core of a simple game for any profile of preferences. This work was completed when B. Tchantcho was Visiting assistant Professor at UTA (University of Texas at Arlington). We acknowledge the support of the Department of Mathematics of UTA. We are most grateful to R. Pongou of Brown University, USA for his help and advice. We sincerely thank N.G Andjiga for his helpful comments and we are indebted to two anonymous referees for their helpful comments.     

Feasible elimination procedures in social choice: An axiomatic characterization

Feasible elimination procedures (Peleg, 1978) play a central role in constructing social choice functions which have the following property: in the associated game form, for any preference profile there exists a strong Nash equilibrium resulting in the sincere outcome. In this paper we provide an axiomatic characterization of the social choice correspondences resulting from applying feasible elimination procedures. The axioms are anonymity, Maskin monotonicity, and independent blocking. We also show that these axioms are logically independent.     

Voluntary Contributions to Multiple Public Projects

The problem of financing a set of discrete public goods (facilities, projects) by private contributions is studied. The corresponding cooperative game, the realization game , is shown to be convex. For the noncooperative setting we study a realization scheme that induces a strategic game. This contribution game is shown to be a generalized ordinal potential game ; a best–response in the contribution game implies a best response in a coordination game in which the payoff to all players is the utilitarian collective welfare function, i.e., the sum of the utility functions of the players. Strategy profiles maximizing utilitarian welfare are strong Nash equilibria of the contribution game. Each strong Nash equilibrium corresponds in a natural way with a core element of the realization game, and vice versa. Moreover, each strong Nash equilibrium is coalitional proof.     

Bilateral commitment

We consider non-cooperative environments in which two players have the power to gradually and unilaterally rule out some of their actions. Formally, we embed a strategic-form game into a multi-stage game, in which players can restrict their action spaces in all but the final stage, and select among the remaining actions in the last stage. We say that an action profile is implementable by commitment if this action profile is played in the last stage of a subgame-perfect equilibrium path. We provide a complete characterization of all implementable action profiles and a simple method to find them. It turns out that the set of implementable profiles does not depend on the length of the commitment process. We show, furthermore, that commitments can have social value in the sense that in some games there are implementable action profiles that dominate all Nash equilibria of the original game.     

Comparative advantage and strategic specialization

This paper shows that a strong comparative advantage is necessary for free trade and specialization in a 2 × 2 symmetric Ricardian model to be achieved in a Nash equilibrium. Governments strategically control labor distribution across industries, and representative agents maximize Cobb–Douglas utilities. A Nash equilibrium with complete specialization is achieved if and only if relative productivity exceeds a key value of 3, which is considered a very large number based on previous empirical studies. This paper also introduces a two‐stage game where each government chooses labor distribution first and then tariffs. In this two‐stage game, complete specialization is never achieved for any relative productivity level. Finally, by generalizing the Cobb–Douglas model into constant elasticity of substitution (CES) preferences, I show that if immiserizing growth effects exist, complete specialization could not be achieved for any level of relative productivity.     

Are incentives against economic justice?

We consider the problem of fairly allocating a social endowment of indivisible goods and money when the domain of admissible preferences contains, but is not restricted to, quasi-linear preferences. We analyze the manipulability of the Generalized Money Rawlsian Fair (GMRF) solutions. (i) We show that the Nash and strong Nash equilibrium correspondences of the “preference revelation game form” associated with each GMRF solution coincide with the no-envy solution (in equilibrium, efficiency is preserved according to agents' true preferences). (ii) A corollary is that the GMRF solutions “naturally implement” the no-envy solution in Nash and strong Nash equilibria.     

Learning by trial and error

A person learns by trial and error if he occasionally tries out new strategies, rejecting choices that are erroneous in the sense that they do not lead to higher payoffs. In a game, however, strategies can become erroneous due to a change of behavior by someone else. We introduce a learning rule in which behavior is conditional on whether a player experiences an error of the first or second type. This rule, called interactive trial and error learning, implements Nash equilibrium behavior in any game with generic payoffs and at least one pure Nash equilibrium.     

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.     

Further results on essential Nash equilibria in normal-form games

A Nash equilibrium \(x\) of a normal-form game \(G\) is essential if any perturbation of \(G\) has an equilibrium close to \(x\). Using payoff perturbations, we identify a new collection of games containing a dense, residual subset of games whose Nash equilibria are all essential. This collection covers economic examples that cannot be handled by extant results and subsumes the sets of games considered in the literature.     

Coalitional Bayesian Nash implementation in differential information economies

Summary. A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally implements it. Our main theorem proves that a social choice set is coalitionally implementable if and only if it is interim individually rational, interim efficient, coalitional B ayesian incentive compatible, and satisfies a coalitional Bayesian monotonicity condition as well as a closure condition. As an application of our main result, we show that the private core and the private Shapley value of an economy with differential information are coalitionally implementable. Received: January 12, 1998; revised version: March 30, 2000     

Service Quality,Competition, and Regulatory Policies in the Postal Sector

This paper presents a simple model which illustrates the possible policy- and welfare-implications of endogenous product selection in the postal sector. The cost of a unit of mail depends on its "quality" (e.g., speed of delivery) and on the type and location of the addressee (firms, urban households, and rural households). Senders have inelastic demands and differ in their willingness to pay for quality. Addressees are passive but their utility may affect social welfare. Two operators play a two-stage game, first choosing qualities and then prices. We first show that the equilibrium with two private (profit maximizing) operators results in an inefficient provision of quality. Then, we consider the mixed (Nash) equilibrium with one private and one (welfare maximizing) public operator. If the budget constraint of the public firm is not binding, this equilibrium is shown to be first-best efficient even if social welfare accounts for the utility of addressees. If the budget constraint is binding, the mixed equilibrium is not efficient but yields a higher level of welfare than the private equilibrium. Finally, we study the impact of minimum quality standards within our setting.     

Intermediate Preferences and Behavioral Conformity in Large Games

Motivated by Wooders, Cartwright, and Selten (2006) , we consider games with a continuum of players and intermediate preferences. We show that any such game has a Nash equilibrium that induces a partition of the set of attributes into a bounded number of convex sets with the following property: all players with an attribute in the interior of the same element of the partition play the same action. We then use this result to show that all sufficiently large, equicontinuous games with intermediate preferences have an approximate equilibrium with the same property. Our result on behavior conformity for large finite game generalizes Theorem 3 of Wooders et al. (2006) by allowing both a wider class of preferences and a more general attribute space.     

International Cross-Ownership and Strategic Trade Policies

The paper analyzes a model of strategic trade policies in the presence of international cross-ownership of firms that are heterogenous both in terms of costs and in terms of extent of foreign ownership. The equilibrium pattern of taxes and subsidies is characterized for any arbitrary cross-ownership profile, and any number of heterogenous firms. The equilibrium subsidy (or tax) given to any firm is shown to depend, in a separable manner, on the firm's characteristics and on the covariance of the distribution of cost and foreign ownership across firms. A neutrality theorem is proved concerning the Nash equilibrium of the game between governments: in equilibrium, the pattern of trade, the value of each firm, and world welfare are independent of the ownership pattern.     

A Public Choice Approach to Strategic and Nonstrategic Environmental Policy

In this paper we take a public choice perspective on strategic environmental policy and international environmental agreements. We examine cooperative and noncooperative environmental policies under governments that are either welfare maximizers (“good dictators”) or tax revenue maximizers (“Leviathans”). We show that Leviathans can perform better in terms of welfare and that good dictators can set higher taxes. We then analyze international environmental agreements and show that the breakdown of environmental cooperation can indeed lead to a welfare gain for all signatory countries. Considering a delegation game between governments, we find that a Pareto‐superior Leviathan outcome can be the unique Nash equilibrium.     

Equilibria under deferred acceptance: Dropping strategies,filled positions,and welfare

We study many-to-one matching markets where hospitals have responsive preferences over students. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling.Roth and Sotomayor (1990) showed that equilibrium outcomes can be unstable. We prove that any stable matching is obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the ‘rural hospital theorem’ cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the equilibrium that is reached and (b) welfare levels are not bounded by the optimal stable matchings (with respect to the true preferences).     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Strong price of anarchy

A strong equilibrium is a pure Nash equilibrium which is resilient to deviations by coalitions. We define the strong price of anarchy (SPoA) to be the ratio of the worst strong equilibrium to the social optimum. Differently from the Price of Anarchy (defined as the ratio of the worst Nash Equilibrium to the social optimum), it quantifies the loss incurred from the lack of a central designer in settings that allow for coordination.We study the SPoA in two settings, namely job scheduling and network creation. In the job scheduling game we show that for unrelated machines the SPoA can be bounded as a function of the number of machines and the size of the coalition. For the network creation game we show that the SPoA is at most 2. In both cases we show that a strong equilibrium always exists, except for a well defined subset of network creation games.     

On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm

This study analyzes a preference revelation game in the student-optimal deferred acceptance algorithm in a college admission problem. We assume that each college's true preferences are known publicly, and analyze the strategic behavior of students. We demonstrate the existence of a strictly strong Nash equilibrium in the preference revelation game through a simple algorithm that finds it. Specifically, (i) the equilibrium outcome from our algorithm is the same matching as in the efficiency-adjusted deferred acceptance algorithm and (ii) in a one-to-one matching market, it coincides with the student-optimal von Neumann–Morgenstern (vNM) stable matching. We also show that (i) when a strict core allocation in a housing market derived from a college admission market exists, it can be supported by a strictly strong Nash equilibrium, and (ii) there exists a strictly strong Nash equilibrium under the college-optimal deferred acceptance algorithm if and only if the student-optimal stable matching is Pareto-efficient for students.