The Partnered Core of a Game without Side Payments

A payoff for a game is partnered if it admits no asymmetric dependencies. We introduce the partnered core of a game without side payments and show that the partnered core of a balanced game is nonempty. The result is a strengthening of Scarf's Theorem on the nonemptiness of the core of a balanced game without side payments. In addition, it is shown that if there are at most a countable number of points in the partnered core of a game then at least one core point isminimallypartnered, meaning that no player requires any other player in particular to obtain his part of the core payoff.Journal of Economic LiteratureClassification Number: C71.     

Information at equilibrium

Summary. In a game with rational expectations, individuals simultaneously refine their information with the information revealed by the strategies of other individuals. At a Nash equilibrium of a game with rational expectations, the information of individuals is essentially symmetric: the same profile of strategies is also an equilibrium of a game with symmetric information; and strategies are common knowledge. If each player has a veto act, which yields a minimum payoff that no other profile of strategies attains, then the veto profile is the only Nash equilibrium, and it is is an equilibrium with rational expectations and essentially symmetric information; which accounts for the impossibility of speculation. Received: June 20, 2001; revised version: January 9, 2002 RID="*" ID="*" We wish to thank Pierpaolo Battigalli, Fran?oise Forges, Franco Donzelli, Leonidas Koutsougeras, Aldo Rustichini, Rajiv Vohra and Nicholas Yannelis for their comments. Correspondence to: H. Polemarchakis     

Connecting the cooperative and competitive structures of the multiple-partners assignment game

Multiple-partners assignment game is the name used by Sotomayor [The multiple partners game, in: M. Majumdar (Ed.), Equilibrium and Dynamics: Essays in Honor of David Gale, The Macmillan Press Ltd., New York, 1992; The lattice structure of the set of stable outcomes of the multiple partners assignment game, Int. J. Game Theory 28 (1999) 567-583] to describe the cooperative structure of the many-to-many matching market with additively separable utilities. Stability concept is proved to be different from the core concept. An economic structure is proposed where the concept of competitive equilibrium payoff is introduced in connection to the equilibrium concept from standard microeconomic theory. The paper examines how this equilibrium concept compares with the cooperative equilibrium concept. Properties of interest to the cooperative and competitive markets are derived.     

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 New Bargaining Set of an N-Person Game and Endogenous Coalition Formation

The two most fundamental questions in cooperative game theory are: When a game is played, what coalitions will be formed and what payoff vectors will be chosen? Few solution concepts or theories in the current literature provide satisfactory answers to both questions; answers are especially lacking for the first one. In this paper we introduce a new bargaining set, which is the first solution concept in cooperative game theory that provides answers to both fundamental questions endogenously. Journal of Economic Literature Classification Number: C71.     

Axiomatizations of two types of Shapley values for games on union closed systems

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson value for games with limited communication.     

A Kantian critique of neoclassical law and economics

Abstract

This paper outlines a critique of neoclassical law and economics based on the ethics of Immanuel Kant, focusing on four central topics: efficiency as the sole evaluative criterion for policy-making, hypothetical compensation in Kaldor–Hicks efficiency, the instrumental nature of rights and the assumption of reciprocal causation, and the role of punishment to both society and the individual. This overview addresses issues of concern not just to Kantians, but to anyone dissatisfied with the utilitarian foundations of law and economics and the amoral view of law upon which it is based.     

Competitive outcomes and the inner core of NTU market games

We consider the inner core as a solution concept for cooperative games with non-transferable utility (NTU) and its relationship to payoffs of competitive equilibria of markets that are induced by NTU games. An NTU game is an NTU market game if there exists a market such that the set of utility allocations a coalition can achieve in the market coincides with the set of utility allocations the coalition can achieve in the game. In this paper, we introduce a new construction of a market based on a closed subset of the inner core which satisfies a strict positive separability. We show that the constructed market represents the NTU game and, further, has the given closed set as the set of payoff vectors of competitive equilibria. It turns out that this market is not uniquely determined, and thus, we obtain a class of markets. Our results generalize those relating to competitive outcomes of NTU market games in the literature.     

Stochastic Cooperative Games: Superadditivity, Convexity, and Certainty Equivalents

This paper extends the notions of superadditivity and convexity to stochastic cooperative games. It is shown that convex games are superadditive and have nonempty cores, and that these results also hold in the context of NTU games. Furthermore, a subclass of stochastic cooperative games to which one can associate a deterministic cooperative game is considered. It is shown that such a stochastic cooperative game satisfies properties like nonemptiness of the core, superadditivity, and convexity if and only if the corresponding deterministic game satisfies these properties.Journal of Economic LiteratureClassification Number: C71.     

Characterization of the extreme core allocations of the assignment game

A characterization of the extreme core allocations of the assignment game is given in terms of the reduced marginal worth vectors. For each ordering in the player set, a payoff vector is defined where each player receives his or her marginal contribution to a certain reduced game played by his or her predecessors. This set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is proved to be the set of extreme points of the core of the assignment game. Therefore, although assignment games are hardly ever convex, the same characterization of extreme core allocations is valid for convex games.     

Sowing Doubt Optimally in Two-Person Repeated Games

Consider a two-person repeated game, where one of the players, P1, can sow doubt, in the mind of his opponent, as to what P1's payoffs are. This results in a two-person repeated game with incomplete information. By sowing doubt, P1 can sometimes increase his minimal equilibrium payoff in the original game. We prove that this minimum is maximal when only one payoff matrix, the negative of the payoff matrix of the opponent, is added (the opponent thus believes that he might play a zero-sum game). We obtain two formulas for calculating this maximal minimum payoff. Journal of Economic Literature Classification Numbers: C7, D8.     

Walras's tâtonnement : a reply to Rebeyrol and Costa

Abstract

About 50 years ago a lively discussion was started in the ‘Notes and Memoranda’ sections of the Economic Journal about the new welfare economics that had been initiated by Kaldor and Hicks 10 years earlier and was heavily criticized by Little in 1950. Altogether 18 Notes appeared dealing with questions of definition, of limitations, of practical relevance and theoretical details. This paper gives an overview of this discussion and presents it as a methodological approach of the past which that declined as a consequence of the spread of the referee process.     

On the core of economies with multilateral environmental externalities

We revisit the cooperative model of coalition formation in economies with environmental externalities. Motivated by recent concerns over the true behavior and incentives of key players in international negotiations over the climate and the environment, we construct a cooperative game where the members of each coalition have uncertainty over the behavior of the nonmembers, and in particular they face uncertainty over their coalition structure. As a result, a coalition assigns various probability distributions over the set of partitions the outsiders can form. We compute the payoff of each coalition under this assumption and we derive conditions under which the core of the induced cooperative game is nonempty.     

The core of some location games

An important problem in Location Theory is that of assigning plants to locations in an optimal manner. In the context of this problem, recognizing interplant transportation costs, Koopmans and Beckmann (1957) introduced the Quadratic Assignment Problem (QAP). It is shown in this paper that when the QAP is formulated as a cooperative location game, its core may be empty. By contrast, the core of the game corresponding to thelinear assignment problem (where transportation costs are disregarded) is assured to be non-empty. Some conditions under which the core is non-empty are discussed.I am grateful to two anonymous referees of this journal for their comments.     

Dissertation abstract: Essays on veto bargaining games

This dissertation experimentally analyzes the outcomes of multilateral legislative bargaining games in the presence of a veto player. The first essay examines veto power—the right of an agent to unilaterally block decisions but without the ability to unilaterally secure his/her preferred outcome. Using Winter’s (1996) theoretical framework, I consider two cases: urgent committees where the total amount of money to be distributed shrinks by 50% if proposals do not pass and non-urgent committees where the total amount of money shrinks by 5% if proposals do not pass. Committees with a veto player take longer to reach decisions (are less efficient) than without a veto player and veto players proposals generate less consensus then non-veto players proposals, outcomes on which the theory is silent. In addition, veto power in conjunction with proposer power generates excessive power for the veto player. This suggests that limiting veto players’ proposer rights (e.g., limiting their ability to chair committees) would go a long way to curbing their power, a major concern in committees in which one or more players has veto power. Finally, non-veto players show substantially more willingness to compromise than veto players, with players in the control game somewhere in between. I relate the results to the theoretical literature on the impact of veto power as well as concerns about the impact of veto power in real-life committees. The second essay discusses in detail the voting patterns in the veto and control games reported in the first essay. The empirical cumulative density functions of shares veto players accepted first degree stochastically dominates that of shares for the controls and the empirical cdfs of shares the controls accepted first degree stochastically dominate that of shares for non-veto players. Random effect probits support this conclusion as well. In addition, regressions imply favorable treatment of voting and proposing between non-veto players which, however, does not result in larger shares in the end. Coalition partners consistently demand more than the stationary subgame perfect Nash equilibrium share except for veto players in non-urgent committees. JEL Classification C7, D7, C78, D72 Dissertation Committee: John H. Kagel, Advisor Massimo Morelli Alan Wiseman Stephen Cosslett     

Lexicographic composition of simple games

Certain voting bodies can be modeled as a simple game where a coalition's winning depends on whether it wins, blocks or loses in two smaller simple games. There are essentially five such ways to combine two proper games into a proper game. The most decisive is the lexicographic rule, where a coalition must either win in G₁, or block in G₁ and win in G₂. When two isomorphic games are combined lexicographically, a given role for a player confers equal or more power when held in the first game than the second, if power is assessed by any semi-value. A game is lexicographically separable when the players of the two components partition the whole set. Games with veto players are not separable, and games of two or more players with identical roles are separable only if decisive. Some separable games are egalitarian in that they give players identical roles.     

Endogenous timing in the presence of non-monotonicities

The aim of this paper is to generalize the endogenous timing game proposed by Hamilton and Slutsky (Games and Economic Behavior, 1990, 2, pp. 29–46) by allowing the payoff or the marginal payoff of a player to become non-monotonic with respect to the strategy of the opponent. We propose a taxonomy of the subgame-perfect Nash equilibria based on the characteristics of the payoff functions proposed by Eaton (Canadian Journal of Economics, 2004, 37, pp. 805–29). We determine under which conditions of the initial payoff functions commitment has a social value and when the simultaneous-move Nash equilibrium is commitment robust and discuss its Pareto efficiency.     

Coalitional Bargaining with Competition to Make Offers

The paper analyzes a simple discrete-time noncooperative coalitional bargaining game in which, at each stage, there is a contest for the right to make a proposal. The pure stationary subgame-perfect equilibrium payoff set is equal to the core.Journal of Economic LiteratureClassification Numbers: 026.     

Correlated Equilibrium in Stochastic Games

We study the existence of uniform correlated equilibrium payoffs in stochastic games. The correlation devices that we use are either autonomous (they base their choice of signal on previous signals, but not on previous states or actions) or stationary (their choice is independent of any data and is drawn according to the same probability distribution at every stage). We prove that any n-player stochastic game admits an autonomous correlated equilibrium payoff. When the game is positive and recursive, a stationary correlated equilibrium payoff exists. Journal of Economic Literature Classification Numbers: C72, C73.     

A “Super” Folk Theorem for dynastic repeated games

We analyze dynastic repeated games. These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained by sequential equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n  ≥  4 players for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize fully the conditions under which a sequential equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a subgame perfect equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “inter-generational agreement.” A previous version of this paper was circulated as Anderlini et al. (2005). We are grateful to Jeff Ely, Leonardo Felli, Navin Kartik, David Levine, Stephen Morris, Michele Piccione, Andrew Postlewaite, Lones Smith and to seminar audiences at Bocconi, Cambridge, CEPR-Guerzensee, Chicago, Columbia, Edinburgh, Essex, Georgetown, Leicester, LSE, Northwestern, Oxford, Rome (La Sapienza), Rutgers, SAET-Vigo, Stanford, SUNY-Albany, UCL, UC-San Diego, Venice and Yale for helpful feedback.