Bargaining foundations of the median voter theorem

We give a game-theoretic foundation for the median voter theorem in a one-dimensional bargaining model based on Baron and Ferejohn's [D. Baron, J. Ferejohn, Bargaining in legislatures, Amer. Polit. Sci. Rev. 83 (1989) 1181-1206] model of distributive politics. We prove that as the agents become arbitrarily patient, the set of proposals that can be passed in any pure strategy, subgame perfect equilibrium collapses to the median voter's ideal point. While we leave the possibility of some delay, we prove that the agents' equilibrium continuation payoffs converge to the utility from the median, so that delay, if it occurs, is inconsequential. We do not impose stationarity or any other refinements. Our result counters intuition based on the folk theorem for repeated games, and it contrasts with the known result for the distributive bargaining model that as agents become patient, any division of the dollar can be supported as a subgame perfect equilibrium outcome.     

An impossibility result for virtual implementation with status quo

In this paper, virtual implementation is restricted to deliver, on the equilibrium path, either a socially optimal outcome or a status quo: an outcome fixed for all preference profiles. Under such a restriction, for any unanimous and implementable social choice function there is a dictator, who obtains her most preferable outcome as long as all agents prefer this outcome to the status quo. Further restrictions on the lottery space and the range of social choice functions allow the dictator to impose her most preferred outcome even when other agents prefer the status quo to this outcome.     

Structural holes in social networks: A remark

In a recent article, [S. Goyal, F. Vega-Redondo, Structural holes in social networks, J. Econ. Theory 137 (1) (2007) 460-492] the authors (GVR) showed the importance of stars and cycles in a given network formation game. Implicitly, in their article, a network is called an equilibrium if it is generated by an equilibrium strategy. We extend the results of GVR to the case of a stronger requirement: namely, that a network can be called an equilibrium only if all the strategies generating it are equilibria. We also show, in a dynamic framework, that both definitions differ in crucial ways.     

Fictitious play property of the Nash demand game

We show that the Nash demand game has the fictitious play property. We also show that almost every fictitious play process and its associated belief path converge to a pure-strategy Nash equilibrium in the Nash demand game.     

Bargaining and markets: complexity and the competitive outcome

Rubinstein and Wolinsky (Rev. Econ. Stud. 57 (1990) 63-78) consider a simple decentralised market game in which agents meet randomly or voluntarily and bargain over the terms of trade. They show that any individually rational price can be sustained as a sequential equilibrium even though the model has a unique competitive outcome. Here, I consider Rubinstein and Wolinsky's model and show that if complexity costs of implementing strategies enter players’ preferences, together with the standard payoff in the game, then every equilibrium is stationary/Markov and induces the unique competitive price. Thus, I demonstrate that aversion to complexity may provide a justification for the competitive outcome.     

ON THE NEUTRALITY OF COALITION FORMATION IN A PURE BARGAINING PROBLEM*

We consider the sequential bargaining game à la Stahl–Binmore–Rubinstein with random proposers, juxtaposing an ex ante coalition formation stage to their bargaining game. On the basis of the expected outcomes in the negotiation over how to split a dollar, players can form coalitions in a sequential manner, within each of which they can redistribute their payoffs. It turns out that the grand coalition does form, and that each player receives his discounted expected payoff, which is obtained by playing as a single player in the negotiation, although there could be many equilibria in the bargaining stage.     

Weak links, good shots and other public good games: Building on BBV

We suggest an alternative way of analyzing the canonical Bergstrom-Blume-Varian model of non-cooperative voluntary contributions to a public good that avoids the proliferation of dimensions as the number of players is increased. We exploit this approach to analyze models in which the aggregate level of public good is determined as a more general social composition function of individual gifts — specifically, as a CES form — rather than as an unweighted sum. We also analyze Hirshleifer's weakest-link and best-shot models. In each case, we characterize the set of equilibria, in some cases establishing existence of a unique equilibrium as well as briefly pointing out some interesting comparative static properties. We also study the weakest-link and best-shot limits of the CES composition function and show how the former can be used for equilibrium selection and the latter to establish that equilibria of some better-shot games are identical to those of the much simpler best-shot game.     

Robust equilibria under non-common priors

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogeneous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.     

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.     

A simple sufficient condition for strong implementation

In an important step forward Maskin [E. Maskin, Nash equilibrium and welfare optimality, Rev. Econ. Stud. 66 (1999) 23–38] showed that two properties – monotonicity and no veto power – are together sufficient for Nash implementation. In contrast to the vast literature that followed, this characterization has two major advantages: First, it is often easy to verify, and second, it has an elegant and simple interpretation. However, there does not exist a similar condition for social choice correspondences that are implementable in strong equilibrium. All existing characterizations are either hard to verify or apply only to comprehensive preference domains. In this paper we improve the situation by giving one such condition. Moreover, using well-known examples we show that this is a practical tool.     

The influence of group size on distributional fairness under voting by veto

Voting by Veto [VBV], developed by Dennis C. Mueller, is a two-stage voting mechanism for committee decision making. In the first stage, every member of the committee makes a proposal. The proposals are joined with the current status quo (or another fallback option). For the second stage, a random mechanism determines the order of voting and the committee members sequentially eliminate one alternative each. After every committee member has exercised her veto, a single winning alternative remains. Game theory predicts that the equality of the resulting distribution under VBV varies with group size. Hence, decisions in two-member groups should result in highly unequal distributions of benefits. With increasing group size, however, VBV should generate more equally distributed outcomes. We examine the effect of group size under VBV in a series of laboratory experiments where groups with a varying number of members play a ‘divide the dollar game’. Our results confirm that larger groups choose more equal distributions than smaller groups. However, we also find deviations from the model's predictions. Some committees in our experiment do not select Pareto-optimal alternatives. An exploratory analysis of possible explanations suggests that individual behavior is most likely motivated by a combination of material self-interest and social preferences such as reciprocity and fairness.     

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.     

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.     

Endogenous private information structures

We formally incorporate the option to gather information into a game and thus endogenize the information structure. We ask whether models with exogenous information structures are robust with respect to this endogenization. Any Nash equilibrium of the game with information acquisition induces a Nash equilibrium in the corresponding game with an exogenous structure. We provide sufficient conditions on the structure of the game for which this remains true when ‘Nash’ is replaced by ‘sequential’. We characterize the (sequential) Nash equilibria of games with exogenous information structures that can arise as a (sequential) Nash equilibrium of games with endogenous information acquisition.     

Generalized potentials and robust sets of equilibria

This paper introduces generalized potential functions of complete information games and studies the robustness of sets of equilibria to incomplete information. A set of equilibria of a complete information game is robust if every incomplete information game where payoffs are almost always given by the complete information game has an equilibrium which generates behavior close to some equilibrium in the set. This paper provides sufficient conditions for the robustness of sets of equilibria in terms of argmax sets of generalized potential functions. These sufficient conditions unify and generalize existing sufficient conditions. Our generalization of potential games is useful in other game theoretic problems where potential methods have been applied.     

Informational control and organizational design

This paper focuses on issues of allocating authority between an uninformed principal and an informed expert. We analyze the benefits of informational control—restricting the precision of the expert's information (without learning its content). In this case, the result of Dessein (2002) [8] that delegating decisions to a perfectly informed expert is better than communication when preferences between the expert and the principal are not too far apart is reversed. We demonstrate that these organizational forms—informational control and delegation—can be either complements or substitutes, depending on the principal's ability to affect the expert's discretion about the set of allowed policies.     

Unmediated communication in games with complete and incomplete information

We study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize S^U(G), the set of outcomes of a game G, that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G. A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more players and rational parameters, then S^U(G) coincides with the set of correlated equilibria of G. Next, we demonstrate that if G is a game of incomplete information with at least five players, rational parameters and full support (i.e., all profiles of types have positive probability), then S^U(G) is equal to the set of communication equilibria of G.     

Local coordination and market equilibria

We reformulate the local stability analysis of market equilibria in a competitive market as a local coordination problem in a market game, where the map associating market prices to best-responses of all traders is common knowledge and well-defined both in and out of equilibrium. Initial expectations over market variables differ from their equilibrium values and are not common knowledge. This results in a coordination problem as traders use the structure of the market game to converge back to equilibrium. We analyse a simultaneous move and a sequential move version of the market game and explore the link with local rationalizability.