Complementarities and the Existence of Strong Berge Equilibrium

Cataloged from PDF version of article.This paper studies the existence and the order structure of strong Berge equilibrium, a refinement of Nash equilibrium, for games with strategic complementarities a la strong Berge. It is shown that the equilibrium set is a nonempty complete lattice. Moreover, we provide a monotone comparative statics result such that the greatest and the lowest equilibria are increasing

A minimally altruistic refinement of Nash equilibrium

Cataloged from PDF version of article.We introduce a minimal notion of altruism and use it to refine Nash equilibria in normal form games. We provide three independent existence proofs, relate minimally altruistic Nash equilibrium to other equilibrium concepts, conduct an in-depth sensitivity analysis, and provide examples where minimally altruistic Nash equilibrium leads to improved predictions. (C) 2013 Elsevier B.V. All rights reserved

Differential information in large games with strategic complementarities

We study equilibrium in large games of strategic complementarities (GSC) with differential information. We define an appropriate notion of distributional Bayesian Nash equilibrium and prove its existence. Furthermore, we characterize order-theoretic properties of the equilibrium set, provide monotone comparative statics for ordered perturbations of the space of games, and provide explicit algorithms for computing extremal equilibria. We complement the paper with new results on the existence of Bayesian Nash equilibrium in the sense of Balder and Rustichini (J Econ Theory 62(2):385–393, 1994) or Kim and Yannelis (J Econ Theory 77(2):330–353, 1997) for large GSC and provide an analogous characterization of the equilibrium set as in the case of distributional Bayesian Nash equilibrium. Finally, we apply our results to riot games, beauty contests, and common value auctions. In all cases, standard existence and comparative statics tools in the theory of supermodular games for finite numbers of agents do not apply in general, and new constructions are required

Heterogeneous Tiebout communities with private production and anonymous crowding

his paper examines, in the context of a multiple types of consumers, a set of necessary and sufficient conditions under which equilibrium and optimum exist, and involve mixing types of consumers in jurisdictions. Pricing includes visa permits for entry. Following Berglas (1976), we assume anonymous crowding and complementarities in production. For a large economy, we prove existence of equilibrium and the first and second welfare theorems. Our simultaneous optimization approach provides a new technique for showing existence of equilibrium in local public good economies with local production and a continuum of agents.Local public goods, Collaborative production, Wages, Anonymous crowding, Visa permits, Societal stratification, Heterogeneous Tiebout communities, Generalized game

On the Strategic Advantage of Negatively Interdependent Preferences

We study certain classes of supermodular and submodular games which are symmetric with respect to material payoffs but in which not all players seek to maximize their material payoffs. Specifically, a subset of players have negatively interdependent preferences and care not only about their own material payoffs but also about their payoffs relative to others. We identify sufficient conditions under which members of the latter group have a strategic advantage in the following sense: at all intragroup symmetric equilibria of the game, they earn strictly higher material payoffs than do players who seek to maximize their material payoffs. We show that these conditions are satisfied by a number of games of economic importance, and discuss the implications of these findings for the evolutionary theory of preference formation and the theory of Cournot competition.Interdependent Preferences, Submodular and Supermodular Games, Relative Profits, Cournot Oligopoly

A minimally altruistic refinement of Nash equilibrium

We introduce a minimal notion of altruism and use it to refine Nash equilibria in normal form games. We provide three independent existence proofs, relate minimally altruistic Nash equilibrium to other equilibrium concepts, conduct an in-depth sensitivity analysis, and provide examples where minimally altruistic Nash equilibrium leads to improved predictions. © 2013 Elsevier B.V

Structural stability and robustness to bounded rationality

The introduction of a small amount of bounded rationality into a model sometimes has little effect, and sometimes has a dramatic impact on predicted behavior. We call a model robust to bounded rationality if small deviations from rationality result only in small changes in the equilibrium set. We also say that a model is structurally stable if the equilibrium set (given fully rational agents) varies continuously with the parameter values of the model. Our notions of a model and of rationality are quite broad, allowing us to cover cases in which bounded rationality refers to imperfect optimization, non-rational expectations, or arbitrary behavior by a subset of agents. We show that a model is robust to bounded rationality if and only if it is structurally stable. Thus, we can characterize which models will be robust to bounded rationality and which ones will not, independently of the exact form that bounded rationality takes. In addition, from our characterization it follows that introducing a small amount of bounded rationality will have large effects on predicted outcomes if and only if parameters are near a critical point where the equilibrium set changes in a discontinuous way JEL classification: C69, C79, D51, E19