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A Qualitative Theory of Large Games with Strategic Complementarities

45 Pages Posted: 30 Jan 2013 Last revised: 17 Jul 2015

Lukasz Balbus

University of Zielona Gora - Institute of Mathematics

Paweł Dziewulski

University of Oxford - Department of Economics

Kevin Reffett

Arizona State University - Department of Economics

Lukasz Patryk Wozny

Warsaw School of Economics - Quantitative Economics Department

Date Written: May 1, 2014

Abstract

We study the existence and computation of equilibrium in large games with strategic complementarities. Using monotone operators (in stochastic dominance orders) defined on the space of distributions, we first prove existence of the greatest and least distributional Nash equilibrium in the sense of Mas-Colell (1984) under different set of assumptions than those in the existing literature. In addition, we provide results on computable monotone distributional equilibrium comparative statics relative to ordered perturbations of the parameters of our games. We then provide similar results for Nash/Schmeidler (1973) equilibria (defined by strategies) in our large games. We conclude by discussing the question of equilibrium uniqueness, as well as presenting applications of our results to models of Bertrand competition, "beauty contests," and existence of equilibrium in large economies.

Keywords: large games, distributional equilibria, supermodular games, games with strategic complementarities, computation of equilibria

JEL Classification: C72

Suggested Citation

Balbus, Lukasz and Dziewulski, Paweł and Reffett, Kevin and Wozny, Lukasz Patryk, A Qualitative Theory of Large Games with Strategic Complementarities (May 1, 2014). Available at SSRN: https://ssrn.com/abstract=2208125 or http://dx.doi.org/10.2139/ssrn.2208125

Lukasz Balbus

University of Zielona Gora - Institute of Mathematics ( email )

65-246 Zielona Góra
Poland

Paweł Dziewulski

University of Oxford - Department of Economics ( email )

Manor Road Building
Manor Road
Oxford, OX1 3UQ
United Kingdom

HOME PAGE: http://users.ox.ac.uk/~shil3804/

Kevin L. Reffett

Arizona State University - Department of Economics ( email )

Tempe, AZ 85287-3806
United States

Lukasz Patryk Wozny (Contact Author)

Warsaw School of Economics - Quantitative Economics Department ( email )

Warsaw
Poland

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