Differential Information in Large Games with Strategic Complementarities

34 Pages Posted: 20 Jan 2013 Last revised: 3 Feb 2013

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: January 19, 2013

Abstract

We study equilibrium in large games of strategic complementarities (GSC) with a differential information and continuum of players. For our game, we define an appropriate notion of distributional Bayesian-Nash equilibrium in the sense of Mas-Colell (1984), and prove its existence. Further, we characterize the order-theoretic properties of the equilibrium set, provide monotone comparative statics results for ordered perturbations of the space of games, and provide explicit algorithms for computing extremal equilibrium. Our results make extensive use of the recent results on aggregating single crossing properties in Quah, Strulovici (2012). We complement these with new results on the existence of Bayesian-Nash equilibrium in the sense of Balder, Rustichini (1994) or Kim, Yannelis (1997) for large GSC, and provide analogous results for this notion of equilibrium. To obtain our results, we prove an new fixed point theorem on monotone operators in countably complete partially ordered sets. Applications of the results include riot games, "beauty contests" and common value auctions.

Keywords: arge games, differential information, distributional equilibria, supermodular games, aggregating single crossing

JEL Classification: C72

Suggested Citation

Balbus, Lukasz and Dziewulski, Paweł and Reffett, Kevin and Wozny, Lukasz Patryk, Differential Information in Large Games with Strategic Complementarities (January 19, 2013). Available at SSRN: https://ssrn.com/abstract=2203424 or http://dx.doi.org/10.2139/ssrn.2203424

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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