Monotone Equilibria in Bayesian Games of Strategic Complementarities

27 Pages Posted: 16 Dec 2003

See all articles by Timothy Van Zandt

Timothy Van Zandt

INSEAD - Economics and Political Sciences; Centre for Economic Policy Research (CEPR)

Xavier Vives

University of Navarra - IESE Business School; Universitat Pompeu Fabra (UPF); Centre for Economic Policy Research (CEPR); CESifo (Center for Economic Studies and Ifo Institute for Economic Research)

Date Written: November 2003

Abstract

For Bayesian games of strategic complementarities, we provide a constructive proof of the existence of a greatest and a least Bayes-Nash equilibrium - each one in strategies monotone in type - if the payoff to a player displays increasing differences in own action and the profile of types, and if the posteriors are increasing in type with respect to first-order stochastic dominance (e.g. if types are affiliated). The result holds for multidimensional action and type spaces and also for continuous and discrete type distributions. It uses an intermediate result on monotone comparative statics under uncertainty, which implies that the extremal equilibria increase when there is a first-order stochastic dominant shift in beliefs. We provide an application to strategic information revelation in games of voluntary disclosure.

Keywords: Supermodular games, incomplete information, first-order stochastic dominance, Cournot tatonnement, monotone comparative statics, voluntary disclosure

Suggested Citation

Van Zandt, Timothy and Vives, Xavier, Monotone Equilibria in Bayesian Games of Strategic Complementarities (November 2003). CEPR Discussion Paper No. 4103. Available at SSRN: https://ssrn.com/abstract=478982

Timothy Van Zandt (Contact Author)

INSEAD - Economics and Political Sciences ( email )

Boulevard de Constance
F-77305 Fontainebleau Cedex
France
+33 1 6072 4981 (Phone)
+33 1 6074 6192 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Xavier Vives

University of Navarra - IESE Business School ( email )

Avenida Pearson 21
Barcelona, 08034
Spain

HOME PAGE: http://wwwapp.iese.edu/faculty/facultyDetail.asp?lang=en&prof=xv

Universitat Pompeu Fabra (UPF) ( email )

Ramon Trias Fargas, 25-27
Barcelona, 08005
Spain

Centre for Economic Policy Research (CEPR)

London
United Kingdom

CESifo (Center for Economic Studies and Ifo Institute for Economic Research) ( email )

Poschinger Str. 5
Munich, DE-81679
Germany

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