On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games

Reny, Philip

doi:10.2139/ssrn.1532929

Abstract

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On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games

Philip Reny

University of Chicago - Department of Economics

November 1, 2009

Milton Friedman Institute Working Paper No. 2009-09

Abstract:
We generalize Athey's (2001) and McAdams' (2003) results on the existence of monotone pure strategy equilibria in Bayesian games. We allow action spaces to be compact locally-complete metrizable semilattices and type spaces to be partially ordered probability spaces. Our proof is based upon contractibility rather than convexity of best reply sets. Several examples illustrate the scope of the result, including new applications to multi-unit auctions with risk-averse bidders.

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Date posted: January 8, 2010 ; Last revised: February 23, 2012

Suggested Citation

Reny, Philip, On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games (November 1, 2009). Milton Friedman Institute Working Paper No. 2009-09. Available at SSRN: http://ssrn.com/abstract=1532929 or http://dx.doi.org/10.2139/ssrn.1532929

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