On the Existence of Monotone Pure-Strategy Equilibria in Bayesian Games


  • Philip J. Reny

    1. Dept. of Economics, University if Chicago, 1126 East 59th Street, Chicago, IL 60637, U.S.A.; preny@uchicago.edu
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    • I wish to thank David McAdams, Roger Myerson, Max Stinchcombe, and Jeroen Swinkels for helpful conversations, and Sergiu Hart and Benjamin Weiss for providing an example of a compact metrizable semilattice that is not locally complete. I also thank three anonymous referees and the editor for a number of helpful remarks. Financial support from the National Science Foundation (SES-0214421, SES-0617884, SES-0922535) is gratefully acknowledged.


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 metric semilattices and type spaces to be partially ordered probability spaces. Our proof is based on 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.