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On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games
Author(s) -
Reny Philip J.
Publication year - 2011
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta8934
Subject(s) - convexity , monotone polygon , mathematical economics , mathematics , common value auction , space (punctuation) , scope (computer science) , metric space , bayesian probability , action (physics) , bayesian game , monotonic function , discrete mathematics , computer science , economics , game theory , repeated game , statistics , mathematical analysis , geometry , physics , quantum mechanics , financial economics , programming language , operating system
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.