Continuity of the value and optimal strategies when common priors change

Ezra Einy (), Ori Haimanko () and Biligbaatar Tumendemberel ()
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Ezra Einy: Dep. of Economics, Ben-Gurion University of the Negev
Biligbaatar Tumendemberel: Graduate School of Economics, Hitotsubashi University, Naka 2-1, Kunitachi, Tokyo, Japan

No 905, Working Papers from Ben-Gurion University of the Negev, Department of Economics

Abstract: We show that the value of a zero-sum Bayesian game is a Lipschitz continuous function of the players?common prior belief, with respect to the total variation metric (that induces the topology of setwise convergence on beliefs). This is unlike the case of general Bayesian games, where lower semi-continuity of Bayesian equilibrium payo¤s rests on the convergence of conditional beliefs (Engl (1995), Kajii and Morris (1998)). We also show upper, and approximate lower, semi- continuity of the optimal strategy correspondence with respect to the total variation norm, and discuss approximate lower semi-continuity of the Bayesian equilibrium correspondence in the context of zero-sum games.

Keywords: Zero-Sum Bayesian Games; Common Prior; Value; Optimal Strategies; Upper Semi-Continuity; Lower Approximate Semi- Continuity. (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2009
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Related works:
Journal Article: Continuity of the value and optimal strategies when common priors change (2012)
Working Paper: Continuity of the value and optimal strategies when common priors change (2009)
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