Continuity of the value and optimal strategies when common priors change |
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Authors: | Ezra Einy Ori Haimanko Biligbaatar Tumendemberel |
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Institution: | 1. Department of Economics, Ben-Gurion University of the Negev, 84105, Beer Sheva, Israel 2. Graduate School of Economics, Hitotsubashi University, Naka 2-1, Kunitachi, Tokyo, 186-8601, Japan 3. Department of Economics, State University of New York at Stony Brook, Stony Brook, NY, 11794-4384, USA
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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 on beliefs. This is unlike the case of general Bayesian games where lower semi-continuity of Bayesian equilibrium (BE) payoffs rests on the ??almost uniform?? convergence of conditional beliefs. We also show upper semi-continuity (USC) and approximate lower semi-continuity (ALSC) of the optimal strategy correspondence, and discuss ALSC of the BE correspondence in the context of zero-sum games. In particular, the interim BE correspondence is shown to be ALSC for some classes of information structures with highly non-uniform convergence of beliefs, that would not give rise to ALSC of BE in non-zero-sum games. |
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