Continuity of the value and optimal strategies when common priors change
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. Copyright Springer-Verlag 2012
Volume (Year): 41 (2012)
Issue (Month): 4 (November)
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- Kajii, Atsushi & Morris, Stephen, 1998.
"Payoff Continuity in Incomplete Information Games,"
Journal of Economic Theory,
Elsevier, vol. 82(1), pages 267-276, September.
- Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
- Atsushi Kajii & Stephen Morris, 1997.
"The Robustness of Equilibria to Incomplete Information,"
Econometric Society, vol. 65(6), pages 1283-1310, November.
- Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
- Atsushi Kajii & Stephen Morris, . ""The Robustness of Equilibria to Incomplete Information*''," CARESS Working Papres 95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Lehrer, Ehud & Rosenberg, Dinah, 2006.
"What restrictions do Bayesian games impose on the value of information?,"
Journal of Mathematical Economics,
Elsevier, vol. 42(3), pages 343-357, June.
- Ehud Lehrer & Dinah Rosenberg, 2003. "What restrictions do Bayesian games impose on the value of information?," Game Theory and Information 0312005, EconWPA.
- Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
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