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.
Original language | American English |
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Pages (from-to) | 829-849 |
Number of pages | 21 |
Journal | International Journal of Game Theory |
Volume | 41 |
Issue number | 4 |
DOIs | |
State | Published - 1 Dec 2012 |
Keywords
- Bayesian equilibrium
- Common prior
- Ex-ante
- Interim
- Lower approximate semi-continuity
- Optimal strategies
- Upper semi-continuity
- Value
- Zero-sum Bayesian games
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Mathematics (miscellaneous)
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Statistics, Probability and Uncertainty