A theorem of the maximin and applications to Bayesian zero-sum games
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- 作者：Timothy Van Zandt (1)
Kaifu Zhang (1) - 关键词：Value of information ; Zero ; sum games ; Primary ; 91A44 ; Secondary ; 60A10 ; 49J35
- 刊名：International Journal of Game Theory
- 出版年：2011
- 出版时间：May 2011
- 年：2011
- 卷：40
- 期：2
- 页码：289-308
- 全文大小：241KB
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Kaifu Zhang (1)
1. INSEAD, Boulevard de Constance, 77300, Fontainebleau, France - ISSN：1432-1270
文摘
Consider a family of zero-sum games indexed by a parameter that determines each player’s payoff function and feasible strategies. Our first main result characterizes continuity assumptions on the payoffs and the constraint correspondence such that the equilibrium value and strategies depend continuously and upper hemicontinuously (respectively) on the parameter. This characterization uses two topologies in order to overcome a topological tension that arises when players-strategy sets are infinite-dimensional. Our second main result is an application to Bayesian zero-sum games in which each player’s information is viewed as a parameter. We model each player’s information as a sub-σ-field, so that it determines her feasible strategies: those that are measurable with respect to the player’s information. We thereby characterize conditions under which the equilibrium value and strategies depend continuously and upper hemicontinuously (respectively) on each player’s information.