On the approximate purification of mixed strategies in games with infinite action sets
On the approximate purification of mixed strategies in games with infinite action sets
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DOI：
10.1007/s40505-022-00219-1
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发表时间：
2021-03
影响因子：
0.3
通讯作者：
Y. Hosoya;Chaowen Yu
中科院分区：
文献类型：
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作者：
Y. Hosoya;Chaowen Yu
我们考虑一个博弈，其中每个玩家的行动集是不可数的，并表明，从弱假设的共同先验，任何混合策略有一个近似等价的纯策略。如果我们考虑纳什均衡的净化，这个结果的假设可以进一步减弱。结合纳什均衡的存在性定理，在充分弱的假设条件下，得到了一个纯策略逼近纳什均衡的存在性定理。我们在本文中推导出的所有纯策略都可以采取有限数量的可能行动。
We consider a game in which the action set of each player is uncountable, and show that, from weak assumptions on the common prior, any mixed strategy has an approximately equivalent pure strategy. The assumption of this result can be further weakened if we consider the purification of a Nash equilibrium. Combined with the existence theorem for a Nash equilibrium, we derive an existence theorem for a pure strategy approximated Nash equilibrium under sufficiently weak assumptions. All of the pure strategies we derive in this paper can take a finite number of possible actions.