Optimal Strategies in n-Person Unilaterally Competitive Games
Optimal Strategies in n-Person Unilaterally Competitive Games
复制标题
n人单方竞争博弈中的最优策略
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
Olivier de Wolf
中科院分区：
文献类型：
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作者：
Olivier de Wolf
本文证明了传统上定义在两人零和博弈类中的价值概念可以充分推广到Kats & Thisse [KT92b]引入的n人弱单边竞争博弈类中。我们随后确定，如果在属于后一类的博弈中存在均衡，那么每个参与者至少拥有一个最优策略（即，至少对该参与者产生价值的策略）。此外，我们证明，在所有具有纳什均衡轮廓的单边竞争博弈中，策略轮廓是均衡当且仅当它是最优轮廓。从这些结果中，我们推断出单边竞争博弈中纳什均衡概念的一个非常坚实的基础
In this paper, we prove that the concept of value traditionally defined in the class of two-person zero-sum games can be adequately generalized to the class of n-person weakly unilaterally competitive games introduced by Kats & Thisse [KT92b]. We subsequently establish that if there exists an equilibrium in a game belonging to the latter class, then every player possesses at least an optimal strategy (i.e., a strategy yielding at least the value to this player). Furthermore, we show that, in all unilaterally competitive games that have a Nash equilibrium profile, a strategy profile is an equilibrium if and only if it is an optimal profile. From these results, we deduce a very strong foundation to the Nash equilibrium concept in unilaterally competitive games