We introduce a new solution concept, called periodicity, for selecting optimal strategies in strategic form games. This periodicity solution concept yields new insight into nontrivial games. In mixed strategy strategic form games, periodic solutions yield values for the utility function of each player that are equal to the Nash equilibrium ones. In contrast to the Nash strategies, here the payoffs of each player are robust against what the opponent plays. Sometimes, periodicity strategies yield higher utilities, and sometimes the Nash strategies do, but often the utilities of these two strategies coincide. We formally define and study periodic strategies in two player perfect information strategic form games with pure strategies and we prove that every nontrivial finite game has at least one periodic strategy, with nontrivial meaning nondegenerate payoffs. In some classes of games where mixed strategies are used, we identify quantitative features. Particularly interesting are the implications for collective action games, since there the collective action strategy can be incorporated in a purely noncooperative context. Moreover, we address the periodicity issue when the players have a continuum set of strategies available.

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周期性策略：非平凡策略形式游戏的新解决方案概念和算法

我们引入了一种新的解决方案概念，称为周期性，用于在战略形式博弈中选择最优策略。这种周期性解决方案的概念产生了对非平凡博弈的新见解。在混合策略战略形式博弈中，周期解产生的每个参与者的效用函数值等于纳什均衡值。与纳什策略相反，这里每个玩家的收益对对手的游戏都是稳健的。有时，周期性策略会产生更高的效用，有时纳什策略会产生更高的效用，但通常这两种策略的效用是一致的。我们正式定义并研究了具有纯策略的两个玩家完全信息策略形式博弈中的周期策略，我们证明了每个非平凡有限博弈至少有一个周期策略，具有非平凡意义的非退化收益。在使用混合策略的某些类别的游戏中，我们确定了定量特征。特别有趣的是对集体动作游戏的影响，因为集体动作策略可以被纳入纯粹的非合作环境中。此外，当玩家有一组连续的可用策略时，我们会解决周期性问题。