Imitation is a simple behavior which uses successful actions of others in order to handle one's tasks. Because success of imitation generally depends on whether profit of an imitating agent coincides with those of other agents or not, game theory is suitable for specifying situations where imitation can be successful. One of the concepts describing successfulness of imitation in repeated two-player symmetric games is unbeatability. For infinitely repeated two-player symmetric games, a necessary and sufficient condition for some imitation strategy to be unbeatable was specified. However, situations where imitation can be unbeatable in multi-player games are still not clear. In order to analyze successfulness of imitation in multi-player situations, here we introduce a class of totally symmetric games called unexploitable games, which is a natural extension of two-player symmetric games without exploitation cycles. We then prove that, for infinitely repeated unexploitable games, there exist unbeatable imitation strategies. Furthermore, we also prove that, for infinitely repeated non-trivial unexploitable games, there exist unbeatable zero-determinant strategies, which unilaterally enforce some relationships on payoffs of players. These claims are demonstrated in the public goods game, which is the simplest unexploitable game. These results show that there are situations where imitation can be unbeatable even in multi-player games.
翻译:模拟是一种简单的行为,它使用他人的成功行动来完成某人的任务。由于模仿的成功一般取决于模仿剂的利润是否与其他代理人的利润相符,因此游戏理论适合具体指明模仿成功的情形。描述在重复的两玩者对称游戏中模仿成功的概念之一是不可打赢的。对于无限重复的双玩对称游戏来说,一个必要和充分的条件可以让某些模仿策略无法打赢。然而,由于模拟游戏在多玩游戏中可能无法打赢的情况仍然不清楚。为了分析多玩者情况下模仿成功与否,我们在这里引入了一套完全对称游戏无法开发的游戏,这是两玩者对称游戏的对称游戏的自然延伸,而没有开发周期。我们随后证明,对于无限重复的无法开发的游戏来说,存在着无法打赢的模拟策略。此外,我们还证明,对于无限重复的、不可打赢的游戏游戏游戏来说,甚至无法打赢赢的游戏仍然很不清楚。为了分析在多玩游戏中成功,这些游戏的游戏的游戏是无法打赢赢的游戏,这些游戏的游戏的游戏的游戏的游戏是单方面的游戏结果。 这些游戏的游戏的游戏是展示的游戏的游戏的游戏,这些游戏的游戏的游戏的游戏的游戏的游戏的游戏,它们是展示,它们可以被展示的。这些是展示的。这些游戏的,这些游戏的游戏的游戏的游戏的游戏的简单的游戏的游戏的游戏的游戏。这些游戏的游戏的游戏的游戏的游戏的游戏的游戏的游戏的游戏是用来。