Unexploitable Games and Unbeatable Strategies
Unexploitable Games and Unbeatable Strategies
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DOI：
10.1109/access.2023.3235922
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发表时间：
2022-11
期刊：
影响因子：
3.9
通讯作者：
M. Ueda
中科院分区：
文献类型：
--
作者：
M. Ueda
模仿是一种简单的行为，它利用他人的成功行为来处理自己的问题。由于模仿的成功通常取决于模仿代理人的利润是否与其他代理人的利润一致，因此博弈论适合于说明模仿可以成功的情况。在重复的两人对称博弈中，描述模仿成功的概念之一是不可战胜。对于无限重复的两人对称对策，给出了某些模仿策略不可战胜的充要条件。然而，在多人游戏中，模仿在哪些情况下是不可战胜的仍然不清楚。为了分析多人情况下模仿的成功与否，我们引入了一类称为不可开发对策的完全对称对策，它是没有开发周期的两人对称对策的自然推广。然后证明了，对于无限重复的不可开发对策，存在不可战胜的模仿策略。此外，我们还证明了，对于无限次重复的非平凡不可开发对策，存在不可战胜的零定策略，它单方面地强制某些关系影响博弈者的收益。这些主张在公共物品博弈中得到了证明，这是最简单的不可开发的博弈。这些结果表明，即使在多人游戏中，模仿也是不可战胜的。
Imitation is simple behavior which uses successful actions of others in order to deal with one’s own problems. 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 is unbeatable even in multi-player games.