IST Austria, Klosterneuburg, Austria.
Max Planck Research Group Dynamics of Social Behavior, Max Planck Institute for Evolutionary Biology, Plön, Germany.
PLoS Comput Biol. 2022 Jun 14;18(6):e1010149. doi: 10.1371/journal.pcbi.1010149. eCollection 2022 Jun.
In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate.
在重复互动中，玩家可以使用针对前几轮结果的策略。直接互惠的现有文献大多假设所有竞争的个体都使用相同的策略空间。在这里，我们研究了在探索策略空间方面存在差异的玩家的学习和进化动态。我们专注于无限重复的捐赠游戏，并比较了三种自然的策略空间：考虑到两名玩家最后移动的记忆-1 策略、对同伴最后移动做出反应的反应策略以及无条件策略。这三个策略空间在所需的记忆容量上有所不同。我们计算了在一对一对学习过程中实现的长期平均收益。我们发现较小的策略空间可以主导较大的策略空间。对于较弱的选择，无条件玩家支配反应性和记忆-1 玩家。对于中等选择，反应性玩家支配记忆-1 玩家。只有在强选择和低成本效益比的情况下，记忆-1 玩家才会支配其他玩家。我们观察到策略空间之间的超级博弈可能是一个社会困境：如果两名玩家都探索更大的策略空间，则可以实现最大收益，但较小的策略空间占主导地位。
