重复多人博弈中零决定策略的演化动力学
Evolutionary dynamics of zero-determinant strategies in repeated multiplayer games
摘要：
自从Press和Dyson在重复囚徒困境博弈中巧妙地发现了ZD（zero-determinant）策略以来，已有多项研究证实了ZD策略在重复多人社会困境中的存在。然而，很少有研究多人ZD策略的进化性能，特别是从理论的角度。在这里，我们使用一个新提出的状态聚类方法，理论上分析了两个代表ZD策略的演化动力学：慷慨ZD策略和勒索ZD策略。除了两种策略和一些经典策略之间的竞争外，我们考虑了多人ZD策略的两种新的设置：在整个ZD策略空间中的竞争和在所有记忆1策略空间中的竞争。此外，我们还研究了慷慨和勒索水平对慷慨和勒索ZD的演化动力学的影响，这在以往的研究中通常被忽略。理论结果表明，有限慷慨的球员是在一个有利的地方，勒索更严重的勒索更容易举行他们的立场。我们的研究结果可能为更好地理解重复多人博弈中ZD策略的演化动力学提供新的见解。
英文摘要：
Since Press and Dyson's ingenious discovery of ZD (zero-determinant) strategy in the repeated Prisoner's Dilemma game, several studies have confirmed the existence of ZD strategy in repeated multiplayer social dilemmas. However, few researches study the evolutionary performance of multiplayer ZD strategies, especially from a theoretical perspective. Here, we use a newly proposed state-clustering method to theoretically analyze the evolutionary dynamics of two representative ZD strategies: generous ZD strategies and extortionate ZD strategies. Apart from the competitions between the two strategies and some classical strategies, we consider two new settings for multiplayer ZD strategies: competitions in the whole ZD strategy space and competitions in the space of all memory-1 strategies. Besides, we investigate the influence of level of generosity and extortion on the evolutionary dynamics of generous and extortionate ZD, which was commonly ignored in previous studies. Theoretical results show players with limited generosity are at an advantageous place and extortioners extorting more severely hold their ground more readily. Our results may provide new insights into better understanding the evolutionary dynamics of ZD strategies in repeated multiplayer games.
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