Center for Systems and Control, College of Engineering, Peking University, Beijing, China.
Center for Complex Systems, Xidian University, Xi'an, China.
J Theor Biol. 2022 Sep 21;549:111209. doi: 10.1016/j.jtbi.2022.111209. Epub 2022 Jun 30.
Several studies have confirmed the existence of zero-determinant (ZD) strategies in repeated social dilemmas since Press and Dyson's ingenious discovery of ZD strategies in iterated prisoner's dilemmas. However, less research studies evolutionary performance of multiplayer ZD strategies, especially from a theoretical perspective. Here, we use a state-clustering method to theoretically analyze evolutionary dynamics of two representative ZD strategies: generous ZD strategies and extortionate ZD strategies. We consider two new settings for multiplayer ZD strategies: competitions with all ZD strategies and competitions with all memory-one strategies, apart from the competitions between these strategies and some classical ones. Moreover, we investigate the influence of the level of generosity and extortion on evolutionary dynamics of generous and extortionate ZD strategies, which was commonly ignored in previous studies. Theoretical results show that 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 evolutionary dynamics of ZD strategies in repeated multiplayer games.
自 Press 和 Dyson 巧妙地发现重复囚徒困境中的零行列式（ZD）策略以来，多项研究已经证实了在重复社会困境中存在零行列式策略。然而，从理论角度来看，对多人 ZD 策略的进化表现的研究相对较少。在这里，我们使用状态聚类方法从理论上分析了两种代表性的 ZD 策略的进化动态：慷慨的 ZD 策略和敲诈的 ZD 策略。我们考虑了多人 ZD 策略的两种新设置：具有所有 ZD 策略的竞争和具有所有记忆一个策略的竞争，除了这些策略与一些经典策略之间的竞争之外。此外，我们研究了慷慨和敲诈 ZD 策略的慷慨和敲诈程度对其进化动态的影响，这在以前的研究中通常被忽略。理论结果表明，慷慨程度有限的玩家处于有利地位，而敲诈者敲诈得越严重，就越容易立足。我们的结果可能为更好地理解重复多人游戏中的 ZD 策略的进化动态提供新的见解。
