Zero-determinant strategies in iterated multi-strategy games  

多策略博弈中的零行列式策略

作　　者：GUO Jinli 郭进利(延安大学西安创新学院,陕西西安710100;上海理工大学管理学院,上海200093)

机构地区：[1]Xi′an Innovation College of Yan’an University,Xi′an 710100,China [2]Business School,University of Shanghai for Science and Technology,Shanghai 200093,China

出　　处：《纯粹数学与应用数学》2024年第3期381-393,共13页Pure and Applied Mathematics

基　　金：国家自然科学基金(71571119).

摘　　要：Self-serving,rational agents sometimes cooperate to their mutual benefit.The two-player iterated prisoner′s dilemma game is a model for including the emergence of cooperation.It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants.The zero-determinant strategy in the iterated prisoner′s dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents.However,strategies in the prisoner′s dilemma game are only two strategies.Are there these results for general multi-strategy games?To address this question,the paper develops a theory for zero-determinant strategies for multi-strategy games,with any number of strategies.The analytical results exhibit a similar yet different scenario to the case of two-strategy games.The results are also applied to the Snowdrift game,the Hawk-Dove game and the Chicken game.自私理性的个体为了共同的利益往往会选择合作策略,两人囚徒困境博弈是研究合作行为产生的一个范例.已有的博弈理论认为没有一个简单的单方面策略可以决定对手的收益,零行列式策略可以单方面决定不知情对手的期望收益.然而,囚徒困境博弈中个体仅仅只有两策略,零行列式策略是否适用于多策略?为了解决这个问题,本文研究多策略下的零行列式策略博弈,结论表明多策略下的零行列式策略结果与两策略相似但是又存在不同.多策略零行列式策略适用于雪堆博弈,鹰鸽博弈,斗鸡博弈等.

关 键 词：prisoner′s dilemma zero-determinant strategy multi-strategy game symmetric game 

分 类 号：O211.6[理学—概率论与数理统计] O211.9[理学—数学]