论无限次重复囚徒困境博弈中的针锋相对策略  

Tit-for-Tat Strategy in the Infinitely Repeated Dilemma of the Prisoner

作　　者：王春雷[1] 黄素心[2] WANG Chunlei;HUANG Suxin(School of Economics,Guangxi University,Nanning Guangxi 530004,China;School of Economics,Guangxi Minzu University,Nanning Guangxi 530006,China)

机构地区：[1]广西大学经济学院,广西南宁530004 [2]广西民族大学经济学院,广西南宁530006

出　　处：《金融理论与教学》2024年第3期53-58,共6页Financial Theory and Teaching

基　　金：广西高等教育本科教学改革工程重点项目“经济类专业课程思政供给侧改革探索与实践”(2021JGZ114)。

摘　　要：在有限次重复囚徒困境博弈中,理性的参与人在每个阶段博弈中选择不合作是唯一的子博弈精炼纳什均衡,因此不会出现合作行为。然而,在无限次重复囚徒困境博弈中,参与人采取某些特定的策略可能会导致合作结果的出现。冷酷触发策略是几乎所有博弈论著作都会讨论的一种促进合作的策略,但学者对于针锋相对策略却甚少涉及。研究严格论证了针锋相对策略构成纳什均衡及子博弈精炼纳什均衡的条件。结果表明,当参与人对未来足够重视时,只有当阶段博弈的支付满足一定条件,针锋相对策略才能构成纳什均衡,其对贴现率的要求要比冷酷触发策略更高。研究还表明针锋相对策略并非不能构成子博弈精炼纳什均衡,只是要求的条件非常严格,除了支付满足特定条件外,贴现率也只能取某一特定值。In the finitely repeated dilemma of the prisoner,the choice of rational players not to cooperate in each stage of the game is the only subgame perfect Nash equilibrium,so there will be no cooperative behavior.However,in the infinitely repeated dilemma of the prisoner,the fact that players adopt certain specific strategies may lead to cooperative outcomes.The grim trigger strategy is a strategy for promoting cooperation that is discussed in almost all game theory books,but scholars rarely refer to the tit-for-tat strategy.This paper rigorously demonstrates the conditions under which the tit-for-tat strategy forms Nash equilibrium and subgame perfect Nash equilibrium.The results indicate that when players pay enough attention to the future and when the payoffs of the stage game meet certain conditions,the tit-for-tat strategy can form Nash equilibrium and its requirements for discount rate are higher than those of the grim trigger strategy.This paper also indicates that the tit-for-tat strategy does form subgame perfect Nash equilibrium,but it requires very strict conditions.In addition to the specific conditions for payoffs,it also requires that the discount rate must take a specific value.

关 键 词：无限次重复囚徒困境博弈 冷酷触发策略 针锋相对策略 子博弈精炼纳什均衡 

分 类 号：F224.32[经济管理—国民经济]