Dong Yali, Li Cong, Tao Yi, Zhang Boyu
School of Statistics, Beijing Normal University, Beijing, China.
Département de Mathmatiques et de Statistique, Université de Montréal, Montreal, Canada.
PLoS One. 2015 Sep 1;10(9):e0137435. doi: 10.1371/journal.pone.0137435. eCollection 2015.
People often deviate from their individual Nash equilibrium strategy in game experiments based on the prisoner's dilemma (PD) game and the public goods game (PGG), whereas conditional cooperation, or conformity, is supported by the data from these experiments. In a complicated environment with no obvious "dominant" strategy, conformists who choose the average strategy of the other players in their group could be able to avoid risk by guaranteeing their income will be close to the group average. In this paper, we study the repeated PD game and the repeated m-person PGG, where individuals' strategies are restricted to the set of conforming strategies. We define a conforming strategy by two parameters, initial action in the game and the influence of the other players' choices in the previous round. We are particularly interested in the tit-for-tat (TFT) strategy, which is the well-known conforming strategy in theoretical and empirical studies. In both the PD game and the PGG, TFT can prevent the invasion of non-cooperative strategy if the expected number of rounds exceeds a critical value. The stability analysis of adaptive dynamics shows that conformity in general promotes the evolution of cooperation, and that a regime of cooperation can be established in an AllD population through TFT-like strategies. These results provide insight into the emergence of cooperation in social dilemma games.
在基于囚徒困境（PD）博弈和公共物品博弈（PGG）的博弈实验中，人们常常偏离其个体纳什均衡策略，而条件合作或从众行为却得到了这些实验数据的支持。在没有明显“占优”策略的复杂环境中，选择所在群体中其他参与者平均策略的从众者，或许能够通过确保自己的收益接近群体平均水平来规避风险。在本文中，我们研究重复囚徒困境博弈和重复m人公共物品博弈，其中个体策略被限制在从众策略集合内。我们通过两个参数定义一个从众策略，即博弈中的初始行动以及上一轮其他参与者选择的影响。我们特别关注针锋相对（TFT）策略，它是理论和实证研究中著名的从众策略。在囚徒困境博弈和公共物品博弈中，如果预期轮数超过一个临界值，针锋相对策略都能防止非合作策略的入侵。自适应动力学的稳定性分析表明，一般来说从众行为会促进合作的演化，并且通过类似针锋相对的策略可以在全背叛群体中建立起合作机制。这些结果为社会困境博弈中合作行为的出现提供了见解。
