Ramazi Pouria, Riehl James, Cao Ming
ENTEG, Faculty of Science and Engineering, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands.
R Soc Open Sci. 2018 Apr 11;5(4):180027. doi: 10.1098/rsos.180027. eCollection 2018 Apr.
To better understand the intriguing mechanisms behind cooperation among decision-making individuals, we study the simple yet appealing use of preplay communication or cheap talk in evolutionary games, when players are able to choose strategies based on whether an opponent sends the same message as they do. So when playing games, in addition to pure cooperation and defection, players have two new strategies in this setting: homophilic (respectively, heterophilic) cooperation which is to cooperate (respectively, defect) only with those who send the same message as they do. We reveal the intrinsic qualities of individuals playing the two strategies and show that under the replicator dynamics, homophilic cooperators engage in a battle of messages and will become dominated by whichever message is the most prevalent at the start, while populations of heterophilic cooperators exhibit a more harmonious behaviour, converging to a state of maximal diversity. Then we take Prisoner's Dilemma (PD) as the base of the cheap-talk game and show that the hostility of heterophilics to individuals with similar messages leaves no possibility for pure cooperators to survive in a population of the two, whereas the one-message dominance of homophilics allows for pure cooperators with the same tag as the dominant homophilics to coexist in the population, demonstrating that homophilics are more cooperative than heterophilics. Finally, we generalize an existing convergence result on population shares associated with weakly dominated strategies to a broadly applicable theorem and complete previous research on PD games with preplay communication by proving that the frequencies of all types of cooperators, i.e. pure, homophilic and heterophilic, converge to zero in the face of defectors. This implies homophily and heterophily cannot facilitate the long-term survival of cooperation in this setting, which urges studying cheap-talk games under other reproduction dynamics.
为了更好地理解决策个体之间合作背后的有趣机制，我们研究了进化博弈中预演通信或廉价交谈这一简单却引人入胜的应用，即玩家能够根据对手是否发送与自己相同的信息来选择策略。所以在玩游戏时，除了纯粹的合作与背叛，玩家在这种情况下还有两种新策略：同嗜性（分别为异嗜性）合作，即仅与发送与自己相同信息的人合作（分别为背叛）。我们揭示了采用这两种策略的个体的内在特质，并表明在复制者动态下，同嗜性合作者会陷入信息之战，并且会被一开始最普遍的信息所主导，而异嗜性合作者群体则表现出更和谐的行为，会收敛到最大多样性的状态。然后我们以囚徒困境（PD）作为廉价交谈博弈的基础，表明异嗜性对具有相似信息个体的敌意使得纯粹合作者在两者共存的群体中没有生存的可能，而同嗜性的单信息主导使得与占主导地位的同嗜性具有相同标签的纯粹合作者能够在群体中共存，这表明同嗜性比异嗜性更具合作性。最后，我们将一个关于与弱占优策略相关的种群份额的现有收敛结果推广为一个广泛适用的定理，并通过证明面对背叛者时所有类型合作者（即纯粹、同嗜性和异嗜性）的频率都收敛到零，完成了之前关于具有预演通信的PD博弈的研究。这意味着在这种情况下，同嗜性和异嗜性都无法促进合作的长期生存，这促使我们研究其他繁殖动态下的廉价交谈博弈。
