Integrating emotion-imitating into strategy learning improves cooperation in social dilemmas with extortion

Abstract

Extortion strategy can play the role of a Trojan horse for cooperators and act as a catalyst for the evolution of cooperation in social dilemma games. Based on the prisoner’s dilemma game model with extortion, an emotion-imitating rule for strategy updating is proposed in this study, which takes into account the diverse attitudes of a player towards a strong or weak opponent. Furthermore, by employing evidential reasoning, we establish an improved rule for strategy updating, which integrates the emotion-imitating rule into strategy learning as well as the original myopic best response rule, and via a fusion weight, the role of emotion-imitating can be subtly adjusted in the process of strategy learning. The effect of emotion-imitating on cooperation is investigated in the presence of extortioners. Through Monte Carlo simulations, it is shown that the new rule can significantly boost cooperation when the fusion weight is close to 0.5. In strategy learning, the emotion-imitating rule relieves the direct exploitation from defectors for cooperators and also facilitates cooperators to cluster and spread in the population. The extortion strategy provides shelter for cooperators to survive even at the extremely high temptation to defect. In addition, the myopic best response rule can also improve the performance of the emotion-imitating rule, especially in the region of high temptation to defect. Based on evidential reasoning, the new rule integrates sophisticatedly the advantage of the two single rules, enhancing the emergence of cooperation as well as the average payoffs of the whole system. The robustness of the shelter effects of extortioners under the new learning rule model is also studied by considering action errors and the cognition cost of extortioners respectively. The results further support the catalyst roles of extortioners, provided that the dilemma strength is not too strong. We also demonstrate the enhancement of cooperation when the model is extended to four competing strategies where the tit for tat (TFT) strategy is also included. The coexistence of extortioners and TFT players restricts the expansion of defectors, and the extortioners’ catalyst role still works prominently in the interval of low tempt values.