Catalyst strategy for the evolution of cooperation in indirect reciprocity

IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED
Ji Quan , Yixin Feng , Jiacheng Nie , Xianjia Wang
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Abstract

Indirect reciprocity, as a primary mechanism for cooperation between unrelated individuals, evaluates individuals' behavior and assigns reputation labels based on social norms. Since evaluating reputation is challenging in practice, unlike previous studies, we do not introduce the reputation evaluation rule but only record two recent action information as individuals' labels, including the most recent actions of the individual and his partner. A new type of strategy set is constructed, in which each strategy is represented by a quadruplet, with each element corresponding to an action when facing a different label partner. We explore the invasion and competition of these strategies in a population when playing donor games in both noiseless and noisy scenarios. By conducting pairwise invasion simulations between all sixteen strategies, we find that in the noiseless case, cooperative strategies with evolutionary stability can identify reasonable cooperative behaviors, tolerate unreasonable cooperative behaviors, and adopt a harsh attitude toward unreasonable defection. In the noisy case, tolerant cooperative strategies that can distinguish unreasonable defection are evolutionary stable. Furthermore, by simulating multiple strategy combinations, we find a key strategy which we call the catalyst strategy that can act as a refuge for cooperators. Although the strategy is not evolutionary stable, it can help conditional cooperative strategies resist the intrusion of defection and help the system reach a fully cooperative steady state. We also verify that the system's evolutionary outcome is robust to noise intensity and that the presence of noise cannot lead to qualitative changes in the system. Action errors have a greater impact on the average cooperation rate and average payoff of the population relative to label errors. In addition, we find that the catalytic potential of the key strategy is fully realized in larger populations. Conversely, smaller population sizes diminish the efficacy of the catalyst strategy in promoting cooperation, and this detrimental effect is exacerbated in the noisy scenario.
间接互惠中合作演化的催化剂策略
间接互惠是无亲缘关系个体间合作的主要机制,它基于社会规范对个体行为进行评价并赋予声誉标签。由于声誉评估在实践中具有挑战性,与以往的研究不同,我们没有引入声誉评估规则,而是只记录两个最近的行为信息作为个人的标签,包括个人和他的伴侣最近的行为。构造了一种新的策略集,其中每个策略用一个四元组表示,每个元素对应一个面对不同标签伙伴时的动作。我们在无噪声和有噪声两种情况下进行捐赠博弈时,探讨了这些策略在群体中的入侵和竞争。通过对这16种策略的两两入侵模拟,我们发现在无噪音情况下,具有进化稳定性的合作策略能够识别合理的合作行为,容忍不合理的合作行为,对不合理的背叛采取严厉的态度。在有噪声情况下,能够区分不合理背叛的容忍合作策略是进化稳定的。此外,通过模拟多种策略组合,我们发现了一个关键策略,我们称之为催化剂策略,它可以作为合作者的避难所。虽然该策略不是进化稳定的,但它可以帮助有条件合作策略抵抗背叛的入侵,使系统达到完全合作的稳定状态。我们还验证了系统的进化结果对噪声强度具有鲁棒性,并且噪声的存在不会导致系统的质变。相对于标签错误,行动错误对群体的平均合作率和平均收益的影响更大。此外,我们发现关键策略的催化潜力在更大的人群中得到充分实现。相反,较小的种群规模会降低催化剂策略在促进合作方面的功效,而这种有害影响在嘈杂的情况下会加剧。
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来源期刊
CiteScore
7.90
自引率
10.00%
发文量
755
审稿时长
36 days
期刊介绍: Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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