Department of Mathematics and Center for Mathematical Biology, University of Pennsylvania, Philadelphia, PA, USA.
Bull Math Biol. 2022 Sep 22;84(11):126. doi: 10.1007/s11538-022-01082-8.
In the study of the evolution of cooperation, many mechanisms have been proposed to help overcome the self-interested cheating that is individually optimal in the Prisoners' Dilemma game. These mechanisms include assortative or networked social interactions, other-regarding preferences considering the payoffs of others, reciprocity rules to establish cooperation as a social norm, and multilevel selection involving simultaneous competition between individuals favoring cheaters and competition between groups favoring cooperators. In this paper, we build on recent work studying PDE replicator equations for multilevel selection to understand how within-group mechanisms of assortment, other-regarding preferences, and both direct and indirect reciprocity can help to facilitate cooperation in concert with evolutionary competition between groups. We consider a group-structured population in which interactions between individuals consist of Prisoners' Dilemma games and study the dynamics of multilevel competition determined by the payoffs individuals receive when interacting according to these within-group mechanisms. We find that the presence of each of these mechanisms acts synergistically with multilevel selection for the promotion of cooperation, decreasing the strength of between-group competition required to sustain long-time cooperation and increasing the collective payoff achieved by the population. However, we find that only other-regarding preferences allow for the achievement of socially optimal collective payoffs for Prisoners' Dilemma games in which average payoff is maximized by an intermediate mix of cooperators and defectors. For the other three mechanisms, the multilevel dynamics remain susceptible to a shadow of lower-level selection, as the collective outcome fails to exceed the payoff of the all-cooperator group.
在合作进化的研究中，已经提出了许多机制来帮助克服囚徒困境博弈中个体最优的自利欺骗行为。这些机制包括基于相似性或网络的社会互动、考虑他人收益的利他偏好、将合作确立为社会规范的互惠规则，以及涉及同时有利于欺骗者的个体竞争和有利于合作者的群体竞争的多层次选择。在本文中，我们基于最近研究多水平选择的 PDE 复制者方程的工作，来理解群体内部的相似性机制、利他偏好以及直接和间接互惠如何与群体之间的进化竞争协同作用，帮助促进合作。我们考虑一个具有群体结构的种群，其中个体之间的相互作用由囚徒困境博弈组成，并研究由根据这些群体内部机制进行相互作用的个体获得的收益决定的多层次竞争的动态。我们发现，这些机制中的每一个都与多层次选择协同作用，促进合作，降低维持长时间合作所需的群体间竞争的强度，并增加种群实现的集体收益。然而，我们发现，只有利他偏好才能实现囚徒困境博弈的社会最优集体收益，在这种博弈中，平均收益通过合作和背叛者的中间混合达到最大化。对于其他三种机制，多层次动态仍然容易受到低级选择的影响，因为集体结果未能超过全合作者群体的收益。
