Sacrificing personal benefits for a common good is at odds with the fundamental principle of Darwinian evolution: if only the fittest survives, then there should be no place for cooperation. But cooperative behavior actually abounds, and constitutes one of the most persistent and fascinating puzzles of nature. One solution to this puzzle is network reciprocity, where the collective dynamics of cooperators affords them protection against invading defectors. Commonly, however, such a competition does not unfold in isolation. Populations are often divided into sub-populations, with different evolutionary rules describing the interactions between them. Here we propose and study a paradigmatic model that captures the essence of this setup. Specifically, if two players belong to the same sub-population, they play the prisoner's dilemma game. If not, they play either the harmony game, the snowdrift game, the stag-hunt game, or the prisoner's dilemma game. Due to such an asymmetry in the interactions across sub-populations, a fascinating evolutionary dynamics sets up that greatly expands the survivability of cooperators. For instance, when the harmony game applies, cyclic dominance spontaneously emerges, wherein cooperators in one sub-population become predators of defectors in the other sub-population. One also may observe self-organized segregation, wherein both sub-populations maintain a mixed state of cooperators and defectors. As a general rule, we show that the lower the dilemma strength between sub-populations, the more abundant the cooperative strategy in the entire population. Results are confirmed by means of Monte Carlo simulations with pair approximation method, which reveals a rich plethora of novel and generally valid paths to cooperation.

中文翻译：

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不对称亚群中的合作动态

为共同利益牺牲个人利益与达尔文进化论的基本原则背道而驰：如果适者生存，则不应有合作的余地。但合作行为实际上比比皆是，并且构成了自然界中最持久和最迷人的谜题之一。这个难题的一个解决方案是网络互惠，合作者的集体动态为他们提供保护，防止入侵的叛逃者。然而，这种竞争通常不会孤立展开。种群通常分为亚种群，不同的进化规则描述了它们之间的相互作用。在这里，我们提出并研究了一个范式模型，它捕捉了这种设置的本质。具体来说，如果两个玩家属于同一个亚群，他们就玩囚徒困境博弈。如果不，他们玩和谐博弈、雪堆博弈、猎鹿博弈或囚徒困境博弈。由于亚群之间相互作用的这种不对称性，一种引人入胜的进化动力学建立起来，极大地扩展了合作者的生存能力。例如，当和谐游戏适用时，循环优势自发出现，其中一个亚群中的合作者成为另一个亚群中叛逃者的掠夺者。人们还可以观察到自组织的隔离，其中两个亚群都保持着合作者和叛逃者的混合状态。作为一般规则，我们表明子种群之间的困境强度越低，整个种群中的合作策略就越丰富。结果通过使用对近似方法的蒙特卡罗模拟得到证实，