Evolutionary game on any hypergraph

Dini Wang, Peng Yi, Yiguang Hong, Jie Chen, Gang Yan
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Abstract

Cooperation plays a fundamental role in societal and biological domains, and the population structure profoundly shapes the dynamics of evolution. Practically, individuals behave either altruistically or egoistically in multiple groups, such as relatives, friends and colleagues, and feedbacks from these groupwise interactions will contribute to one's cognition and behavior. Due to the intricacy within and between groups, exploration of evolutionary dynamics over hypergraphs is relatively limited to date. To uncover this conundrum, we develop a higher-order random walk framework for five distinct updating rules, thus establishing explicit conditions for cooperation emergence on hypergraphs, and finding the overlaps between groups tend to foster cooperative behaviors. Our systematic analysis quantifies how the order and hyperdegree govern evolutionary outcomes. We also discover that whenever following a group wisdom update protocol, choosing a high-fitness group to interact equally within its members, cooperators will significantly prevail throughout the community. These findings underscore a crucial role of higher-order interaction and interdisciplinary collaboration throughout a broad range of living systems, favoring social prosperity.
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任意超图上的进化游戏
合作在社会和生物领域发挥着根本性的作用,群体结构深刻地影响着进化的动力。实际上,个体在多个群体(如亲戚、朋友和同事)中或利他主义或利己主义地行为,这些群体间的互动反馈将有助于个体的认知和行为。由于群体内部和群体之间的错综复杂,迄今为止对超图谱进化动力的探索相对有限。为了揭开这个谜团,我们为五种不同的更新规则开发了一个高阶随机游走框架,从而为超图上合作的出现建立了明确的条件,并发现群体间的重叠倾向于促进合作行为。我们的系统分析量化了阶数和超度对进化结果的影响。我们还发现,只要遵循群体智慧更新协议,选择一个高匹配度群体在其成员内部平等互动,合作者就会在整个群体中明显占优。这些发现强调了高阶互动和跨学科合作在广泛的生命系统中的关键作用,有利于社会繁荣。
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