Evolutionary game on any hypergraph
arxiv(2024)
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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