Evolutionary game dynamics with environmental feedback in a network with two communities
arxiv(2024)
摘要
Recent developments of eco-evolutionary models have shown that evolving
feedbacks between behavioral strategies and the environment of game
interactions, leading to changes in the underlying payoff matrix, can impact
the underlying population dynamics in various manners. We propose and analyze
an eco-evolutionary game dynamics model on a network with two communities such
that players interact with other players in the same community and those in the
opposite community at different rates. In our model, we consider two-person
matrix games with pairwise interactions occurring on individual edges and
assume that the environmental state depends on edges rather than on nodes or
being globally shared in the population. We analytically determine the
equilibria and their stability under a symmetric population structure
assumption, and we also numerically study the replicator dynamics of the
general model. The model shows rich dynamical behavior, such as multiple
transcritical bifurcations, multistability, and anti-synchronous oscillations.
Our work offers insights into understanding how the presence of community
structure impacts the eco-evolutionary dynamics within and between niches.
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