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arXiv · 2304.14913

Evolutionary Games on Networks: Phase Transition, Quasi-equilibrium, and Mathematical Principles

Jiangjiang Cheng·Wenjun Mei·Wei Su·Ge Chen
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Abstract

The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be actually stable, but correspond to quasi-equilibriums instead. We find that various classic game models, like the evolutionary snowdrift game, evolutionary prisoner's dilemma, and spatial public goods game on square lattices and scale-free networks, exhibit the phase transition in convergence time to the equilibrium state. Moreover, mathematical principles are provided to explain the phase transition of convergence time and quasi-equilibrium of cooperation ratio. The findings explain why and when cooperation and defection have a long-term coexistence.

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Jiangjiang Cheng, Wenjun Mei, Wei Su, Ge Chen. 2023-04-26. Evolutionary Games on Networks: Phase Transition, Quasi-equilibrium, and Mathematical Principles. https://doi.org/10.1016/j.physa.2023.128447

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