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

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.

11 pages, 7 figures

References in corpus (8)

• The structure and dynamics of multilayer networks
• Evolutionary games on graphs
• Statistical physics of human cooperation
• Fixation of strategies for an evolutionary game in finite populations
• Probabilistic sharing solves the problem of costly punishment
• Effect of memory on the prisoner's dilemma game in a square lattice
• Cooperation in regular lattices
• Mean-potential law in evolutionary games