Nonlinear Dynamics of the Rock-Paper-Scissors Game with Mutations

Abstract

We analyze the replicator-mutator equations for the Rock-Paper-Scissors game. Various graph-theoretic patterns of mutation are considered, ranging from a single unidirectional mutation pathway between two of the species, to global bidirectional mutation among all the species. Our main result is that the coexistence state, in which all three species exist in equilibrium, can be destabilized by arbitrarily small mutation rates. After it loses stability, the coexistence state gives birth to a stable limit cycle solution created in a supercritical Hopf bifurcation. This attracting periodic solution exists for all the mutation patterns considered, and persists arbitrarily close to the limit of zero mutation rate and a zero-sum game.

6 pages, 5 figures

References in corpus (6)

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Cited by in corpus (6)

• Stochastic population dynamics in spatially extended predator-prey systems
• The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games
• Evolutionary dynamics of the delayed replicator-mutator equation: Limit cycle and cooperation
• Chimera states in a network-organized public goods game with destructive agents
• Amplitude death in coupled replicator map lattice: averting migration dilemma
• Community Formation in Wealth-Mediated Thermodynamic Strategy Evolution