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07-01-2022

Noise-Induced Quasi-Heteroclinic Cycle in a Rock–Paper–Scissors Game with Random Payoffs

Authors: Tian-Jiao Feng, Jie Mei, Rui-Wu Wang, Sabin Lessard, Yi Tao, Xiu-Deng Zheng

Published in: Dynamic Games and Applications

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Abstract

The rock–paper–scissors game is one of the main theoretical models in evolutionary game theory and has been used successfully to explain some observed phenomena in biology, economics and social science. In order to explore the influence of environmental noise on cyclic dominance in the rock–paper–scissors game, stochastic stability in a continuous-time dynamics of the game with random payoffs in pairwise interactions is investigated by using the stochastic stability theory of Itô’s stochastic differential equations. After deducing a stochastic replicator equation for the strategy frequencies in a symmetric version of the game, stochastic stability conditions for constant equilibrium states are obtained and stochastic simulations of the global dynamics are performed. The main results are that (1) none of the fixation states of the system can be stochastically stable; and (2) an increase in the noise level (or stochastic fluctuation intensity) can result in the loss of stochastic stability of the constant interior equilibrium. More importantly, the simulation results not only match the theoretical predictions but also show the appearance of a noise-induced quasi-heteroclinic cycle when the constant interior equilibrium loses its stochastic stability as the noise level increases.

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Appendix
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Metadata
Title
Noise-Induced Quasi-Heteroclinic Cycle in a Rock–Paper–Scissors Game with Random Payoffs
Authors
Tian-Jiao Feng
Jie Mei
Rui-Wu Wang
Sabin Lessard
Yi Tao
Xiu-Deng Zheng
Publication date
07-01-2022
Publisher
Springer US
Published in
Dynamic Games and Applications
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-021-00414-y

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