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Title: Evolutionary Stability Concepts in a Stochastic Environment
Author: Xiu-Deng Zheng, Cong Li, Sabin Lessard, Yi Tao
Abstract: Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.
Corresponding author: Yi Tao
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PubYear: 2017
Volume: 96
Issue: 3
Page: Article No. 032414
Journal: Physical Review E
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URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.032414