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This study clarifies evolutionary game dynamics in fluctuating environments. It introduces stochastic evolutionary stability (SES) and stochastic convergence stability (SCS), showing stability conditions differ from constant environments.

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Behavioral Economics

Background:

  • Evolutionary game theory and evolutionarily stable strategies are well-established in animal behavior, economics, and social sciences.
  • Stochastic dynamical properties of evolutionary games in fluctuating environments remain poorly understood.
  • Existing models often assume constant payoffs, neglecting environmental randomness.

Purpose of the Study:

  • To investigate conditions for stochastic local stability in evolutionary games with random payoffs.
  • To develop novel concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS).
  • To analyze how environmental fluctuations impact the stability of pure and mixed strategies.

Main Methods:

  • Developed a two-phenotype model with random payoffs from pairwise interactions.
  • Analyzed fixation states and constant interior equilibria under stochastic conditions.
  • Derived mathematical conditions for SES and SCS.

Main Results:

  • The condition for a pure strategy to be SES and SCS is more stringent in fluctuating environments compared to constant ones.
  • The condition for a constant mixed strategy to be SES is less stringent than for SCS.
  • The condition for SCS is less stringent than in a constant environment.

Conclusions:

  • Environmental stochasticity significantly alters the stability landscape of evolutionary games.
  • SES and SCS provide new metrics for understanding strategy stability in dynamic environments.
  • The findings have implications for explaining the evolution of behaviors and strategies in unpredictable settings.