Evolutionarily stable strategies for a finite population and a variable contest size

Area of Science:

• Evolutionary Game Theory
• Population Genetics
• Behavioral Ecology

Background:

• John Maynard Smith's concept of evolutionarily stable strategies (ESS) is foundational in evolutionary game theory.
• The standard ESS model assumes infinite populations and pairwise contests, limiting its applicability to real-world scenarios.
• Finite populations and variable contest sizes introduce complexities not addressed by the classical ESS framework.

Purpose of the Study:

• To generalize the evolutionarily stable strategy (ESS) concept to finite populations and variable contest sizes.
• To analyze the equilibrium and stability conditions of this generalized ESS.
• To investigate the behavioral implications of ESS in finite populations, particularly 'spiteful' behavior.

Main Methods:

• Mathematical modeling and analysis of game theory principles.
• Generalization of Maynard Smith's ESS conditions.
• Analysis of symmetric two-pure-strategies, two-player games in a finite population context.

Main Results:

• The standard ESS for infinite populations and pairwise contests is a special case of the generalized ESS.
• In finite populations, ESS players exhibit 'spiteful' behavior, actively decreasing competitors' payoffs.
• The degree of spiteful behavior intensifies as population size decreases, being most pronounced in small populations.

Conclusions:

• The generalized ESS provides a more realistic framework for understanding strategy evolution in finite populations.
• Spiteful behavior is an emergent property of ESS in finite populations, influenced by population size.
• Mixed strategy ESS demonstrates global stability against single-type mutant invasion, with conditions for simultaneous invasion identified.