Strategy abundance in evolutionary many-player games with multiple strategies

Area of Science:

• Evolutionary biology
• Game theory
• Population genetics

Background:

• Evolutionary game theory commonly uses two-player models.
• Complex biological and social phenomena often involve multi-player interactions.
• Modeling multi-player dynamics is crucial for understanding evolutionary success.

Purpose of the Study:

• To derive the composition of a many-player, multiple-strategy system at mutation-selection equilibrium.
• To develop a simplified analytical approach for complex evolutionary scenarios.
• To provide a framework applicable to diverse evolutionary contexts.

Main Methods:

• Abstracting complex interactions into a many-player game framework.
• Utilizing recursion and coalescence theory.
• Deriving an expression for mutation-selection equilibrium.

Main Results:

• A simple expression for the composition of many-player systems at equilibrium was derived.
• The method leverages recursions from coalescence theory.
• The approach simplifies complex multi-player evolutionary dynamics.

Conclusions:

• The derived expression offers a powerful tool for analyzing multi-player evolutionary systems.
• This framework can be adapted for studying genetic polymorphism and cultural evolution.
• The study advances the modeling of evolutionary dynamics beyond pairwise interactions.