Average abundancy of cooperation in multi-player games with random payoffs

Area of Science:

• Evolutionary Game Theory
• Mathematical Biology
• Population Dynamics

Background:

• Examines interactions in finite groups with time-varying random payoffs.
• Models population updates using a Moran birth-death process.
• Considers cooperation and defection strategies with recurrent symmetric mutation.

Purpose of the Study:

• To derive an approximation for the average abundance of cooperation at equilibrium.
• To analyze the impact of payoff variances and covariances on cooperation levels.
• To investigate specific social dilemmas: public goods, stag hunt, and snowdrift games.

Main Methods:

• Derivation of a first-order approximation for cooperation abundance.
• Analysis of selection-mutation equilibrium under fluctuating payoffs.
• Application of the model to classic social dilemma games.

Main Results:

• Increasing defection payoff variance or decreasing cooperation payoff variance enhances cooperation.
• Payoff covariance effects depend on the number of cooperators.
• Reduced scaled variance or increased scaled covariance of benefits/costs favors cooperation in stag hunt and snowdrift games.

Conclusions:

• Payoff randomness significantly influences the prevalence of cooperation in evolutionary games.
• Group size can alter the balance between cooperation and defection, especially under weak selection.
• Mutation rate has a minor impact on the equilibrium strategy abundance.