Cooperation driven by mutations in multi-person Prisoner's Dilemma

Area of Science:

• Evolutionary game theory
• Population dynamics
• Computational biology

Background:

• The n-person Prisoner's Dilemma models group interactions.
• Previous studies assumed isolated mutations, limiting evolutionary stability analysis.
• Group size amplifies issues with infrequent mutation assumptions.

Purpose of the Study:

• Analyze convergence rates to evolutionarily stable populations under isolated mutations.
• Develop a deterministic approximation for evolutionary dynamics with stochastic mutations.
• Investigate the impact of mutation rate, group size, payoff parameters, and initial population structure.

Main Methods:

• Analysis of convergence rates for trigger strategies in the n-person Prisoner's Dilemma.
• Derivation of a deterministic approximation for large populations with explicit mutation processes.
• Efficient calculation of fitness values for large group simulations.

Main Results:

• Low mutation rates lead to slow convergence, challenging prior assumptions.
• Increased mutation rates stabilize cooperative dynamics and introduce new fixed points.
• Stable limit cycles favoring cooperation emerge for certain payoff parameters.
• Cooperative regions expand with mutation rate and group size.

Conclusions:

• Traditional models with infrequent mutations are insufficient for understanding evolutionary stability in groups.
• Stochastic mutation processes are crucial for accurate modeling of population dynamics.
• Cooperation can be promoted by specific mutation rates and group structures, leading to complex dynamics.