Defector-accelerated cooperativeness and punishment in public goods games with mutations

TL;DR

This paper investigates how strategy mutations influence cooperation and punishment in spatial public goods games, revealing that rare mutations accelerate the spread of costly punishment, affecting the dynamics but not the final state.

Contribution

It introduces the impact of strategy mutations on cooperation and punishment dynamics, highlighting how rare mutations accelerate costly punishment spread in spatial public goods games.

Findings

Rare mutations accelerate costly punishment spreading.

Final states are similar with or without mutations at low mutation rates.

Mutations influence the relaxation dynamics but not the ultimate equilibrium.

Abstract

We study the evolution of cooperation in spatial public goods games with four competing strategies: cooperators, defectors, punishing cooperators, and punishing defectors. To explore the robustness of the cooperation-promoting effect of costly punishment, besides the usual strategy adoption dynamics we also apply strategy mutations. As expected, frequent mutations create kind of well-mixed conditions, which support the spreading of defectors. However, when the mutation rate is small, the final stationary state does not significantly differ from the state of the mutation-free model, independently of the values of the punishment fine and cost. Nevertheless, the mutation rate affects the relaxation dynamics. Rare mutations can largely accelerate the spreading of costly punishment. This is due to the fact that the presence of defectors breaks the balance of power between both cooperative strategies, which leads to a different kind of dynamics.