Mutation mitigates finite-size effects in spatial evolutionary games

TL;DR

This paper shows that adding mutation to spatial evolutionary game simulations on small networks effectively reduces finite-size effects, leading to more reliable outcomes without requiring large networks or extensive computational resources.

Contribution

The study demonstrates that mutation can serve as a resource-efficient method to mitigate finite-size effects in agent-based spatial game simulations, enhancing their reliability.

Findings

Mutation preserves stable equilibria in small networks.

Moderate mutation rates prevent strategy dominance caused by finite-size effects.

Results with mutation align with large-network simulations.

Abstract

Agent-based simulations are essential for studying cooperation on spatial networks. However, finite-size effects -- random fluctuations due to limited network sizes -- can cause certain strategies to unexpectedly dominate or disappear, leading to unreliable outcomes. While enlarging network sizes or carefully preparing initial states can reduce these effects, both approaches require significant computational resources. In this study, we demonstrate that incorporating mutation into simulations on limited networks offers an effective and resource-efficient alternative. Using spatial optional public goods games and a more intricate tolerance-based variant, we find that rare mutations preserve inherently stable equilibria. When equilibria are affected by finite-size effects, introducing moderate mutation rates prevent finite-size-induced strategy dominance or extinction, producing results consistent with large-network simulations. Our findings position mutation as a practical tool for improving the reliability of agent-based models and emphasize the importance of mutation sensitivity analysis in managing finite-size effects across spatial networks.