Selection of noise level in strategy adoption for spatial social dilemmas

TL;DR

This paper investigates how the evolution of individual noise levels affects strategy adoption in spatial social dilemmas, showing that systems tend to settle on a noise level that maximizes cooperation.

Contribution

It introduces a model where both strategies and individual noise levels co-evolve, revealing that the system converges to a single noise level optimal for cooperation.

Findings

The system converges to a single noise level after co-evolution.

The surviving noise level aligns with the one that maximizes cooperation.

Coexistence of strategies is influenced by the evolved noise parameter.

Abstract

We studied spatial Prisoner's Dilemma and Stag Hunt games where both the strategy distribution and the players' individual noise level could evolve to reach higher individual payoff. Players are located on the sites of different two-dimensional lattices and gain their payoff from games with their neighbors by choosing unconditional cooperation or defection. The way of strategy adoption can be characterized by a single $K$ (temperature-like) parameter describing how strongly adoptions depend on the payoff-difference. If we start the system from a random strategy distribution with many different player specific $K$ parameters, the simultaneous evolution of strategies and $K$ parameters drives the system to a final stationary state where only one $K$ value remains. In the coexistence phase of cooperator and defector strategies the surviving $K$ parameter is in good agreement with the noise level that ensures the highest cooperation level if uniform $K$ is supposed for all players. In this paper we give a thorough overview about the properties of this evolutionary process.