Optional games on cycles and complete graphs

TL;DR

This paper investigates how optional strategies, including loner options, influence the evolution of cooperation on simple graphs, revealing that increased optionality promotes cooperation in various population structures.

Contribution

It provides a comprehensive analysis of optional games on cycles and complete graphs, deriving new theoretical limits and numerical results for strategy evolution under different conditions.

Findings

Increasing loner strategies promotes cooperation.

Optionality facilitates cooperation in both well-mixed and structured populations.

Derived analytic results for weak and strong selection regimes.

Abstract

We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition there are one or several possibilities to opt out from the game by adopting loner strategies. Optional games lead to relaxed social dilemmas. Here we explore the interaction between spatial structure and optional games. We find that increasing the number of loner strategies (or equivalently increasing mutational bias toward loner strategies) facilitates evolution of cooperation both in well-mixed and in structured populations. We derive various limits for weak selection and large population size. For some cases we derive analytic results for strong selection. We also analyze strategy selection numerically for finite selection intensity and discuss combined effects of optionality and spatial structure.