Evolution of cooperation in a three-strategy game combining snowdrift and stag hunt games

TL;DR

This paper explores how combining snowdrift and stag hunt game strategies affects the evolution of cooperation, revealing complex dynamics and coexistence of strategies influenced by population structure and parameters.

Contribution

It introduces a three-strategy model incorporating individual solutions, expanding understanding of cooperation evolution beyond traditional two-strategy frameworks.

Findings

Multiple stable states exist in well-mixed populations.

Spatial structure on a square lattice promotes cooperation.

Various mechanisms enable strategy coexistence depending on parameters.

Abstract

This study aimed to investigate the evolutionary dynamics of a three-strategy game that combines snowdrift and stag hunt games. This game is motivated by an experimental study, which found that individual solution lowers cooperation levels. Agents adopting this option aim to address a problem to the extent necessary to remove negative impact on themselves, although they do not free ride on cooperation effort provided by others. This property of the individual solution is similar to that of option defection in the stag hunt. Thus, the role of the interplay of defection in the snowdrift game and individual solution was examined in this study. The well-mixed population has two asymptotically stable rest points, one wherein the individual solution occupies the population, and the other wherein cooperation and defection coexist. The interactions on a square lattice enlarge the parameter region wherein cooperation survives, and the three strategies often coexist. The scrutinization of the evolutionary process shows that multiple mechanisms lead to the coexistence of the three strategies depending on parameter values. Our analysis suggests that considering the individual solution adds complexity to the evolutionary process, which might contribute to our understanding on the evolution of cooperation.