On Evolutionary Spatial Heterogeneous Games

TL;DR

This paper investigates how spatial heterogeneities and asymmetries in environmental interactions influence the evolution of cooperation among self-interested individuals using extended evolutionary game models with variable payoff matrices.

Contribution

It introduces models with spatially heterogeneous and evolving payoff matrices, advancing understanding of cooperation dynamics in complex environments.

Findings

Spatial heterogeneity affects cooperation levels.

Evolving payoffs influence strategy stability.

Heterogeneous environments can promote cooperation.

Abstract

How coperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model to take into account the spatial dimension in evolutionary games is in terms of cellular automata with just a one-parameter payoff matrix. Here, the effects of spatial heterogeneities of the environment and/or asymmetries in the interactions among the individuals are analysed through different extensions of this model. Instead of using the same universal payoff matrix, bimatrix games in which each cell at site (i,j) has its own different `temptation to defect' parameter T(i,j) are considered. Firstly, the case in which these individual payoffs are constant in time is studied. Secondly, an evolving evolutionary spatial game such that T=T(i,j;t), i.e. besides depending on the position evolves (by natural selection), is used to explore the combination of spatial heterogeneity and natural selection of payoff matrices.