Social diversity and promotion of cooperation in the spatial prisoner's dilemma game

TL;DR

This study investigates how social diversity, modeled through various distributions including power-law, influences cooperation in the spatial prisoner's dilemma game, highlighting the role of social hierarchy and spatial correlation in promoting cooperative behavior.

Contribution

It introduces a model incorporating extrinsic social factors affecting payoffs, demonstrating that power-law social diversity best promotes cooperation and that spatial correlation impacts cooperative clusters.

Findings

Power-law social diversity enhances cooperation.

High-ranking players form cooperative clusters.

Spatial correlation reduces cooperation levels.

Abstract

The diversity in wealth and social status is present not only among humans, but throughout the animal world. We account for this observation by generating random variables that determ ine the social diversity of players engaging in the prisoner's dilemma game. Here the term social diversity is used to address extrinsic factors that determine the mapping of game pay offs to individual fitness. These factors may increase or decrease the fitness of a player depending on its location on the spatial grid. We consider different distributions of extrin sic factors that determine the social diversity of players, and find that the power-law distribution enables the best promotion of cooperation. The facilitation of the cooperative str ategy relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to prevail against the defectors even when there is a large temptation to defect. To confirm this, we also study the impact of spatially correlated social diversity and find that coopera tion deteriorates as the spatial correlation length increases. Our results suggest that the distribution of wealth and social status might have played a crucial role by the evolution of cooperation amongst egoistic individuals.