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

TLDR

Social diversity, the variation in wealth and status observed across species, is treated here as extrinsic factors that modulate how game payoffs translate into individual fitness depending on a player’s spatial position. The study seeks to model how such social diversity affects cooperation in the spatial prisoner's dilemma by assigning random variables to players. These random variables generate heterogeneous social states that alter payoff‑to‑fitness mappings across the grid, enabling the analysis of different extrinsic factor distributions. Power‑law distributed social diversity most strongly promotes cooperation, forming clusters led by high‑ranking players that can defeat defectors even under strong temptation, while increasing spatial correlation length weakens cooperation, implying that wealth and status distributions may have driven cooperative evolution.

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 determine 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 payoffs 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 extrinsic 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 strategy 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 cooperation 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.