The evolution of cooperation in spatial prisoner’s dilemma games with heterogeneous relationships

• We introduce heterogeneous relationships in evolutionary prisoner’s dilemma game models.
• We argue that players tend to preferentially allocate their investments to the intimate friends.
• The presence of diverse relationships guarantees the emergence of cooperation
• Extremely strong investment preference hinders the diffusion of cooperative strategy.

This paper investigates how the introduction of heterogeneous relationships and the subsequent investment preference influences the evolution of cooperation in prisoner’s dilemma games. We consider random tie strength values drawn from distributions with different heterogeneity. We show that cooperation is significantly promoted if players preferentially allocate their investments to the friends with strong relationships. The facilitation of cooperation relies mostly on the heterogeneous distribution of relationships and the subsequent investment preference, resulting in strong cooperative allies between good friends and the formation of cooperative clusters around such allies. Moreover, we discover that the investment preference has a sophisticated impact on the evolution of cooperation. Consequently, the level of cooperation will be greatly enhanced by a weak investment preference, but will be significantly depressed if such preference exceeds a critical value. We attribute this finding to the extreme allocation of investments brought by strong preference that hinders the diffusion of cooperative strategy all over the network. Our results suggest that heterogeneous relationships and the subsequent investment preference might have played a crucial role by the evolution of cooperation amongst egoistic individuals.