Can weak diversity help in propagating cooperation? Invasion of cooperators at the conformity-conflict boundary

The influence of social diversity on cooperation promotion has been frequently studied in the literature. This work classifies the diversity into strong and weak based on its impact on payoffs. Strong diversity is typically known to the players and relates to, for example, the scope of the players’ neighborhoods. In contrast, weak diversity's impact is irrelevant to the payoff and thus may be ignored by the agents. In this work, a model with both strong and weak diversity is set up to study the impact of weak diversity in the presence of strong diversity. Additionally, a conformity-conflict model (i.e., a model with a designed boundary of weak diversity) is used to study the weak diversity's impact on the level of cooperation among agents. While strong diversity defines basic cooperation patterns, weak diversity adds extra influence on the cooperation but depends on the players’ payoff sensitivity. When the dilemma strength is low, weak diversity enables the cooperation level to increase gradually over a long period. Simulation results highlight a specific pattern: the clusters formed at the equilibrium may be “distorted” into expanding ones due to the impact of the weak diversity boundary. Such propagation of cooperation explains the impact of weak diversity on the global change in cooperation. Thus, weak diversity allows modeling a gradual variation in features using deterministic evolutionary games. Such an impact of weak diversity can also be observed in the network structure with long-range connections (such as the small-world structure).