In this study, we mathematically demonstrate that heterogeneous networks accelerate the social learning process, using a mean-field approximation of networks.
Network heterogeneity, characterized by the variance in the number of links per vertex, is effectively measured by the mean degree of nearest neighbors, denoted as ⟨knn⟩. This mean degree of nearest neighbors plays a crucial role in network dynamics, often being more significant than the average number of links (mean degree). Social learning, conceptualized as the imitation of superior strategies from neighbors within a social network, is influenced by this network feature. We find that a larger mean degree of nearest neighbors ⟨knn⟩ correlates with a faster spread of advantageous strategies. Scale-free networks, which exhibit the highest ⟨knn⟩, are most effective in enhancing social learning, in contrast to regular networks, which are the least effective due to their lower ⟨knn⟩.
Furthermore, we establish the conditions under which a general strategy A proliferates over time in a network. Applying these findings to coordination games, we identify the conditions for the spread of Pareto optimal strategies. Specifically, we determine that the initial probability of players adopting a Pareto optimal strategy must exceed a certain threshold for it to spread across the network. Our analysis reveals that a higher mean degree ⟨k⟩ leads to a lower threshold initial probability.
We provide an intuitive explanation for why networks with a large mean degree of nearest neighbors, such as scale-free networks, facilitate widespread strategy adoption. These findings are derived mathematically using mean-field approximations of networks and are further supported by numerical experiments.
JEL: C73, D85, D83, R10