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Scale-Free Networks Enhance the Spread of Better Strategy

Author

Listed:
  • Tomohiko Konno

    (Kwansei Gakuin University)

Abstract

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 $$\langle k_{nn}\rangle $$ ⟨ k nn ⟩ . 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 $$\langle k_{nn}\rangle $$ ⟨ k nn ⟩ correlates with a faster spread of advantageous strategies. Scale-free networks, which exhibit the highest $$\langle k_{nn}\rangle $$ ⟨ k nn ⟩ , are most effective in enhancing social learning, in contrast to regular networks, which are the least effective due to their lower $$\langle k_{nn}\rangle $$ ⟨ k nn ⟩ . 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 $$\langle k \rangle $$ ⟨ 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.

Suggested Citation

  • Tomohiko Konno, 2025. "Scale-Free Networks Enhance the Spread of Better Strategy," Dynamic Games and Applications, Springer, vol. 15(1), pages 103-128, March.
  • Handle: RePEc:spr:dyngam:v:15:y:2025:i:1:d:10.1007_s13235-024-00571-w
    DOI: 10.1007/s13235-024-00571-w
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    Keywords

    Evolutionary games; Imitation and learning; Network heterogeneity; Scale-free networks; Coordination games; Cooperation;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • R10 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - General

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