Scale-Free Networks Enhance the Spread of Better Strategy

Tomohiko Konno ()
Additional contact information
Tomohiko Konno: Kwansei Gakuin University

Dynamic Games and Applications, 2025, vol. 15, issue 1, No 5, 103-128

Abstract: 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.

Keywords: Evolutionary games; Imitation and learning; Network heterogeneity; Scale-free networks; Coordination games; Cooperation (search for similar items in EconPapers)
JEL-codes: C73 D83 D85 R10 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13235-024-00571-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:dyngam:v:15:y:2025:i:1:d:10.1007_s13235-024-00571-w

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/13235

DOI: 10.1007/s13235-024-00571-w

Access Statistics for this article

Dynamic Games and Applications is currently edited by Georges Zaccour

More articles in Dynamic Games and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().