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Related Experiment Video

Updated: Jun 7, 2026

The HoneyComb Paradigm for Research on Collective Human Behavior

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

A condition for cooperation in a game on complex networks.

Tomohiko Konno¹

¹The Institute of Industrial Science, The University of Tokyo, and Research Fellow of the Japan Society for the Promotion of Science, Komaba 4-6-1, Meguro, Tokyo 153-8505, Japan. tomo.konno@gmail.com

Journal of Theoretical Biology

|November 4, 2010

Summary

Cooperation thrives in Prisoner's Dilemma games on networks when the benefit-to-cost ratio exceeds the average nearest neighbors' degree, not just the average degree. Regular networks best support cooperation, while scale-free networks hinder it.

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Area of Science:

Evolutionary Game Theory
Network Science
Computational Social Science

Background:

Cooperation dynamics in social dilemmas are crucial for understanding collective behavior.
The Prisoner's Dilemma game on networks is a key model for studying cooperation.
Previous work suggested average degree (〈k〉) as the threshold for cooperation.

Purpose of the Study:

To identify the precise condition favoring cooperation in Prisoner's Dilemma on complex networks.
To compare cooperation levels across different network structures (regular, random, scale-free).
To investigate the role of network heterogeneity in promoting cooperation.

Main Methods:

Simulations of the Prisoner's Dilemma using a death-birth process with weak selection.
Analysis of cooperation dynamics on regular, random, and scale-free networks.
Derivation of the theoretical condition for cooperation based on network topology.

Main Results:

The condition for favoring cooperation is b/c > 〈k(nn)〉, where 〈k(nn)〉 is the average nearest neighbors' degree.
Regular networks show the highest propensity for cooperation.
Scale-free networks exhibit the least cooperation, with cooperation being absent in ideal scale-free networks.

Conclusions:

The average nearest neighbors' degree is the critical factor for cooperation, not the average degree.
Network structure significantly impacts cooperation; regular networks are conducive, while scale-free networks are detrimental.
The influence of scale-free networks and heterogeneity on cooperation is context-dependent and not universally favorable.