Collaboration drives phase transitions towards cooperation in prisoner's dilemma

2026-02-12

AI Summary

This study addresses the central question in game theory of how cooperation emerges among self-interested individuals in the Prisoner’s Dilemma. The authors propose a novel “cooperation loop” model that, for the first time, integrates shared intentionality and a predisposition to cooperate into the phase transition analysis of structured populations. By enabling neighboring players to form coalitions and combining self-interested incentives with intentionality-driven strategy updating, the model reveals—through microscopic stochastic dynamics on networks and non-equilibrium phase transition theory—that cooperation robustly emerges under the joint influence of collaborative propensity and the payoff advantage of cooperators. This mechanism proves resilient to variations in both neighborhood size and coalition scale, thereby uncovering the non-equilibrium phase transition nature underlying the evolution of cooperation.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Applications and emergent phenomena

Abstract

We present a collaboration ring model -- a network of players playing the prisoner's dilemma game and collaborating among the nearest neighbours by forming coalitions. The microscopic stochastic updating of the players'strategies are driven by their innate nature of seeking selfish gains and shared intentionality. Cooperation emerges in such a structured population through non-equilibrium phase transitions driven by propensity of the players to collaborate and by the benefit that a cooperator generates. The robust results are qualitatively independent of number of neighbours and collaborators.

Problem

• prisoner's dilemma
• cooperation
• phase transitions
• collaboration
• structured population

Innovation

• collaboration ring model
• prisoner's dilemma
• non-equilibrium phase transitions
• shared intentionality
• cooperation emergence