Social Network Reciprocity as a Phase Transition in Evolutionary Cooperation

TL;DR

This paper models the emergence of cooperation in social networks as a phase transition, using statistical mechanics to analyze how lattice reciprocity promotes cooperation in evolutionary games.

Contribution

It introduces an exact dipole model and demonstrates that lattice reciprocity acts as a thermodynamic phase transition, surpassing mean-field limitations in social cooperation modeling.

Findings

Lattice reciprocity enhances cooperation in social networks.

Phase transition behavior explains the onset of cooperation.

Mean-field approaches fail to capture the phase transition dynamics.

Abstract

In Evolutionary Dynamics the understanding of cooperative phenomena in natural and social systems has been the subject of intense research during decades. We focus attention here on the so-called "Lattice Reciprocity" mechanisms that enhance evolutionary survival of the cooperative phenotype in the Prisoner's Dilemma game when the population of darwinian replicators interact through a fixed network of social contacts. Exact results on a "Dipole Model" are presented, along with a mean-field analysis as well as results from extensive numerical Monte Carlo simulations. The theoretical framework used is that of standard Statistical Mechanics of macroscopic systems, but with no energy considerations. We illustrate the power of this perspective on social modeling, by consistently interpreting the onset of lattice reciprocity as a thermodynamical phase transition that, moreover, cannot be captured by a purely mean-field approach.