2008/06/30 by L. M. Florı́a, L. M. Floria, C. Gracia-Lazaro +5
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Opinion Dynamics and Social Influence #physics.soc-ph
paper · pdf · doi:10.1103/physreve.79.026106
10 pages. APS style
arxiv created 2008/06/30 · openalex publication_date 2009/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.