2007/11/30 by Vasils Hatzopoulos, Vasilis Hatzopoulos, Henrik Jeldtoft Jensen
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Social Sciences · #Artificial intelligence #Computer science #Demography #Dilemma #Econometrics #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Field (mathematics) #Gaussian #Limit (mathematics) #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematical economics #Mathematics #Mean field theory #Physics #Population #Replicator equation #Selection (genetic algorithm) #Sociology #Statistical physics #Tournament #Tournament selection #q-bio.OT #q-bio.PE
paper · pdf · doi:10.1103/physreve.78.011904
8 pages, 8 figures
arxiv created 2007/11/30 · openalex publication_date 2008/07/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the evolution of cooperation on a nongrowth dynamic network model with a death-birth dynamics based on tournament selection. In the limit of large population size, the equilibrium cooperator density is well described by our mean field approximations and inversely related to the average degree in the system. Small populations are also examined and found to deviate considerably from their expected mean field behavior. An expanded replicator equation incorporating Gaussian fluctuations in the strategy densities is then constructed, with its output agreeing well with our simulation data for all sizes. We also briefly comment on the role of strategy mutation in sustaining polymorphic populations in small systems.