Prisoner's dilemma on a stochastic nongrowth network evolution model.

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.