Imitation of Cooperation in Prisoner's Dilemma Games with Some Local Interaction

In this paper I study conditions for the emergence of cooperative behavior in a dynamic model of population interaction. The model has finitely many individuals located on a circle. The pay-off of each individual is partly based on the (local) interaction with neighbors and partly on (uniform) interaction with the whole population. The dynamics is driven by imitative behavior. I show that for a large class of parameters cooperation will emerge if the population is large; if the population is small, defection will prevail in the long run. The result contrasts with conventional wisdom which says that the larger the population, the less likely cooperation will be.