Evolutionar Dnamics of Populations wirth a Local Interaction Structure

A model of a population with a Local Interaction structure is presented. Individuals interact with others in a given Inter- action neighborhood to obtain their payof. Individuals either imitate or else they die and are replaced by one of their neigh- bors in another neighborhood- the Propagation neighborhood. An individual with a higher payo is more likely to be imitated or to replace his neighbor. An unbeatable strategy can repel the invasion of any mutant. We show that the (unique, if it exists) unbeatable strategy is an ESS of a population game with inclu- sive tness parameter which depends on the size of the interac- tion and propagation neighborhoods. We analyze the evolution of altruistic traits in such populations and observe that allowing the players more information eases the development of altruistic behavior.