Evolutionary Dynamics of Populations with a Local Interaction Structure

A model of a population with a Local Interaction structure is presented. Individuals interact with others in a given Interaction neighborhood to obtain their payoff. Individuals either imitate or else they die and are replaced by one of their neighbors in another neighborhood- the Propagation neighborhood. An individual with a higher payoff 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 interaction 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.