Naïve imitation and partial cooperation in a local public goods model

In a local interaction model agents situated on a circle play bilateral prisoners’ dilemmas with their immediate neighbors and have three possible strategies: cooperate in all interactions (altruistic), defect in all interactions (egoistic), or cooperate with one immediate neighbor with probability 1=2 (partial cooperation). After each period the agents adopt the strategy with the highest average payoff in their observed local neighborhood (naïve imitation). The absorbing states of the process are outlined and analysed. There does not exist an absorbing state in which the partially cooperative strategy coexists with any of the other strategies. The partially cooperative strategy limits the diffusion of altruistic behavior in the population. Even though clustering of altruists is generally beneficial for sustaining altruism, relatively big groups of altruists at the onset actually enable the spread of the partially cooperative strategy.