On Local Prisoner's Dilemma game with Pareto updating rule

Prisoner's Dilemma games with two and three strategies are studied. The cor responding replicator equations, their steady states and their asymptotic s tability are discussed. Local Prisoner's Dilemma games are studied using Pa reto optimality. As in the case with Nash updating rule, the existence of t it for rat strategy is crucial to imply cooperation even in one dimension. Pareto updating implies less erratic behavior since the steady state config urations are mostly fixed points or at most 2-cycle. Finally, Prisoner's Di lemma game is simulated on small-world networks which are closer to real sy stems than regular lattices. There are no significant changes compared to t he results of the regular lattice.