The lower convergence tendency of imitators compared to best responders

Imitation is widely observed in nature and often used to model populations of decision-making agents, but it not yet known under what conditions a network imitators will reach state where they are satisfied with their decisions. We show that every which agents imitate the best performing strategy neighborhood an equilibrium finite time, provided all opponent coordinating, i.e., earn higher payoff if plays same as do. It follows any non-convergence imitative networks necessarily result population heterogeneity nor special topology, rather must be caused by other factors such presence non-opponent-coordinating agents. To strengthen this result, we large classes containing never equilibrate even when homogeneous. Comparing best-response dynamics equilibration guaranteed for homogeneous playing 2 × matrix games, our results imply have lower tendency.