Abstract
We have studied the evolution of cooperation in structured populations whose topology coevolves with the game strategies of the individuals. Strategy evolution proceeds according to an update rule with a free parameter, which measures the selection pressure. We explore how this parameter affects the interplay between network dynamics and strategy dynamics. A dynamical network topology can influence the strategy dynamics in two ways: (i) by modifying the expected payoff associated with each strategy and (ii) by reshaping the imitation network that underlies the evolutionary process. We show here that the selection pressure tunes the relative contribution of each of these two forces to the final outcome of strategy evolution. The dynamics of the imitation network plays only a minor role under strong selection, but becomes the dominant force under weak selection. We demonstrate how these findings constitute a mechanism supporting cooperative behavior.