  We study the effect of contingent movement on the persistence of cooperation
on complex networks with empty nodes. Each agent plays Prisoner's Dilemma game
with its neighbors and then it either updates the strategy depending on the
payoff difference with neighbors or it moves to another empty node if not
satisfied with its own payoff. If no neighboring node is empty, each agent
stays at the same site. By extensive evolutionary simulations, we show that the
medium density of agents enhances cooperation where the network flow of mobile
agents is also medium. Moreover, if the movements of agents are more frequent
than the strategy updating, cooperation is further promoted. In scale-free
networks, the optimal density for cooperation is lower than other networks
because agents get stuck at hubs. Our study suggests that keeping a smooth
network flow is significant for the persistence of cooperation in ever-changing
societies.
