  We address the problem of how the survival of cooperation in a social system
depends on the motion of the individuals. Specifically, we study a model in
which Prisoner's Dilemma players are allowed to move in a two-dimensional
plane. Our results show that cooperation can survive in such a system provided
that both the temptation to defect and the velocity at which agents move are
not too high. Moreover, we show that when these conditions are fulfilled, the
only asymptotic state of the system is that in which all players are
cooperators. Our results might have implications for the design of cooperative
strategies in motion coordination and other applications including wireless
networks.
