Cooperation for volunteering and partially random partnerships.

Competition among cooperative, defective, and loner strategies is studied by considering an evolutionary prisoner's dilemma game for different partnerships. In this game each player can adopt one of its coplayer's strategy with a probability depending on the difference of payoffs coming from games with the corresponding coplayers. Our attention is focused on the effects of annealed and quenched randomness in the partnership for fixed number of coplayers. It is shown that only the loners survive if the four coplayers are chosen randomly (mean-field limit). On the contrary, on the square lattice all the three strategies are maintained by the cyclic invasions resulting in a self-organizing spatial pattern. If the fixed partnership is described by a regular small-world structure then a homogeneous oscillation occurs in the population dynamics when the measure of quenched randomness exceeds a threshold value. Similar behavior with higher sensitivity to the randomness is found if temporary partners are substituted for the standard ones with some probability at each step of iteration.