We explore the model of cooperation in the Prisoner’s Dilemma, based on reputation [1]. Here, for altruisms equal zero, the probability *P*(*W*(*k*,*i*)) that agent *k* cooperates with agent *i* is assumed as *P*(*W*(*k*,*i*),*a*)={1+th[*a*(*W*(*k*,*i*)-1/2)]}/2, where *W*(*k*,*i*)∈(0,1) is the reputation of agent *i* in eyes of *k* and 1/*a* is a measure of errors of the players. In the limit of infinite *a*, the game is deterministic. Then, the game has three possible outcomes: a) both cooperate (probability 0.25), b) both defect (probability 0.25) and c) a cyclic series of games where either *k* cooperates and *i* defects, or the opposite, exchanging the strategies at each time step. Then, the distribution of *W*(*i*,*k*)+*W*(*k*,*i*) consists of three sharp peaks. For finite values of *a*, the probability of c) decreases exponentially in time. For small values of *a*, a crossover is observed from the state where only options a) and b) appear (*a* = 5) to a homogeneous distribution of *W*(*i,k*) at the most fuzzy case *a*=0.
[1] K. Kułakowski, P. Gawroński, Physica A, 388 (2009) 3581. |