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.

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