Promotion of cooperation induced by nonlinear attractive effect in spatial Prisoner’s Dilemma game

– We introduce nonlinear attractive effects into a spatial Prisoner’s Dilemma game where the players located on a square lattice can either cooperate with their nearest neighbors or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbors with a probability proportional to A denoting the attractiveness of the neighbor, where A is the payoff collected by it and α (≥0) is a free parameter characterizing the extent of the nonlinear effect; and then adopting its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density ρC of cooperators in the stationary state for different values of α. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect. In particular, for large values of α, i.e., strong nonlinear attractive effects, the system exhibits two absorbing states (all cooperators or all defectors) separated by an active state (coexistence of cooperators and defectors) when varying the temptation to defect. In the critical region where ρC goes to zero, the extinction behavior is power lawlike ρC ∼ (bc − b) , where the exponent β accords approximatively with the critical exponent (β ≈ 0.584) of the two-dimensional directed percolation and depends weakly on the value of α. Introduction. – Cooperation plays an important role in real world, ranging from biological systems to economic and social systems [1]. Scientists from many different fields of natural and social sciences often resort to Evolutionary Game Theory [2,3] as a common mathematical framework and the prisoner’s dilemma game (PDG) as a metaphor for studying cooperation between unrelated individuals [3]. The original PDG describes the pairwise interactions of individuals with two behavioral options: the two players must simultaneously decide whether to cooperate or to defect. For mutual cooperation both players receive the rewards R, but only the punishment P for mutual defection. A defector exploiting a cooperator gets an amount T (temptation to defect) and the exploited cooperator receives S (sucker’s payoff). These elements satisfy the following two conditions: T > R > P > S and 2R > T + S. It is easy to see that defection is the better choice irrespective of the opponent’s decision. Thus, the undesired outcome of mutual defection emerges in well-mixed populations [4], which has