Proper aspiration level promotes generous behavior in the spatial prisoner's dilemma game

Zero-determinant strategies, which can unilaterally define a linear relationship between two individuals' long-term payoff, have drawn much attention to comprehend the emergence of cooperation among individuals with repeated interactions. A subset of zero-determinant strategies, extortion strategy, can let an extortioner's surplus exceed her opponent's by a fixed percentage. On the other hand, the dual generosity strategy can ensure that a complier's payoff is never larger than her opponent's. In the framework of the prisoner's dilemma game driven by payoff aspiration, we investigate in this paper the evolution of generosity strategy, in competition with extortion and unconditional defection strategies. We show that extortioners act as a catalyst to induce more defectors to change to compliers. Such influence will enhance when extortioners become more greedy. At a low aspiration level where individuals are easy to be satisfied with their current payoffs, different strategies can coexist. With the increase of aspiration level, unsatisfied individuals are likely to turn to compliers and build long-term reciprocity with their neighbors. However, at a high aspiration level, individuals are difficult to be satisfied with their payoffs and may randomly change their behaviors. Thus proper aspiration level promotes the emergence of generous behavior in the spatial prisoner's dilemma game.