Temporal assortment of cooperators in the spatial prisoner’s dilemma

We study a spatial, one-shot prisoner’s dilemma (PD) model in which selection operates on both an organism’s behavioral strategy (cooperate or defect) and its decision of when to implement that strategy, which we depict as an organism’s choice of one point in time, out of a set of discrete time slots, at which to carry out its PD strategy. Results indicate selection for cooperators across various time slots and parameter settings, including parameter settings in which cooperation would not evolve in an exclusively spatial model—as in work investigating exogenously imposed temporal networks. Moreover, in the presence of time slots, cooperators’ portion of the population grows even under different combinations of spatial structure, transition rules, and update dynamics, though rates of cooperator fixation decline under pairwise comparison and synchronous updating. These findings indicate that, under certain evolutionary processes, merely existing in time and space promotes the evolution of cooperation.

Degree of Satisfaction-based Adaptive Interaction in Spatial Prisoner's Dilemma

To study why the altruistic cooperation behavior can emerge and maintain among egoistical individuals, researchers across several disciplines have made great contributions for the solutions of this fascinating problem. Ordinarily, the spatial structure is a most-often used framework to investigate the cooperative dynamics of evolutionary game. However, very few researchers take into account the reaction of evolutionary game dynamics to interactive intensity between individuals. On account of this, we propose a computational model of automatic adjustment the interactive intensity based on individual’s degree of satisfaction to study the iterated prisoner’s dilemma game in a two-dimensional square lattice. In this model, selfish individual considers whether the benefits obtained from the other party satisfies its own requirements to determine the intensity of interaction from it to the other party. More specifically, the interactive intensity from an individual x to its some neighbor y is driven by the relations between x obtained current benefit from y (denoted by Px→y) and x’s satisfaction payoff (denoted by Sp). If Px→y > Sp, x will increase the intensity of interaction from itself to y; On the contrary, if Px→y < Sp, x will weaken the intensity of interaction; Other scenario remain the same. Simulation results show that the proposed mechanism can effectively promote the emergence and maintain of cooperation in population, and the satisfying coefficient α (0 < α < 1) plays an essential role on cooperation. Interestingly, we found that there are some optimal values α can lead to the best promotion of cooperation. But individual’s overclaim (α > 1) is not conducive to the effective promotion of cooperation between selfish individuals even for some very small temptation to defect. Our results may contribute to the understanding of cooperative dynamics by considering the reaction of evolutionary game dynamics to network.

Cooperation evolves by the payoff-difference-based probabilistic reward

In the previous studies, the author proposes the payoff-difference-based probabilistic peer-punishment that the probability of punishing a defector increases as the difference of payoff between a player and a defector increases and shows that the proposed peer-punishment effectively increases the number of cooperators and the average payoff of all players. On the other hand, reward as well as punishment is considered to be a mechanism promoting cooperation, and many studies have discussed the effect of reward in the public goods game, a multiplayer version of the prisoner’s dilemma game. Based on the discussion of those existing studies, this study introduces the payoff-difference-based probabilistic reward that the probability of rewarding a cooperator increases as the difference of payoff between a player and a cooperator increases. The author utilizes the framework of the spatial prisoner’s dilemma game of the previous study and shows that the reward of this study realizes the evolution of cooperation except some cases. Graphic abstract