The analysis of evolutionary prisoner’s dilemma game based on weighting effect

In this paper, an improved evolutionary prisoner’s dilemma (PD) game model is proposed by considering the weighting effect. Taking into account individual’s perceived payoff (benefits), the evolutionary tendency of the cooperators and three equilibrium points of the proposed model are obtained. We then numerically investigate how different exterior and interior factors influence on individuals’ cooperative behavior and their payoff both in the ER random network and the BA scale-free network. Our results reveal that the heterogeneous network structure is conducive to cooperation. In addition, the existence of leader nodes is an important driving force for promoting individuals’ cooperation. By further analyzing the rationality coefficient which appears in the weighting function, we obtain that a greater of irrationality could lead more people to take cooperative strategies. Finally, two indicators which are used to measure the real average payoff and perceived average payoff are defined. The results show that the real average payoff and perceived average payoff are larger in the heterogeneity network than that in homogeneous network.

Nice Invincible Strategy for the Average-Payoff IPD

The Iterated Prisoner's Dilemma (IPD) is a well-known benchmark for studying the long term behaviours of rational agents. Many well-known strategies have been studied, from the simple tit-for-tat (TFT) to more involved ones like zero determinant and extortionate strategies studied recently by Press and Dyson. In this paper, we consider what we call invincible strategies. These are ones that will never lose against any other strategy in terms of average payoff in the limit. We provide a simple characterization of this class of strategies, and show that invincible strategies can also be nice. We discuss its relationship with some important strategies and generalize our results to some typical repeated 2x2 games. It's known that experimentally, nice strategies like the TFT and extortionate ones can act as catalysts for the evolution of cooperation. Our experiments show that this is also the case for some invincible strategies that are neither nice nor extortionate.

Evolution of cooperation under the influence of environments on individual-performed interactions

Traditionally, individual intensities to perform games are always assumed to be fixed in networks (e.g. to depend on the number of their neighbors). However, to increase their own fitness or payoffs, individuals may adjust their intensities in reaction to external environment changes in real scenarios. With this motivation, we have studied this adjustment by considering the average payoff of individual neighbors to be the network environment in a spatial prisoner’s dilemma game. An individual will unilaterally increase (decrease) its intensity to perform games between itself and its neighbors when its payoff is greater than or equal to (lower than) the average payoff of its neighbors. Compared with the normal situation, we find that individual cooperation is significantly facilitated either on the cooperator fraction or the effective cooperation fraction when the environment-induced intensity adjustment is considered, and the value of intensity adjustment per time has a positive influence on the maintenance of cooperation. Evolution snapshots and a formulated typical schematic are used to explain the results. We find that cooperation behaviors are enhanced because of the existence of defectors with lower intensities who are near the boundaries between cooperator and defector clusters. Finally, the promotion is also validated in random networks. We hope that our results may shed light on a greater understanding of the role of individual adaptive behaviors in reaction to network environments in the maintenance of cooperation in societies.

Invasion of Cooperation in Scale-Free Networks: Accumulated versus Average Payoffs

It is well known that cooperation cannot be an evolutionarily stable strategy for a non-iterative game in a well-mixed population. In contrast, structured populations favor cooperation, since cooperators can benefit each other by forming local clusters. Previous studies have shown that scale-free networks strongly promote cooperation. However, little is known about the invasion mechanism of cooperation in scale-free networks. To study microscopic and macroscopic behaviors of cooperators' invasion, we conducted computational experiments on the evolution of cooperation in scale-free networks where, starting from all defectors, cooperators can spontaneously emerge by mutation. Since the evolutionary dynamics are influenced by the definition of fitness, we tested two commonly adopted fitness functions: accumulated payoff and average payoff. Simulation results show that cooperation is strongly enhanced with the accumulated payoff fitness compared to the average payoff fitness. However, the difference between the two functions decreases as the average degree increases. As the average degree increases, cooperation decreases for the accumulated payoff fitness, while it increases for the average payoff fitness. Moreover, for the average payoff fitness, low-degree nodes play a more important role in spreading cooperative strategies than for the accumulated payoff fitness.