Social dilemma alleviated by sharing the gains with immediate neighbors

Peer pressure induced punishment resolves social dilemma on interdependent networks

Despite the fruitful evidence to support the emergence of cooperation, irrational decisions are still an essential part of promoting cooperation. Among the many factors that affect human rational decision-making, peer pressure is unique to social organisms and directly affects individual cooperative behaviors in the process of social interaction. This kind of pressure psychologically forces individuals to behave consistently with their partners, and partners with inconsistent behaviors may suffer psychological blows. As feedback, this psychological harm may in turn affect individual cooperative decisions. There is evidence that when peer pressure exists, partnerships can reduce free-riding in enterprise. Based on interdependent networks, this paper studies the impact of peer pressure on cooperation dynamics when the strategies of corresponding partners from different layers of the networks are inconsistent. We assume that when individuals are under peer pressure, their payoffs will be compromised. The simulation results show that the punishment effect will force the expulsion of partners with different strategies, which will further reduce the proportion of partners with inconsistent strategies in the system. However, in most cases, only moderate fines are most conductive to the evolution of cooperation, and the punishment mechanisms can effectively promote the interdependent network reciprocity. The results on the small world and random network prove the robustness of the result. In addition, under this mechanism, the greater the payoff dependence between partners, the better the effect of interdependent network reciprocity.

Evolution of Cooperation on Spatial Network with Limited Resource

Considering the external resource offered by environment is limited, here, we will explore the cooperation on spatial networks with limited resource. The individual distributes the limited resource according to the payoffs acquired in games, and one with resource amounts is lower than critical survival resource level will be replaced by the offspring of its neighbors. We find that, for larger temptation to defect, the number of the dead decreases with the resource amount. However the cooperation behavior is interesting, the lower total resource and intermediate temptation to defect can greatly promote the cooperation on square lattice. Our result reveals that the limited resource contributes most to the cooperation.

Dependency links can hinder the evolution of cooperation in the prisoner's dilemma game on lattices and networks

Networks with dependency links are more vulnerable when facing the attacks. Recent research also has demonstrated that the interdependent groups support the spreading of cooperation. We study the prisoner's dilemma games on spatial networks with dependency links, in which a fraction of individual pairs is selected to depend on each other. The dependency individuals can gain an extra payoff whose value is between the payoff of mutual cooperation and the value of temptation to defect. Thus, this mechanism reflects that the dependency relation is stronger than the relation of ordinary mutual cooperation, but it is not large enough to cause the defection of the dependency pair. We show that the dependence of individuals hinders, promotes and never affects the cooperation on regular ring networks, square lattice, random and scale-free networks, respectively. The results for the square lattice and regular ring networks are demonstrated by the pair approximation.

Peer pressure: enhancement of cooperation through mutual punishment

An open problem in evolutionary game dynamics is to understand the effect of peer pressure on cooperation in a quantitative manner. Peer pressure can be modeled by punishment, which has been proved to be an effective mechanism to sustain cooperation among selfish individuals. We investigate a symmetric punishment strategy, in which an individual will punish each neighbor if their strategies are different, and vice versa. Because of the symmetry in imposing the punishment, one might intuitively expect the strategy to have little effect on cooperation. Utilizing the prisoner's dilemma game as a prototypical model of interactions at the individual level, we find, through simulation and theoretical analysis, that proper punishment, when even symmetrically imposed on individuals, can enhance cooperation. Also, we find that the initial density of cooperators plays an important role in the evolution of cooperation driven by mutual punishment.

Boosting cooperation by involving extortion in spatial prisoner's dilemma games

We study the evolution of cooperation in spatial prisoner's dilemma games with and without extortion by adopting the aspiration-driven strategy updating rule. We focus explicitly on how the strategy updating manner (whether synchronous or asynchronous) and also the introduction of extortion strategy affect the collective outcome of the games. By means of Monte Carlo simulations as well as dynamical cluster techniques, we find that the involvement of extortioners facilitates the boom of cooperators in the population (and whom can always dominate the population if the temptation to defect is not too large) for both synchronous and asynchronous strategy updating, in stark contrast to the other case, where cooperation is promoted for an intermediate aspiration level with synchronous strategy updating, but is remarkably inhibited if the strategy updating is implemented asynchronously. We explain the results by configurational analysis and find that the presence of extortion leads to the checkerboard-like ordering of cooperators and extortioners, which enable cooperators to prevail in the population with both strategy updating manners. Moreover, extortion itself is evolutionary stable, and therefore acts as the incubator for the evolution of cooperation.

Punishment based on public benefit fund significantly promotes cooperation

In prisoner's dilemma game (shortly, PD game), punishment is most frequently used to promote cooperation. However, outcome varies when different punishment approaches are applied. Here the PD game is studied on a square lattice when different punishment patterns are adopted. As is known to all, tax system, a common tool to adjust the temperature of the economy, is widely used in human society. Inspired by this philosophy, players in this study would pay corresponding taxes in accordance with their payoff level. In this way, public benefit fund is established consequently and it would be utilized to punish defectors. There are two main methods for punishing: slight intensity of punishment (shortly, SLP) and severe intensity of punishment (shortly, SEP). When the totaling of public benefit fund keeps relatively fixed, SLP extends further, which means more defectors would be punished; by contrast, SEP has a smaller coverage. It is of interest to verify whether these two measures can promote cooperation and which one is more efficient. Simulate results reveal that both of them can promote cooperation remarkably. Specifically speaking, SLP shows constant advantage from the point of view either of fractions of cooperation or average payoff.