Evolution Of Cooperation In Prisoner Research Articles

Impact of peer pressure on the evolution of cooperation in prisoner’s dilemma game

Assuming that cooperators and defectors are influenced by peer pressure with a certain probability. The influence mode is that the neighbors who adopts the opposite strategy to the central individual will reduce the fitness of the central individual. This paper explores the impact of peer pressure on the evolution of cooperation in the prisoner’s dilemma game under the condition that the pressure sensitivity of the cooperators and defectors are equal and unequal. The simulation results show that peer pressure can promote cooperation. When the pressure sensitivity of the cooperators and defectors are equal, the influence of pressure sensitivity on the system is non-trivial. According to the value of pressure intensity, evolution of the system can be roughly divided into three categories. When the pressure intensity is weak, the system is not affected by pressure sensitivity and remains in a state of full defection. When the pressure intensity is moderate, the system undergoes a continuous phase transition from full defection to coexistence and then to full cooperation with the increase of the pressure sensitivity. When the pressure intensity is high, the system undergoes a discontinuous phase transition from full defection to full cooperation and even to full defection with the increase of the pressure sensitivity. In addition, when cooperators and defectors have different pressure sensitivities, the cooperation promotion effect is better than that when cooperators and defectors have the same pressure sensitivities. Specifically, cooperation can be promoted or even dominated under lower pressure sensitivity and pressure intensity, which can explain the emergence of cooperation.

Effects of exposure-based reward and punishment on the evolution of cooperation in prisoner’s dilemma game

Reward and punishment are important factors in maintaining cooperation among selfish individuals. This paper explores the effects of exposure-based reward and punishment on the evolution of cooperation. In this model, players can choose to expose their opponent’s cooperation or defection status, leading to the identification of four strategies: exposure cooperation, exposure defection, ordinary cooperation, and ordinary defection. Exposing one’s behavior incurs a cost, and exposed cooperators are rewarded while exposed defectors are punished. The exposure is, in turn, rewarded for exposing the defection. The evolutionary results show that three states emerge after the population stabilizes: only ordinary defection remains, exposure cooperation coexists with exposure defection, and all four strategies coexist. Cooperative behavior can occur when the exposure cost is less than the punishment for defection. Simply rewarding exposed cooperators is insufficient to promote cooperation. Simultaneous reward and punishment can significantly promote cooperation. There exists an optimal minimum reward threshold for cooperation, which varies nonlinear with increasing punishment. Larger temptation to defect and smaller cooperation reward favor the survival of exposure-oriented players and can effectively discourage second-order free-riding behavior. Our study provides insights into effective solutions to social dilemmas.

Prisoner’s dilemma game model Based on historical strategy information

In many dilemmas, decisions are determined not by a single factor, but by multiple ones, including memory, reputation, reward and punishment. In recent years, how to design a mechanism to promote cooperation has become a research hot-spot. However, most of the previous studies mainly consider the historical benefits of the game, and pay less attention to the stability of the strategy (the frequency of strategy changes in the length of memory) and the proportion of memory in decision-making. The decision-making process of group evolution involves the influence of memory information on cooperative evolution in multi round games. It makes up for the lack of stability factors and weights in previous studies. Based on the above factors, a new strategy update rule is proposed to study the influence of the stability of historical strategy information on the evolution of cooperation in prisoner’s dilemma game, and the influence of memory weight on cooperation is considered. The stability of the current strategy is measured by the strategy in historical memory (the number of times the strategy in memory is continuous and consistent with the current strategy), which can determine the probability of an individual learning the neighbor strategy next time. Numerical simulation shows that an appropriate increase in the length of historical memory is more conducive to the emergence of cooperation, and the greater the weight of historical strategy information is, the more conducive to promoting cooperation, which shows that historical strategy information is still the main factor in decision-making. This study will help us understand the cooperative evolution of many real systems, such as nature, biology, society and so on, and effectively design reasonable mechanisms to promote cooperation.

Evolution of cooperation in prisoner's dilemma game under the coupling of aspiration and imitation rules

Considering the important roles played by aspiration and imitation rules, we explore how cooperation evolves in the spatial prisoner's dilemma game. In detail, the strategy updating rule couples the inner aspiration payoff and the external neighborâs payoff through the parameter α. Intriguingly, we find that there exists an optimal value of α leading to the highest density of cooperators for each aspiration level A. By analyzing the dynamical strategy changes of the system, we find that an optimal α helps individuals form cooperator clusters and curbs the further spread of high-payoff defectors, and thus improves the density of cooperators. Moreover, when , the optimal value of α, which leads to the highest density of cooperators, decreases with A, the optimal range of α gradually expands and the highest cooperation level is on the rise.

Inclusive fitness and Hamilton’s rule in a stochastic environment

The evolution of cooperation in Prisoner’s Dilemmas with additive random cost and benefit for cooperation cannot be accounted for by Hamilton’s rule based on mean effects transferred from recipients to donors weighted by coefficients of relatedness, which defines inclusive fitness in a constant environment. Extensions that involve higher moments of stochastic effects are possible, however, and these are connected to a concept of random inclusive fitness that is frequency-dependent. This is shown in the setting of pairwise interactions in a haploid population with the same coefficient of relatedness between interacting players. In an infinite population, fixation of cooperation is stochastically stable if a mean geometric inclusive fitness of defection when rare is negative, while fixation of defection is stochastically unstable if a mean geometric inclusive fitness of cooperation when rare is positive, and these conditions are generally not equivalent. In a finite population, the probability for cooperation to ultimately fix when represented once exceeds the probability under neutrality or the corresponding probability for defection if the mean inclusive fitness of cooperation when its frequency is 1/3 or 1/2, respectively, exceeds 1. All these results rely on the simplifying assumption of a linear fitness function. It is argued that meaningful applications of random inclusive fitness in complex settings (multi-player game, diploidy, population structure) would generally require conditions of weak selection and additive gene action.

The evolution of cooperation in multi-games with popularity-driven fitness calculation

Popularity-driven fitness updating rule has been confirmed to be an effective mechanism to understand the evolution of cooperation in prisoner's dilemma game (PD). Inspired by this, we explore cooperation behavior in pure dilemma and multigames with popularity-driven updating rule. And we obtain the popularity by calculating player's fitness via parameter α. Numerous simulations show that different update rules in pure PD or snowdrift (SD) dilemma perform different on promoting cooperative behavior under S, T-values by comparing with mean field results and then comparing the spatial results of various updates. While in multigames, we observe that positive α can lead cooperators grow and thrive as the proportion of SD increases. On the other hand, negative α also can enhance cooperation, but hardly dominate in the population. Meanwhile, compared with zero α (traditional version), it has a stronger impact on cooperation when SD proportion is small. As the frequency of SD increases, the situation reversed.

Impact of informers on the evolution of cooperation in prisoner's dilemma game

In the society, cooperation development is a significant challenge. In this paper, participation of informers is considered to affect cooperation behavior efficiently. Informers can label defectors after competing with them in the first time. Then other players can recognize defectors and keep away from them, so labeled defectors are isolated and cannot interact with others. It is indisputable that informers play a significant role during this process. In order to lucubrate the effect of informer on cooperation in prisoner's dilemma, we introduce a parameter ε to represent the proportion of inform. Numerous simulations show that informers lead surrounding defectors to be labeled and exposed. Then they are isolated by other players and cannot affect cooperation behavior negatively in a large scale, so cooperation level promotes. Besides, with the increasing of ε, cooperation can be enhanced further. We find an obvious threshold in the proportion change of informers. When ε is less than the threshold, cooperative behavior promotes but slightly. Otherwise when ε achieve a certain threshold, cooperators flourish. Out novel recognitions may provide some new perspectives for develop better social mechanism.

Autonomy promotes the evolution of cooperation in prisoner's dilemma.

Population structure has been widely reported to foster cooperation in spatially structured populations, where individuals interact with all of their network neighbors defined by the spatial structure in each generation. However, most results rely on the assumption that individuals strictly interact with all of their neighbors during evolution. In reality, human beings, with sophisticated psychology, are willing to interact with some of their neighbors from time to time. Thus, individuals may not play games with all neighbors due to their psychological factors. Here we investigate how the autonomy, one of the basic psychological needs, affects the fate of cooperators in various social networks. By constructing a dynamical effective network, we find that the introduction of autonomy favors cooperative behavior. Further systematical studies by eliminating heterogeneity and the dynamic characteristics of the network reveal that autonomy plays a pivotal role in the evolution of cooperation. Moreover, we find that a moderate effective network degree, defined by the product of the original network degree and the level of autonomy, maximizes the cooperation on networks connecting individuals with fixed neighbors. Our results offer a possible way for organizations to improve individuals' cooperation and shed light on the importance of individuals' psychology on the evolution of cooperation.

Rational conformity behavior can promote cooperation in the prisoner's dilemma game

In this paper, we explore the effects of rational conformity behavior on the evolution of cooperation in prisoner's dilemma. In general, we think individual updates strategy is based on the difference in income between himself and his neighbors. In real life, in order to avoid risks, they may be consistent with most individuals in the group, because they are not the worst. Therefore, we divide the players into two categories, one is traditional players and the other is rational conformists who update their strategies are based on the two factors: payoffs and the behavior of most individuals in their nearest neighbors. Through a large number of simulations, we find that, rational conformity behavior can promote cooperation in the prisoner's dilemma game, and the greater the proportion of rational players, the more obvious the promotion of cooperation. Our work may provide further insight in understanding the evolution of cooperation, players selectively follow others and make some adjustments according to the current environment to make their own situation better.

Promotion of cooperation by adaptive interaction: The role of heterogeneity in neighborhoods

Evolution of cooperation in prisoner’s dilemma games has been studied extensively in the past decades. Recent studies have investigated the effect of adaptive interaction intensity on spatial prisoner’s dilemma, showing that if individuals can adjust their interaction intensity with each opponent at the same extent, cooperation can be promoted in a proper scale. However, the previous studies about adaptive interaction willingness do not consider the heterogeneity of the opponents. In this paper, a simulative model is developed to examine whether and how the interactive diversity influences cooperation in the spatial prisoner’s dilemma games, in which individuals consider the corresponding behavior of different opponents. The simulation results show that the proposed mechanism can effectively promote cooperation, and the average payoff of the system can significantly be improved by high interaction intensity between cooperators. In addition, we also show four kinds of different individuals to analyze the evolution progresses. The simulations show that cooperators on the boundary decrease their interaction willingness, which makes the boundary defectors lose their opportunity to participate in the interaction and be invaded by cooperators.

The evolution of cooperation in spatial prisoner’s dilemma games with heterogeneous relationships

This paper investigates how the introduction of heterogeneous relationships and the subsequent investment preference influences the evolution of cooperation in prisoner’s dilemma games. We consider random tie strength values drawn from distributions with different heterogeneity. We show that cooperation is significantly promoted if players preferentially allocate their investments to the friends with strong relationships. The facilitation of cooperation relies mostly on the heterogeneous distribution of relationships and the subsequent investment preference, resulting in strong cooperative allies between good friends and the formation of cooperative clusters around such allies. Moreover, we discover that the investment preference has a sophisticated impact on the evolution of cooperation. Consequently, the level of cooperation will be greatly enhanced by a weak investment preference, but will be significantly depressed if such preference exceeds a critical value. We attribute this finding to the extreme allocation of investments brought by strong preference that hinders the diffusion of cooperative strategy all over the network. Our results suggest that heterogeneous relationships and the subsequent investment preference might have played a crucial role by the evolution of cooperation amongst egoistic individuals.

Evolution of Cooperation in Prisoner's Dilemma Game and the Cost of Partner change

Evolution of Cooperation in Prisoner's Dilemma Game and the Cost of Partner change