Cooperation In Spatial Prisoner Research Articles

Asymmetric population promotes and jeopardizes cooperation in spatial prisoner’s dilemma game

The evolution of cooperation in asymmetric populations has recently garnered widespread attention. In this study, we propose a new asymmetric model to explore the impact of asymmetric behavior on cooperation evolution. Our model assumes that weak players are always forced to cooperate when interacting with strong players, while strong players always receive the temptation payoff. When encountering peers from the same category, players engage in a prisoner’s dilemma game, differing only in the intensity of the dilemma between population categories. Results suggest that in scenarios where traditional network reciprocity can support cooperation, asymmetric interactions between strong and weak players undermine this reciprocity and jeopardize the maintenance of cooperation. Conversely, in scenarios where traditional network reciprocity fails to support cooperation, asymmetric interactions enable strong players to leverage weak cooperative clusters to establish cooperation. However, as the prevalence of asymmetric interactions increases, it becomes detrimental to cooperation within the weak player subgroups, thus undermining overall cooperation. These findings contribute to a deeper understanding of how asymmetry impacts cooperation.

Memory–based adaptive interaction willingness enhances cooperation in spatial prisoner's dilemma

As an important part of the evolution of cooperation, interaction diversity has attracted extensive attention. Traditional studies mainly focus exclusively on either time or space, and the comprehensive impact of these two dimensions on the evolution of cooperation deserves further exploration. In this paper, the interaction willingness is abstracted as the network weight, and an adaptive mechanism for interaction willingness based on the delay effect is proposed by combining the network weight and accumulated payoff. Specifically, individuals adjust their willingness to participate in the game with a delay, considering the change in accumulated payoffs within a certain period, rather than the change in immediate payoffs. The degree of delay is reflected in the length of individuals' memory of historical payoffs. Simulation results deviate from the intuition that more information facilitates cooperation, and in certain modes of interaction willingness adjustment, the correlation between cooperation level and memory–length is non–monotonic. Long–memory is conducive to promoting cooperation under the condition of a relatively large range adjustment of interaction willingness. Conversely, with a narrow adjustment range of interaction willingness, cooperation can be effectively established with short–memory. These results hold substantial implications for both theory and practice, as slight adjustment often corresponds to low loss and high operability. In addition, the underlying mechanism is furthermore explored, revealing that the ‘isolation zones’ composed of individuals with low interaction willingness play an important role in promoting cooperation.

The influence of environment-based reputation on cooperation in spatial prisoner's dilemma game

Research has shown that reputation mechanism can be effective in facilitating the generation and maintenance of cooperation in social dilemmas. In the traditional reputation mechanism, the amount of change in reputation is fixed. However, in real life, people's impression scores of a player are often influenced by the environment in which he lives. In other words, we prefer to celebrate the cooperative heroes who are surrounded by defectors and spurn the defectors who are hidden among the many cooperators. Thus, this paper proposes an environment-based reputation model, in which the increment of a player's reputation will be influenced by the local and global environment. The results of the research indicate that the greater the intensity of the environmental influence, the more it promotes the evolution of cooperation. It is worth noting that the local and global environmental focus shows peculiarities. Focusing on the global environment can improve the fraction of cooperators at low defection temptations while focusing on the local environment will facilitate cooperators’ survival at higher defection temptations.

Twisted strategy may enhance the evolution of cooperation in spatial prisoner’s dilemma

Twisted strategy may enhance the evolution of cooperation in spatial prisoner’s dilemma

Information accuracy of migration and imitation influences the evolution of cooperation in spatial prisoner's dilemma

Migration is ubiquitous in both biological worlds and human societies for seeking more suitable environments or greater benefits. Intensive studies have revealed that it may provide an effective mechanism to promote cooperation in the context of spatial prisoner' dilemma. As an attempt to give a more generic analysis on how migration influences the evolution of cooperation, we in this work propose a dynamic model that takes into account the agents' different tendencies on migration and imitation. More importantly, we introduce two information accuracy parameters that respectively affect the agents' decisions on the migration destination and on their imitation in the current neighborhood. The simulation results show that the higher accuracy of the information on imitation and migration contributes to a higher cooperation level. In particular, the imitation-oriented mode is more conducive to cooperation when the imitation information accuracy is high. Likewise, the migration-oriented mode is more conducive to cooperation with higher accuracy of the migration information. When imitation and migration information accuracies are both high, cooperation is effectively maintained in two different ways: the imitation-dominant pattern and the migration-dominant pattern, while the scenario in which the imitation tendency is close to the migration tendency has an inhibitory effect on cooperation. Finally, we analyse the robustness of the results under different population densities.

Heterogeneity of strategy persistence promotes cooperation in spatial prisoner’s dilemma game

Heterogeneity plays a critical role in promoting cooperation for various evolutionary systems, which has received widespread attention and research from relevant scholars. Additionally, reputation has a significant impact on an individual’s decision-making, and scholars have proposed reputation-based evolutionary mechanisms to promote cooperation. Most of these mechanisms measure reputation as part of an individual’s payoff, and influencing the individual’s decision-making. However, the influence of reputation on the individual’s decision-making should be more through heterogeneous way. Here we propose the heterogeneity of strategy persistence evolutionary mechanism, in which the heterogeneity factor and the number of strategy persistence together influence the evolution of cooperation. We measure the reputation of individuals by the number of strategy persistence. The proposed mechanism effectively highlights the heterogeneity of an individual’s reputation and has shown to be successful in promoting cooperation.

Emotion-based renewal strategies to promote cooperation in spatial prisoner’s dilemma games

Individual interactions are accompanied by changes in emotions, and emotion can influence people’s decisions and thus the evolution of cooperation in a group. Therefore, it is very important and meaningful to consider how to apply emotions in the game so as to promote cooperation. However, emotions are not affected unilaterally in the interaction. It includes both the individual’s own emotions and their acceptance of the external, as well as the shock brought to the individual by the external emotions. In this paper, we propose a new model based on the prisoner’s dilemma to fully consider the influence of both internal and external factors in the change of emotion and the proportion of both sides on cooperation. The simulation shows that emotional stability is more effective in fostering cooperation. In other words, when the proportion of their own emotional continuity is higher and individuals are less accepting of their neighbors’ emotions, the more cooperation is facilitated and the former has a greater degree of influence on cooperation. Taken together, this results maybe provide a perspective, to some extent, on how to apply the condition of emotional change to facilitate the evolution of cooperation in groups in real-life situations.

The Sense of Cooperation on Interdependent Networks Inspired by Influence-Based Self-Organization

Influence, as an inherently special attribute, is bound to profoundly affect a player’s behavior. Meanwhile, a growing body of studies suggests that interactions among networks may be more important than isolated ones. Thus, we try our best to research whether such a setup can stimulate the sense of cooperation in spatial prisoner’s dilemma games through the co-evolution of strategy imitation and interdependence networks structures. To be specific, once a player’s influence exceeds the critical threshold τ, they will be permitted to build a connection with the corresponding partner on another network in a self-organized way, thus gaining additional payoff. However, a player’s influence changes dynamically with the spread of strategy, resulting in time-varying connections between networks. Our results show that influence-based self-organization can facilitate cooperation, even under quite poor conditions, where cooperation cannot flourish in a single network. Furthermore, there is an optimal threshold τ to optimize the evolution of cooperation. Through microcosmic statistical analysis, we are surprised to find that the spontaneous emergence of connections between interdependence networks, especially those between cooperators, plays a key role in alleviating social dilemmas. Finally, we uncover that if the corresponding links between interdependence networks are adjusted to random ones, the evolution of cooperation will be blocked, but it is still better than relying on simple spatial reciprocity on an isolated lattice.

Based on reputation consistent strategy times promotes cooperation in spatial prisoner’s dilemma game

As we all know, the reputation has important influence on individual’s decision-making. How to effectively and objectively measure reputation is very important in based-reputation evolutionary game theory. In this paper, a novel evolutionary mechanism for based on reputation consistent strategy times is proposed, in which the reputation income of each player is positive or negative related to its consistent strategy times for cooperation or defection at the initial moment of the current time step. The reward or punishment scheme of the proposed evolutionary mechanism is relatively consistent with the real world understanding of reputation. It’s especially worth pointing out that, when the player’s strategy state changes, the player can get reasonable and timely reward or punishment, which can better promote cooperation compared to existing reputation-based evolutionary mechanisms. Specifically, the proposed evolutionary mechanism has the following two advantages in the evolutionary systems. First, the player who has insisted on cooperation for a long time is not inclined to adopt defection, mainly because the cost of reputation is too high. In addition, the player who has long insisted on defection tends to adopt cooperation. This is mainly because the reputation of the player is easily restored from notoriety to general. Obviously, the above two points can effectively promote cooperation. Based on prisoner’s dilemma game (PDG) model, simulation and analysis also show that the proposed evolutionary mechanism can better promote cooperation compared to the traditional evolutionary mechanism, and can also speed up the evolutionary process, especially when the reputation factor is large. Furthermore, we also find that the cooperation level enhances when consistent strategy times upper bound becomes larger.

Incorporating social payoff into reinforcement learning promotes cooperation.

Reinforcement learning has been demonstrated to be an effective approach to investigate the dynamic of strategy updating and the learning process of agents in game theory. Most studies have shown that Q-learning failed to resolve the problem of cooperation in well-mixed populations or homogeneous networks. To this aim, we investigate the self-regarding Q-learning's effect on cooperation in spatial prisoner's dilemma games by incorporating the social payoff. Here, we redefine the reward term of self-regarding Q-learning by involving the social payoff; that is, the reward is defined as a monotonic function of the individual payoff and the social payoff represented by its neighbors' payoff. Numerical simulations reveal that such a framework can facilitate cooperation remarkably because the social payoff ensures agents learn to cooperate toward socially optimal outcomes. Moreover, we find that self-regarding Q-learning is an innovative rule that ensures cooperators coexist with defectors even at high temptations to defection. The investigation of the emergence and stability of the sublattice-ordered structure shows that such a mechanism tends to generate a checkerboard pattern to increase agents' payoff. Finally, the effects of Q-learning parameters are also analyzed, and the robustness of this mechanism is verified on different networks.

Effects of stubborn players and noise on the evolution of cooperation in spatial prisoner’s dilemma game

The question of whether a minority of extremists can dominate the collective behavior in social dilemmas is crucial for understanding the evolution of cooperation in both human societies and animal worlds. We establish a spatial prisoner’s dilemma game model consisting of both stubborn cooperators and stubborn defectors who never change their behavior. The results reveal that a minority of stubborn players can effectively inhibit the evolution of cooperation. By introducing noise faced by stubborn players, however, we find that the inhibition of cooperation by the stubborn players can be easily canceled by the noise, which suggests a reasonable method for undermining the detrimental effects induced by extremists.

Aspiration Adjustment Based on Environmental Factors and Aspiration Duration Promote Cooperation in Spatial Prisoner's Dilemma Game

Aspiration Adjustment Based on Environmental Factors and Aspiration Duration Promote Cooperation in Spatial Prisoner's Dilemma Game

Effects of Stubborn Players and Noise on the Evolution of Cooperation in Spatial Prisoner's Dilemma Game

Effects of Stubborn Players and Noise on the Evolution of Cooperation in Spatial Prisoner's Dilemma Game

Progressive-Interaction-Mechanism Induce by Aspiration Promote Cooperation in Spatial Prisoner's Dilemma Game

Progressive-Interaction-Mechanism Induce by Aspiration Promote Cooperation in Spatial Prisoner's Dilemma Game

Ability-based asymmetrical fitness calculation promotes cooperation in spatial prisoner's dilemma game

We investigate the ability-based fitness calculation in an asymmetric setup to the evolution of cooperation on square lattice. In particular, if players can maintain its strategy for a round, then its abilities will increase 1, otherwise, its ability will turn to 0. We also assume that if players’ abilities exceed a certain threshold M, then its environment is integrated into its fitness calculation via a simple parameter α. Through extensive numerical simulation, we find that large threshold M decreases cooperation, and large α, players’ fitness is mainly decided by its dynamical environment, promotes cooperation. We also provide theoretical analysis and get the same results with simulation. Finally, we test its robustness on homogeneous random network and small-world network. Our work provides a deeper insight to network reciprocity.

Dynamic aspiration based on Win-Stay-Lose-Learn rule in spatial prisoner's dilemma game.

Prisoner's dilemma game is the most commonly used model of spatial evolutionary game which is considered as a paradigm to portray competition among selfish individuals. In recent years, Win-Stay-Lose-Learn, a strategy updating rule base on aspiration, has been proved to be an effective model to promote cooperation in spatial prisoner's dilemma game, which leads aspiration to receive lots of attention. In this paper, according to Expected Value Theory and Achievement Motivation Theory, we propose a dynamic aspiration model based on Win-Stay-Lose-Learn rule in which individual's aspiration is inspired by its payoff. It is found that dynamic aspiration has a significant impact on the evolution process, and different initial aspirations lead to different results, which are called Stable Coexistence under Low Aspiration, Dependent Coexistence under Moderate aspiration and Defection Explosion under High Aspiration respectively. Furthermore, a deep analysis is performed on the local structures which cause defectors' re-expansion, the concept of END- and EXP-periods are used to justify the mechanism of network reciprocity in view of time-evolution, typical feature nodes for defectors' re-expansion called Infectors, Infected nodes and High-risk cooperators respectively are found. Compared to fixed aspiration model, dynamic aspiration introduces a more satisfactory explanation on population evolution laws and can promote deeper comprehension for the principle of prisoner's dilemma.

Reciprocal rewards promote the evolution of cooperation in spatial prisoner's dilemma game

To investigate the incentive mechanisms of cooperation, we propose an other-regarding preference based reciprocal rewarding mechanism by incorporating the dynamic adjustment of link weight into the spatial prisoner's dilemma game. Under the influence of other-regarding preference, players are willing to sacrifice personal payoff to reward the cooperative neighbor who has the greatest link weight. The reciprocal reward is dynamically adjusted according to the adaptive adjustment of link weight and the intensity of other-regarding preference. Extensive simulations reveal that the proposed rewarding mechanism significantly promotes the evolution of cooperation. Both the dynamic adjustment of link weight and the other-regarding preference impact factor play an essential role in the emergence of cooperative behavior. To further validate the above outcome, the evolution of cooperators' density and the alteration of average payoff and fitness are explored in a microscopic perspective.

Behavior inertia of individuals promotes cooperation in spatial prisoner's dilemma game

Cooperation is ubiquitous in real world, even in a fierce competitive environment, which is in contrast with natural selection theory. To address this contradiction, many scholars pay more attention to researching the emergence and maintenance of cooperation. In recent decades, lots of mechanisms about individual behavior are put forward to promote cooperation in spatial prisoner's dilemma game. However, fewer studies focus on the effects of behavior inertia on cooperation. For example, insistence is the key to habit formation, and every extra day you insist, the more motivation you have to keep going, the bigger the inertia of the same behavior is, and the weaker the intention you have to make a change. In other words, it is easier to insist than to change. To this end, we propose a new mechanism, called inertia mechanism of individual behavior to explore the evolution of cooperation, in which each player's behavior inertia relies on the persistence of his/her current strategy: the longer the strategy duration is, the bigger his/her behavior inertia is, and, as a result, the weaker the willingness he/she has to update strategy. Moreover, a reinforcement parameter, α, which characterizes the degree of the impact of the strategy persistence on the behavior inertia, is introduced. The results of numerical simulation show that our inertia mechanism can promote cooperation effectively, compared with the traditional model, and the mechanism performs better with the decrease of α.

The effects of heterogeneous confidence on cooperation in spatial prisoner's dilemma game

Confidence, which characterizes the feeling when people evaluate something, could influence their choices or behaviors significantly. Under the framework of evolutionary game theory, Szolnoki and Chen (Phys. Rev. E, 98 (2018) 022309) found that, both underconfident and overconfident individuals can promote cooperation in the population. In their work, underconfident and overconfident individuals are both assumed to have homogeneous confidence levels and the confidence levels remain unchanged during the whole evolutionary process. As a direct extension, in this work, we treat confidence level as an attribute of the individuals and assign each one a confidence level, which may be static or time-varied. The effects of heterogeneous confidence on cooperation in evolutionary games are investigated and two different cases are considered. For the static case, we assume that individuals' confidence levels are drawn from a uniform distribution in a certain interval. Whereas, for the time-varied case, the confidence levels of individuals can coevolve with the strategies. By numerical simulation, we find that the static heterogeneous confidence can enhance cooperation when the parameters of distribution satisfy certain conditions. Some analytic explanations based on the observations of strategy configurations among the population are provided. Furthermore, when individuals' confidence levels are allowed to coevolve with their strategies during the evolutionary dynamics, cooperation could be significantly improved. We also find that there exists an optimal increment for the confidence level which leads to the highest cooperation level.

Heterogeneous aspiration resolves social dilemma in structured populations

In this paper, we study the impact of heterogeneous aspiration-driven strategy update rules on the evolution of cooperation in spatial prisoner's dilemma game. Individuals on network are divided into two categories: one part is the traditional players who update their strategies by imitating their neighbors’ strategies, the remaining of the individuals update their strategies based on heterogeneous aspiration. In the latter case, the probability of aspiration-driven updating is closely related to the payoffs of neighbors. Through Monte Carlo simulation, it found that heterogeneous aspiration can efficiently promote the network reciprocity. From the micro perspective, we find that such a mechanism can reserve the classical spatial distribution of cooperators, where cooperator clusters will be exploited by defectors. Based on the classical distribution, the strategies transitions show the essential reason for promotion of cooperation. In order to verify the generality of the conclusion, we further introduce the proposed mechanism into the snowdrift game and the public goods game, and obtain the observations consistent with the prisoner's dilemma game.