Evolution Of Cooperation In Games Research Articles

A social monitoring mechanism for third-party judges promotes cooperation in evolutionary games

Corruption of third-party judges seriously undermines the level of cooperation. Without intervention, more corruptors and defectors would emerge, disrupting social harmony. Therefore, introducing an anti-corruption mechanism is crucial for the evolution of cooperation. In this paper, we propose a social monitoring mechanism to monitor third-party judges so that their payoffs are affected by the proportions of cooperators. Monte Carlo simulations on periodic boundary lattices. The results show that the social monitoring mechanism is effective in promoting cooperation and inhibiting corruption, and enhances the effectiveness of zealots in promoting cooperation. This facilitation effect is not only manifested in the Prisoner's Dilemma Game but also in the Snowdrift Game, which confirms the robustness of the results. Our research provides new insights for solving social dilemmas and curbing corruption.

The effect of multi-tasks mechanism on cooperation in evolutionary game.

Human games are inherently diverse, involving more than mere identity interactions. The diversity of game tasks offers a more authentic explanation in the exploration of social dilemmas. Human behavior is also influenced by conformity, and prosociality is a crucial factor in addressing social dilemmas. This study proposes a generalized prisoner's dilemma model of task diversity that incorporates a conformity-driven interaction. Simulation findings indicate that the diversity of multi-tasks and the path dependence contribute to the flourishing of cooperation in games. Conformity-driven interactions also promote cooperation. However, this promotion effect does not increase linearly, and only appropriate task sizes and suitable proportions of conformity-driven interactions yield optimal results. From a broader group perspective, the interplay of network adaptation, task size, and conformity-driven interaction can form a structure of attractors or repellents.

Fixation of cooperation in evolutionary games with environmental feedbacks

The interaction between strategy and environment widely exists in nature and society. Traditionally, evolutionary dynamics in finite populations are described by the Moran process, where the environment is constant. Therefore, we model the Moran process with environmental feedbacks. Our results show that the selection intensity, which is closely related to the population size, exerts varying influences on evolutionary dynamics. In the case of the specific payoff matrix, cooperation cannot be favored by selection in extremely small-sized populations. The medium-sized populations are beneficial for the evolution of cooperation under intermediate selection intensities. For weak or strong selection intensities, the larger the population size, the more favorable it is for the evolution of cooperation. In the case of the generalized payoff matrix, the low incentives for the defector to cooperate in the degraded state cannot promote the emergence of cooperation. As the incentive for the defector to cooperate in the degraded state increases, selection favors cooperation or defection depending on the population size and selection intensity. For large values of the incentive for the defector facing the cooperative opponent to cooperate in the degraded state, selection always favors cooperation. We further investigate the impact of the time-scale on the fixation probability of cooperation.

Impact of discrepant accumulations strategy on collective cooperation in multilayer networks

Understanding large-scale cooperation among related individuals has been one of the largest challenges. Since humans are in multiple social networks, the theoretical framework of multilayer networks is perfectly suited for studying this fascinating aspect of our biology. To that effect, we here study the cooperation in evolutionary game on interdependent networks. Importantly, a part of players are set to adopt Discrepant Accumulations Strategy. Players employing this mechanism not only use their payoffs in the multilayer network as the basis for the updating process as in previous experiments, but also take into account the similarities and differences in strategies across different layers. Monte Carlo simulations demonstrate that considering the similarities and differences in strategies across layers when calculating fitness can significantly enhance the cooperation level in the system. By examining the behavior of different pairing modes within cooperators and defectors, the equilibrium state can be attributed to the evolution of correlated pairing modes between interdependent networks. Our results provide a theoretical analysis of the group cooperation induced by the Discrepant Accumulations Strategy. And we also discuss potential implications of these findings for future human experiments concerning the cooperation on multilayer networks.

Reputation incentives with public supervision promote cooperation in evolutionary games

Public supervision, as a source of social behavioral norms and moral guidelines, exerts important guidance and influence on individuals. To maintain public order, in this study, we propose a reputation incentives mechanism with public supervision, in which each player is granted the authority to evaluate others. These players, by observing, can make positive or negative evaluations that derive from the satisfaction level of the interactive behavior to neighbors choosing cooperation or defection in each round of the evolutionary game. Evaluations made by defectors are considered untrustworthy, resulting in the evaluation values assigned to others being halved. After mutual evaluation, the reputation is an average of the evaluations given by all their neighbors and then is consequently granted to each player. The results of numerical simulations demonstrate that reputation provides rewards that positively incentivize cooperation. And we observe that a weaker evaluation intensity leads to more stable and higher levels of cooperation among individuals. This mechanism provides valuable insights into the evolution of reputation and the optimization of supervising mechanisms.

Evolution of cooperation in games with dual attribute strategy

Cooperation and defection are two common strategies in game theory. Considering that there may be a kind of middle state between the two as a third option in the real dilemma, we introduce the dual attribute strategy. Compared with cooperation, this strategy possesses the defection attribute, while compared with defection, this strategy possesses the cooperation attribute. Here, it is assumed that players holding the dual attribute strategy play snowdrift games with cooperators based on their defection attribute, meanwhile, they play another snowdrift game with defectors based on their cooperation attribute. Furthermore, we explore the evolution of the three strategies in the well-mixed population and the structured population, respectively. The results show that the dual attribute strategy is more likely to survive. Additionally, the smaller the two kinds of cost-to-benefit ratios are, the more likely cooperation is to exist. Moreover, in the well-mixed population, the existence of cooperation is independent of the temptation to defect. In the structured population, cooperation is more favorable when the cost-to-benefit ratio between the cooperation strategy and the dual attribute strategy is moderate, regardless of the temptation to defect. The dual attribute strategy is actually the embodiment of the simultaneous weakening of cooperation and defection.

How do the joint effects of aspiration and social influence promote cooperation in the prisoner’s dilemma game?

Various mechanisms have been proposed to promote cooperation in evolutionary games, including aspiration and social influence. However, the joint effects of aspiration and social influence have so far been ignored in the literature. Thus, we discuss the joint effects of aspiration and social influence on promoting cooperation in the Prisoner’s Dilemma Game (PDG). We introduce different aspiration tags as different aspirations and different types of neighborhoods as different social influences to reveal how the level of cooperation changes in four heterogeneous micro-environments composed of diverse aspirations and social influences. The Fermi function is adopted as the priority strategy updating rule. Simulation results show that aspiration and social influence mechanisms are jointly effective at improving cooperation in the PDG. More precisely, the aspiration mechanism promotes cooperation unconditionally, but that the social influence mechanism promotes it conditionally.

Preferential selection to promote cooperation on degree–degree correlation networks in spatial snowdrift games

Degree–degree correlation is an important topological characteristic of real-world networks and has been shown to have a significant effect on cooperation in a population. Meanwhile, the preferential selection of individuals could be exploited as an effective mechanism to improve cooperation in evolutionary games. Network structure and strategy evolution are two essential factors affecting the level of cooperation in spatial evolutionary games, and by considering both of them, proposed here is a spatial snowdrift game with preferential selection on scale-free networks with degree–degree correlation. How two main parameters—the Pearson correlation coefficient r and the intensity of preferential selection δ—affect the cooperation is investigated, and simulation results show that when preferential selection is involved in evolutionary games, then larger δ can give a higher level of cooperation. Importantly, an optimal value of r is found that gives maximum cooperation in the population, and how r and δ affect the cooperation is found to depend on the cost parameter of the game. Furthermore, corresponding microcosmic explanations are provided based on the quantity χ, the time series of links, and the strategy distribution.

Inequality-induced emotions might promote cooperation in evolutionary games

Inequality-induced emotions might promote cooperation in evolutionary games

Reward and Punishment Mechanism with weighting enhances cooperation in evolutionary games

The essential of the human cooperative behavior is to find an effective mechanism to promote cooperation. In reality, there is a class of professionals who punish evil and promote good, such as police officers, judges, and volunteers. Their actions and responsibilities can profoundly affect the actions of other individuals by fines and bonuses. Motivated by this phenomenon, we propose a Reward and Punishment Mechanism with weighting (RPMW) for promoting cooperation. The core of RPMW lies in three aspects: (i) A subset of players are tagged as supervisors, who are generated by a random algorithm. If the supervisor chooses to cooperate, she/he acts as the doer of rewards and punishments, otherwise she/he is a general player. (ii) Each supervisor asks their neighbors in turn as well as rewards cooperators and punishes defectors. Bonuses (penalties) are calculated according to a weighting which is the ratio of the number of current evolutionary round cooperators (defectors) to the total of players. (iii) A factor α is added to control the intensity of rewards and punishments, and the β is denoted as the percentage of supervisors in the group. Furthermore, we do a detailed ablation study on the Reward Mechanism with Weighting (RMW) and Punishment Mechanism with Weighting (PMW) in three social dilemmas. The simulation results show that RPMW can effectively promote cooperation in prisoner’s dilemma (PDG), snowdrift game (SDG) and stag-hunt game (SHG). We find that the frequency of cooperation reaches highest when the α is at its maximum and the β is in a positive impact on evolutionary cooperation. The results prove that RPMW is more effective than RMW and PMW on enhancing cooperation in PDG, SDG.

Spatial structure might impede cooperation in evolutionary games with reinforcement learning

Cooperation has attracted considerable attention in recent years. In order to explain altruistic cooperation behaviors that emerged in social dilemmas, a large number of mechanisms have been proposed under the framework of traditional evolutionary game (EG) theory, especially network reciprocity, which has achieved great success. On the other hand, the design of AI algorithm provides a new idea for agents’ decision-making behaviors. The influence of multi-agent reinforcement learning (RL) on cooperation has also received a lot of attention. However, the study of EG with AI algorithm in a population located on spatial structures has not been thoroughly considered. In this paper, we incorporate RL into EGs conducted on spatial structures. By numerical simulations, we find that, in comparison to the well-mixed case, cooperation might be impeded in the population located on spatial structures when the agents update their strategies by adopting Q-learning algorithm instead of pairwise imitation that widely used in traditional EGs. We further reveal the mechanism for the evolution of cooperation in the EGs with Q-learning algorithm, by investigating the distributions of the Q-tables held by agents in the population. Our findings may help understand the different outcomes on spatial structures in EGs with Q-learning algorithm when compared with that in traditional EGs.

Migration based on environment comparison promotes cooperation in evolutionary games

Human beings and natural creatures often migrate in search of better environments. When both local and global environments can be perceived by individuals, they may determine whether to migrate or not based on the comparison. If the individuals realize the local environments are worse than the global ones, they are more likely to leave their original place. Otherwise, they may choose to stay still. Considering these, we study the evolutionary games in a dynamically changing population on a square lattice, in which the players migrate based on the comparison between local and global environments. The simulation results show that cooperation can be significantly promoted. By examining the strategy patterns during the evolution, we find there exist two evolutionary stages that account for the enhancement of cooperation. One is the clustering of cooperators, in which cooperator clusters get strengthened by slow migration of cooperators and fast migration of defectors. The other is the coalescence of cooperator clusters, which induces further increment of the cooperation level. Besides, we investigate the effects of two different types of noises on cooperation, which are introduced in migration and in strategy imitation, respectively. The results reveal that cooperation could be enhanced by low migration noise whereas high strategy-adoption noise.

Adaptive persistence based on environment comparison enhances cooperation in evolutionary games

Switching strategy is generally accompanied by material cost or mental pressure to players in reality. An efficient solution is to hold the current strategy for a period time before the next updating. In evolutionary games, it has been reported that strategy persistence or strategy inertia could promote cooperation. There arises a question that how players determine the duration of their strategy persistence time, which is also called the persistence level. Here, we consider the evolutionary prisoner’s dilemma games in which players can adapt their persistence levels based on the comparison between the local and global environments. We assume that, the players who have better local environments tend to preserve their current strategies longer and increase the persistence levels. In contrast, those whose local environments are worse than the global environment tend to decrease their persistence levels. The results show that network reciprocity can get greatly enhanced by such an adaptive strategy persistence, especially in hostile environments to cooperation. Moreover, by comparing with the fixed and randomly adaptive persistence level cases, we emphasize the importance of the environment comparison in enlarging the persistence levels of cooperators, which could be further enhanced by a larger upper limit or a smaller increment of persistence level. Our results provide insights into the promotion of cooperation by the adaptive strategy persistence when players can perceive both the local and global environments in evolutionary games.

Unfixed-neighbor-mechanism promotes cooperation in evolutionary snowdrift game on lattice

Addressed in this paper is the issue of how to promote cooperation among selfish individuals by changing the number of interactive neighbors in the evolutionary snowdrift game on a square lattice. Quite a few mechanisms that promoted cooperation in evolutionary games have been reported. It was usually assumed in past literature that each player had fixed neighbors to interact. However, such an assumption is inconsistent with most actual situations in society since the neighbors of each individual are not fixed in real life. Therefore, this paper takes into account a relatively realistic situation where each player has own potential neighbors and, in each round, has interactive neighbors randomly selected from potential neighbors. That is, for each player, its interactive neighbors in any round may be different from those in the next round. So interactive neighbors of each individual are unfixed. The results of Monte Carlo simulations reveal that compared with traditional fixed-neighbor-mechanism (FNM), the unfixed-neighbor-mechanism (UFNM) can lead to a higher level of cooperation in a larger range for both of the Fermi update and proportional update. In general, due to introducing the UFNM in snowdrift game, the number of interactive neighbors may be less than fixed neighbors in whole evolutionary process and thus the game cost is reduced. Therefore this modified mechanism has potential role in social management.

Effects of directional migration for pursuit of profitable circumstances in evolutionary games

Migration has been verified to promote the evolution of cooperation in evolutionary games. Two factors determine the impacts of migration on cooperation, the migration speed and the migration direction of individuals. In previous works, migration direction is determined either in a random way or by referring to some rational factors, such as moving closer to cooperators and escaping away from defectors. However, in order to pursue profitable circumstances, individuals might decide their migration direction based on the neighbors’ trends instead of their positions. In this work, we propose two models by introducing two different directional migrations respectively into evolutionary games in a continuous two-dimensional plane. In one model, individuals adopt the average migration directions of their cooperative neighbors, which is called the cooperator-following (CF) migration model. In the other one, the defector-leaving (DL) migration model, individuals move in the opposite directions to their defective neighbors. Our results show that, for both models, the appropriate migration speeds can significantly promote cooperation and there exist optimal speeds to maximize the cooperation level in the population. Moreover, we find that the CF model is superior to the DL model in improving cooperation in most parameter regions. Besides, we simulate the models with different interaction radiuses and different population densities, and find that the optimization of cooperation by the migration speed still exist.

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.

Reputation-based strategy persistence promotes cooperation in spatial social dilemma

Understanding the emergence and maintenance of cooperation in social dilemma has received a lot of attention. In previous research, many scholars found that the reputation mechanism can promote cooperation, and the variation of reputation is consistent. However, in reality, according to both one's current action and past experiences, every individual's impression from others is modified to varying extent everyday. In other words, the length of duration of the same performance influences the diverse scale of their own reputation fluctuation. Therefore, a reputation-based strategy persistence mechanism, in which the increment of current reputation is determined by the persistence of last strategy, is proposed. Moreover, we introduce a parameter α to illustrate the impact of strategy persistence on reputation variation. The results of simulation show that the new mechanism paves the way for cooperation in evolutionary game, and the smaller α is, the better the mechanism performs.

Spontaneous punishment promotes cooperation in public good game

Abstract Punishment widely exists in social and biological systems and it has been proved to be an effective way to promote cooperation in evolutionary game in previous work. In this paper, we introduce a new mechanism of punishment that the punishment fine can be multiplied if there are several punishers decide to punish a defector, which leads to a low payoff of defector and promotes the level of cooperation. This mechanism can simulate group hunt which is common in natural animal world, for example, in biological system, a pack of animal in which every individual cooperates with each other can hunt a prey which is stronger than an individual inside the pack. This phenomenon can be explained by that the ability of punishment is multiplied by individuals cooperating with each other to carry out the punishment. A pack of wolves can make the process of hunt easier than the hunt implemented by a lone wolf, inspired by which we construct this mechanism of punishment to simulate the group punishment. Interestingly, we find that this mechanism can dramatically promotes the level of cooperation when we compare the simulation result with traditional evolutionary public good game. In order to figure out how our new mechanism of punishment promotes the cooperation, we have drawn several figures below to explain the mechanism. Our work simulates a widely existing phenomenon in biological and social systems and reveals some essential principles in the process of evolution.

Heterogeneous indirect reciprocity promotes the evolution of cooperation in structured populations

A fundamental aspect of all biological system is cooperation. Human society is based to a large extent on mechanisms that favor cooperation. Indirect reciprocity is a crucial factor for the emergence and maintenance of cooperation in evolutionary games. In this work, we introduce a mechanism of heterogeneous indirect reciprocity in the prisoner's dilemma game, where an altruistic attribute is considered. The so-called altruistic attribute refers to the trait that when an altruistic individual cooperates, its neighbors, regardless of their strategies, can gain additional benefits. Intuitively, altruistic cooperative agents seem to do only what is beneficial for others, but in fact, their neighbors tend to cooperate in order to maintain the cooperative strategies of altruistic individuals. In this way, the neighbors of cooperative altruistic individuals not only guarantee their own additional benefits, but also indirectly protect the income of altruistic individuals, which strengthens the links between cooperative individuals, thus promoting the evolution of cooperation. The robustness of the results is verified on homogeneous and heterogeneous networks. Moreover, the results of individual heterogeneity corroborate the existing evidence that heterogeneity, almost irrespective of its origin, promotes cooperative actions. Our conclusions might provide additional insights into understanding the roots of cooperation in social systems.

The effects of attribute persistence on cooperation in evolutionary games

In ordinary evolutionary game theory, players update their strategies according to a certain payoff-driven rule. Szolnoki and Perc (2015) [44] found conformity-enhanced network reciprocity by introducing conformity-driven strategy-updating rule to an appropriate fraction of players. In this work, we treat strategy-updating rule as an attribute of players and allow for the evolution of the attribute, for example, the alternation of the strategy-updating rule between payoff-driven and conformity-driven rules with time. We introduce the persistence parameter T by assuming that players change their strategy-updating rules every T Monte Carlo time unit according to either unbiased rule or aspiration rule. We find that frequent alternation of strategy-updating rule improves the conformity-enhanced network reciprocity for the unbiased rule, which leads that small T greatly promotes cooperation. On the other hand, we find no improvement of conformity-enhanced network reciprocity for the aspiration rule.