Cooperation, a cornerstone of natural and human systems, remains a complex phenomenon whose mechanisms require deeper exploration. A reputation-driven extension of the Prisoners Dilemma was introduced in this study, integrated wit the Q-learning algorithm, to examine how reputation mechanisms interact with extortion strategies in promoting cooperation. By incorporating zero-determinant strategies, notably extortion, cooperation and defection, we simulate strategic evolution on a structured population. Here, the evolution of cooperation is governed by a critical synergy between individual payoffs and reputation. In this framework, cooperation evolves through a critical synergy between individual payoffs and reputation, transforming the game from a mere payoff-optimization task into a dynamic socio-ecological system where agents continuously weigh economic gains against social standing. Our results demonstrated that although reputation mechanisms exhibit hysteresis and require time to accumulate, they ultimately suppress defection effectively. Rational agents prioritize payoff maximization only after surpassing a reputation threshold. Consequently, misaligned incentives can trap the population in a socially inefficient equilibrium characterized by non-negative reputations yet low payoffs. However, realigning incentives within a reasonable range could resolve this dilemma, prompting consistent cooperation. Well-structured payoff incentives thus harmonize individual and collective rationality, leading to high-payoff, high- reputation outcomes.

Elucidating the neural mechanisms underlying decision-making in complex social interactions hinges on resolving the nonlinear dynamic properties of collaborative brain network operations and their relationship with cognitive load. To this end, this study investigated the nonlinear dynamic characteristics of decision-making processes by quantifying the complexity of Electroencephalogram (EEG) signals during the Prisoner’s Dilemma game using multivariate multiscale entropy (mMSE). The results demonstrated that task-positive networks, particularly the Dorsal Attention Network (DAN) and Ventral Attention Network (VAN), exhibited higher complexity, which is associated with the heavier cognitive load of the brain in the process of rapid local information processing and global information integration during decision-making. The elevated complexities exhibited in performing Tit-for-Tat (TFT) strategy and making cooperative decisions, as higher cognitive load demanding tasks, confirm that mMSE can effectively quantify neural activity related to decision-making and feasibly depict the variations of EEG complexity corresponding to cognitive load, thus revealing the nonlinear dynamic neural mechanisms underlying the gaming process.

Many real-world social dilemmas involve individuals who strategically hesitate or withdraw, a behavior that is not captured by models restricted to cooperation and defection, and is often missed by three-strategy models that ignore realistic network structure and mobility. We therefore study an evolutionary game with three strategies: cooperate, defect and exit, where policy parameter & vartheta; quantifies the population coverage of the exit option. To improve societal relevance, we embed mobility in a multiplex framework that combines empirical social networks with BA scale-free layers. We show that allowing exit strategy benefits cooperators through two complementary mechanisms. First, the exit strategy provides a viable alternative for individuals who hesitate or become trapped in unfavorable interactions, preventing their exploitation and stabilizing cooperative clusters. Second, exiting individuals form a spatial buffer that limits the spread of defectors and creates room for cooperators to persist and expand. We further quantify the macro-level consequences of exit policies and find that, rather than imposing a lasting burden, exit allowances can increase net income and per capita income while reducing inequality, as measured by the Gini coefficient. The fiscal outlay is short-lived and small relative to the long-run gains. Finally, we show that the allowance level is a tunable policy instrument: when 0 < eta < R, organizations can adjust the allowance eta to match financial constraints and developmental stages, thereby promoting fairer resource distribution that supports cooperative norms and improves economic efficiency. Our results provide a policy-oriented framework for engineering cooperation while enhancing economic performance.

Given the distinct advantages of higher-order networks over pairwise interaction networks in capturing the intricate interdependencies among individuals, the study of cooperation dynamics based on higher-order interactions has attracted increasing attention. However, little research has explored how the transition from pairwise to higher-order interactions influences the evolution of cooperation. In this study, we develop an evolutionary game model on a two-layer coupled network, wherein agents participate in both pairwise and higher-order interactions. To integrate strategies across layers, we introduce a novel self-regarding Q-learning algorithm. Our results reveal a significant non-monotonic effect of interlayer coupling strength on cooperation, which strongly depends on the intensity of the social dilemma. Moderate interlayer coupling promotes cooperation through payoff synergy under low dilemma intensity, whereas under high dilemma intensity, it inhibits cooperation due to conflicting payoff signals between layers. Micro-level analysis reveals that varying the coupling strength shifts agents’ decision-making from pairwise to higher-order interactions, thereby altering evolutionary trajectories and collective outcomes. These findings remain robust across different network topologies, highlighting how environmental pressure and interlayer coupling jointly shape the emergence of cooperation in complex systems.

To characterize the evolution of cooperation in real-world scenarios, this paper develops an evolutionary game model with dynamic asymmetric activity. In the model, players are classified into leaders and followers according to the comparison between their strategy persistence and the threshold beta, and each individual x's node-weight (influence) w(x) is adjusted adaptively based on whether the game payoff meets the aspiration level A(x). Importantly, the leader-type player is allowed to incorporate the node-weight (influence) w(x) into fitness calculation, whereas the follower-type player solely relies on the game payoff, which induces a role-dependent and dynamically evolving asymmetry in effective competitiveness. Extensive Monte Carlo simulations show that this mechanism can substantially promote cooperation and mitigate spatial social dilemmas. Micro-level analyses further reveal that cooperation enhancement requires the coordinated emergence of leader-type cooperators and follower-type cooperators, which together suppress the spread of defection. Moreover, the statistical results indicate that the facilitating effect of cooperation is not strictly positively correlated with the heterogeneity of node-weight. At last, robustness tests across different dilemma types, network topologies, and strategy update schemes confirm that the main findings remain qualitatively unchanged, demonstrating the generality of the proposed mechanism. These results provide a parsimonious framework for understanding how dynamic asymmetry can reshape evolutionary pathways toward cooperative behavior.

The learning activities in collective intelligence have inspired many collective behaviors, such as self-organization, which is extremely important for human society. Most learning relations are unilateral or asymmetrical, depending on social status. In particular, the status involving asymmetric learning, which is characterized by nodes with different degrees in social networks, affects how the collective intelligence responds to the evolutionary environment, especially its collective cooperation behavior. In order to figure out how both high degree ($H$) and low degree ($L$) individuals behave, we introduce an asymmetric learning method, where individuals respond to the environment in the opposite way characterized by an asymmetric parameter. It is found that there exists a range of asymmetric parameters with the optimal promotion of cooperation. A conspicuous cluster has emerged by dividing all individuals into four different clusters according to their strategies at the given asymmetric parameter. This cluster consists of individuals who devote their utmost resources to investment. Remarkably, the preponderant majority of these individuals possess high levels of connectivity and, driven by the cumulative payoff effect, display a pronounced propensity to engage in cooperative behaviors. By contrast, within small clusters, a substantial quantity of individuals, notwithstanding their relatively high payoff coefficient, frequently encounter cooperation predicaments. A particularly salient finding is the vulnerability of $H$ individuals positioned on medium-connected nodes to the influence of asymmetric learning modalities. The triggering and subsequent diffusion of cooperative behavior throughout the population is contingent upon the fulfillment of two cardinal conditions: the existence of inborn altruistic behavior exhibitors on super hubs and a diminished self-centered learning framework among the $H$ individuals. This phenomenon holds significance as it could deepen our understanding of the system and offer potential ways to restructure its overall dynamics, leading to more efficient cooperative outcomes.

The lack of cooperation can easily result in inequality among members of a society, which provides an increasing gap between individual incomes. To tackle this issue, we introduce an incentive mechanism based on individual strategies and incomes, wherein a portion of the income from defectors is allocated to reward low-income cooperators, aiming to enhance cooperation by improving the equitable distribution of wealth across the entire population. Moreover, previous research has typically employed network structures or game mechanisms characterized by homogeneity. In this study, we present a network framework that more accurately reflects real-world conditions, where agents are engaged in multiple games, including prisoner's dilemma games in the top-layer and public good games in the down-layer networks. Within this framework, we introduce the concept of “external coupling” which connects agents across different networks as acquaintances, thereby facilitating access to shared datasets. Our results indicate that the combined positive effects of external coupling and incentive mechanism lead to optimal cooperation rates and lower Gini coefficients, demonstrating a negative correlation between cooperation and inequality. From a micro-level perspective, this phenomenon primarily arises from the regular network, whereas suboptimal outcomes are observed within the scale-free network. These observations help to give a deeper insight into the interplay between cooperation and wealth disparity in evolutionary games in large populations.

Researchers have long been intrigued by cooperative behavior in populations of selfish individuals. Recently, the focus has shifted to how social networks shape human interactions, as well as cooperation and moral behavior in general. Real-world situations often require an interdependent network, combining multiple layers of sub-networks. Previous studies have mostly examined cases with similar network structures across layers. Here, we go beyond this by investigating a coupled bilayer network, comprising a real-world collaborative network and a scale-free network, using the Prisoner's Dilemma to study its evolutionary dynamics. Individuals make decisions through social learning, moving within or between layers. We introduce a parameter that measures individuals' ability to communicate across layers. Without this communication, both trans-layer mobility and network structures impact cooperation. A small trans-layer mobility probability boosts cooperation, but excessive mobility erodes network reciprocity, decreasing cooperation in the collaborative layer network. Cooperation frequency is generally lower in the collaborative layer network compared to isolated networks, with individuals migrating to the scale-free layer network. However, with some information exchange, trans-layer mobility facilitates mutual social learning, reversing the decline in cooperation in the collaborative layer network and promoting overall cooperation. These findings may offer insights into population migration as well as regional development strategies.

Relationships in social networks change over time due to various factors, including mobility, preferences for moral behavior, and the consequent making and breaking of social ties. We therefore study how these factors affect cooperation in actual collaborative networks, where individuals adaptively move with a certain probability. We find that individuals preferentially move towards the sites with a high degree, which yields networks with a higher average degree, but at the same time is conducive to cooperation because positions at the hubs are most beneficial in that way. On the one hand, social mobility thus enhances network reciprocity by generating much more cooperation seeds than the original network, but on the other, it also washes out the network structure and creates well-mixed like conditions if too frequent. Thus, only with limited mobility is network reciprocity optimally enhanced and can yield best conditions for robust cooperation in social networks. And we expect optimal conditions for other forms of moral behavior to require the same patterns of moderate social mobility.

Collective risk social dilemmas are at the heart of the most pressing global challenges we are facing today, including climate change mitigation and the overuse of natural resources. Previous research has framed this problem as a public goods game (PGG), where a dilemma arises between short-term interests and long-term sustainability. In the PGG, subjects are placed in groups and asked to choose between cooperation and defection, while keeping in mind their personal interests as well as the commons. Here, we explore how and to what extent the costly punishment of defectors is successful in enforcing cooperation by means of human experiments. We show that an apparent irrational underestimation of the risk of being punished plays an important role, and that for sufficiently high punishment fines, this vanishes and the threat of deterrence suffices to preserve the commons. Interestingly, however, we find that high fines not only avert freeriders, but they also demotivate some of the most generous altruists. As a consequence, the tragedy of the commons is predominantly averted due to cooperators that contribute only their "fair share" to the common pool. We also find that larger groups require larger fines for the deterrence of punishment to have the desired prosocial effect.

Human beings are easily impacted by social influences, due to their social nature. As an essential manifestation of social influences, conformity is associated with the frequency witnessed in others' behavior, involving normative conformity and informational conformity according to the reaction of individuals. The former comes from the fear of a normative environment, while the latter means most behaviors are followed due to information asymmetry. Normative conformity significantly enhances network reciprocity, producing optimal cooperation at a moderate proportion, which induces within-cluster behavioral homogeneity and between-cluster behavioral diversity. On the contrary, informational conformity has an inhibitory effect on the evolution of cooperation for a low proportion of the conformity population, which contributes to the formation of defectors' clusters. The symmetry and duality of the two types of conformity on cooperation evolution provide an interesting and unexplored approach for future research, revealing the mechanism of conformity in evolutionary games.

• Multidimensional mobility induces rich synergistic phenomena with network reciprocity, which depends on the cost of mobility. • The synergistic effects of mobility superposed upon network reciprocity are best expressed for small flow rates. • The increasing of radius of mobility may weaken network reciprocity. Collective cooperation and social mobility are ubiquitous in human societies. Due to information sharing and the complexity of everyday life, multidimensional mobility is also common, for example when moving into different districts of a city for better education or when settling permanently abroad due to better job prospects. Nevertheless, it is not clear how such complex mobility might affect cooperation in situations that constitute social dilemmas, where individual and public interests are at odds. Here, as an initial step to understand the impact of multidimensional mobility, we investigate one of its significant dimensions, namely the range of mobility. We propose an updating algorithm where individuals either move adaptively in the area bounded by a mobility radius or stay put for social learning. We use this on the prisoner’s dilemma and the snowdrift game, and we find that an increase in either probability or radius of mobility may weaken network reciprocity, simply by decreasing the odds of meeting old interaction partners. However, if mobility is free, there is a window of parameters where synergies with network reciprocity are possible, and where indeed cooperation can be robust and significantly elevated. Local mobility in particular may favorably affect cooperation. In fact, even if mobility is costly, the failure of local mobility can often be associated with the risk caused by the shortage of available empty sites. We also find that the synergistic effects of mobility superposed upon network reciprocity are best expressed for small flow rates. Overall, we hope that our research will promote the better understanding of the complex interplay between networks reciprocity and mobility and their coaction.

Numerous social problems can be directly related to poverty, and its elimination is thus often declared a grand challenge in modern human societies. Nevertheless, it is difficult to shake the belief that certain fractions of the population would like to see it maintained to ensure the availability of cheap workforce and its readiness to do the hardest jobs, as well as to keep the prices of natural resources in the afflicted countries as low as possible. Here we show, however, that by allowing low-income individuals to escape poverty, either by means of mobility to pursue potential opportunities in remote areas or by ending dilemmas through social learning in local areas, greatly increases cooperation and thus has the potential to raise the social capital. In particular, we find that mobility of low-income individuals can promote cooperation when the per capita mobility rate is as low as 10(-3) in the order of magnitude as long as network reciprocity is still active. This synergy between network reciprocity and mobility is due to the emergence of large cooperative clusters that are in this size impossible without mobility. Moreover, we find that the mobility of defectors undermines cooperation, but only a few defectors actually move as they are typically well off when surrounded by cooperators. On the contrary, the higher the cooperation level, the greater the proportion of low-income cooperator that move. Our research thus shows that by providing ways out of poverty for individuals can raise whole societies out of economic gridlocks by elevating cooperation levels. (C)& nbsp;2022 Elsevier Ltd. All rights reserved.& nbsp;

In this paper, we investigate current reversal (CR) of overdamped traveling wave system subjected to an symmetric periodic driving. Numerical results shown that current takes the form of sawtooth-shape, and its direction can reverse more than ten times with traveling wave velocity, called multiple sawtooth-shape CR here. In virtue of transformation of reference frame, we reveal that occurrence of the sawtooth-shape CR comes from step amplitudes induced by the periodic driving in the new reference frame, and reversal time of current depends on the driving and the spatial potential. Moreover, direction of the current changes with the increment of noise intensity in the rocking system, i.e., noise-induced CR, which has not been reported in previous works on stochastic traveling system, and the intrinsic physical mechanisms responsible for the CR is analyzed in detail.

Neural systems are inherently noisy and time-delay, and these effects influence our perception from time to time. This is particularly apparent in binocular rivalry, where our perception alternates between com-peting stimuli shown to the two eyes. Here, we investigated the binocular rivalry behavior under the action of time delay and two noise sources. Our numerical results find that (i) the time delay and ad-ditive noise make the stationary probability distribution function of the binocular rivalry jump among two, three and four stabilities, breaking or maintaining balance of the binocular rivalry; (ii) the depen-dence of mean first passage time on multiplicative noise intensity shows a maximum, i.e., noise enhance perceptual stability, while the stability can be enhanced many times by the time delay; (iii) the charac-teristic correlation time not only exhibits a underdamped oscillation behavior as a function of delay time (i.e., multiple coherence resonances), but also shows a nonmonotonic behavior with the additive noise intensity. These findings have the significant implication for understanding and controlling perception alteration from a new perspective. (c) 2021 Elsevier Ltd. All rights reserved.

Individuals often move to distance themselves from defectors, or to seek better chances for higher payoffs, for example moving from rural to urban areas. Regardless of the rea-son, however, moving frequently also means alienation, which in turn means bearing costs for seeking new opportunities. With this motivation, we study a prisoner's dilemma game, where individuals with defectors in their communities either move or update their strategy. We find that the alienation from defectors reinforces larger and more compact cooperative clusters. However, the number of cooperative clusters depends on the viscosity of the interaction network, where network reciprocity still works well. And it is the finetuned interplay between the mobility to alienate from defectors and a still functioning network reciprocity that works best in promoting cooperation. Our results suggest that a limited mobility of minorities could spare public resources in social dilemma situations more effectively than reward and punishment. (c) 2020 Elsevier Inc. All rights reserved.

Collective cooperation is essential to human society, and it exists in many social dilemmas. In the scenario of a collective-risk social dilemma, a group of players have to collectively contribute to a public fund to prevent the tragedy of the commons, such as dangerous climate change, because everybody will lose all their remaining money when the damage happens with a certain probability if the group fails to reach a fixed fundraising target. Yet, it remains largely unclear how the group size affects the probability of reaching the collective target and the mechanism that drives different outcomes of the collective cooperation. Here, we contribute to the literature by exploring the role of group size in the collective-risk social dilemma and the potential underlying mechanism using both model simulations and human experiments. Through simulations we found that the rate of failure for collective cooperation increases for larger groups, along with the arising of bystander effect and a decrease in average contributions, which are confirmed by our experimental observations. We further analyze the patterns of investment behaviors in the experiment setting by categorizing players into cooperators, altruists, and free riders using both a clustering method and a golden standard. We found that altruists who tend to contribute more, rather than cooperators who prefer contributing a fair-share investment, play a crucial role in groups with success outcome in early and/or middle stages of the game. Our results indicate that bystanders are dynamic and their amount depends on the contribution of others. When others contribute less, bystanders also contribute less. If the collective goal is unlikely to achieve, more players choose to be bystanders who strategically contribute less, intriguing the failure of the collective goal. Our findings suggest a potentially effective way to solve the collective-risk social dilemma by reducing the bystander effect through the mechanism design of forming small groups. (c) 2021 Elsevier Inc. All rights reserved.

In general, no transport can emerge in a spatially symmetric periodic system subjected to an unbiased dichotomous periodic driving. Here, we used a noise, which switches synchronously with the driving in three cases [switch between Gaussian white noise and colored noise, two colored noises with different colors (e.g., autocorrelation rate), and Gaussian white noise and harmonic velocity noise], to drive such a symmetric system. Numerical results for the cases indicate that the directed transport of the symmetric system can be induced merely by the color breaking (the difference in two autocorrelation rates) of the switch noise. The amplitude of current depends on the difference, i.e., the greater the difference, the greater the current. Also, the greater autocorrelation rate between the two noises determines the direction of current. The current as a function of the noise intensity for all cases has in common that appropriate noise intensity induces optimal transport. Further investigations show that the color breaking comes from the difference of barrier heights between the left and right-tilted potentials induced by the different autocorrelation rates.

We study how mobile individuals affect the evolution of cooperation in social dilemmas. In doing so, we consider two types of players. The traditional type simply copies the most successful strategy in its neighborhood in order to improve its future payoff, while the advantageous type moves away in the hope of settling in a better community. We show that the introduction of the advantageous type leads to larger and more compact cooperative clusters in the prisoner's dilemma game. This in turn facilitates the evolutionary stability of cooperation even under adverse conditions that are characterized by high temptations to defect. We also verify that the average payoff of a community unit remains proportional to the number of cooperators in this community, which hence indicates that the players pursuing mobil ity to attain a competitive advantage also foster cooperation in their new communities. Another way to communicate this result in the light of the costs associated with moving is to say that optimal mobility, such that yields higher payoffs to the individual who moved and the community as a whole, is similar to the optimization of the allocation of limited resources. We thus hope that these results will shed new light on how to effectively allocate resources and how to optimize mobility for optimal cooperation. (C) 2020 Elsevier Ltd. All rights reserved.

组织10名色觉正常、生理和心理健康、年龄和教育背景相近的观察者进行心理物理实验.通过记录和分析观察者观察不同颜色、不同色差大小刺激的32个电极上的脑电波数据,探讨了CIELAB颜色空间中红、绿、蓝、灰四种颜色、大小分别为10和5的两组色差刺激产生的事件相关电位(ERP)的区别.实验结果表明,在注视色差刺激时,脑部右侧和枕区N1成分呈现明显的规律性,N1电位从脑前到脑后逐渐减小、振幅逐渐增大,且色差越大N1电位越大(振幅越小);而P3成分在脑部中线区域比其他区域较有规律,但其规律性比N1成分弱.