Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas

Evolution of indirect reciprocity under emotion expression

Do emotion expressions impact the evolution of cooperation? Indirect Reciprocity offers a solution to the cooperation dilemma with prior work focusing on the role of social norms in propagating others' reputations and contributing to evolutionarily stable cooperation. Recent experimental studies, however, show that emotion expressions shape pro-social behaviour, communicate one's intentions to others, and serve an error-correcting function; yet, the role of emotion signals in the evolution of cooperation remains unexplored. We present the first model of IR based on evolutionary game theory that exposes how emotion expressions positively influence the evolution of cooperation, particularly in scenarios of frequent errors. Our findings provide evolutionary support for the existence of emotion-based social norms, which help foster cooperation among unrelated individuals.

Co-evolution model of traffic travel and disease transmission under limited resources

The co-evolution mechanisms between traffic mobility and disease transmission under resource constraints remain poorly understood. This study proposes a two-layer transportation network model integrating the Susceptible-Infectious-Susceptible (SIS) epidemic framework to address this gap. The model incorporates critical factors such as total medical resources, inter-network infection delays, travel willingness, and network topology. Through simulations, we demonstrate that increasing medical resources significantly reduces infection scale during outbreaks, while prolonging inter-network delays slows transmission rates but extends epidemic persistence. Complex network topologies amplify the impact of travel behavior on disease spread, and multi-factor interventions (e.g., combined resource allocation and delay extension) outperform single-factor controls in suppressing transmission. Furthermore, reducing network connectivity (lower average degree) proves effective in mitigating outbreaks, especially under low travel willingness. These findings highlight the necessity of coordinated policies that leverage resource optimization, travel regulation, and network simplification to manage epidemics. This work provides actionable insights for policymakers to design efficient epidemic control strategies in transportation-dependent societies.

Social dilemma for 30 years: Progress, framework, and future based on CiteSpace analysis

Social dilemmas have been a popular research topic in the past 30 years, yet there is still a lack of interdisciplinary reviews. This study represents the first attempt to conduct a bibliometric analysis of social dilemma research over the past 30 years, aiming to identify the research status, research hotspots, and future trends in this domain. We conduct an interdisciplinary analysis of 3630 articles from 1993 to 2023 using CiteSpace software. We find that: (1) this research domain exhibits a fluctuating upward trend and possesses evident interdisciplinary characteristics. (2) Collaboration among authors, institutional and regional, is much more prevalent, especially in the evolutionary dynamics of human behavior, cooperation, and reinforcement learning. (3) The current hot trend in this field of research is to investigate the influencing factors and solutions for social dilemmas. Researchers have shown great interest in value orientation, social norms, fairness, punishment, and rewards in promoting cooperation. (4) In the future, this field will cover different disciplines, develop theoretical frameworks grounded in bounded rationality, explore the boundary conditions of effective strategies, and integrate emerging technologies. This study serves as a valuable reference for scholars seeking to navigate social dilemma research while also providing insights for managers aiming to devise practical solutions to social dilemmas.

Heterogeneous decision-making dynamics of threshold-switching agents on complex networks

In the classical two-player decision-making scenario, individuals may have different tendencies to take a certain action, given that there exists a sufficient number of neighbors adopting a particular option. This is ubiquitous in many real-life contexts including traffic congestion, crowd evacuation, and minimal vertex cover problem. Under best-response dynamics, we investigate the decision-making behaviors of heterogeneous agents on complex networks. Results of the networked games are twofold: for networks of uniform degree distribution (e.g., the lattice) and fraction of the strategy is of a linear function of the threshold setting. Moreover, the equilibrium analysis is provided and the relationship between the equilibrium dynamics and the change of the threshold value is given quantitatively. Next, if the games are played on networks with non-uniform degree distribution (e.g., random regular and scale-free networks), influence of the threshold-switching will be weakened. Robust experiments indicate that it is not the value of the average degree, but the degree distribution that influences how the strategy evolves affected by the threshold settings. Our result shows that the decision-making behaviors can be effectively manipulated by tuning the parameters in the utility function (i.e., thresholds) of some agents for more regular network structures.

Effect of heterogeneous investment induced by payoff and emotion on cooperation in public goods games by considering memory decline effects

Payoff, emotion, and historical memory directly determine investment decision-making for incomplete rational men in a public goods game (PGG). How these factors affect investment and cooperation behavior has not been investigated yet. Thus, we proposed a new investment model involving theses three factors to examine its coupling effect on cooperation in PGG. An emotional increment was employed to describe the emotional change in every round by supposing an investor' pleasure to a cooperator but regret to a defector. Furthermore, an emotional index was formed by accumulating these historical changes with a memory decline effect. Then an investment formula was proposed by considering this emotional index and a historical payoff. Moreover, the cooperation level affected by these factors was investigated. Results show a mutually reinforcing relationship between emotional and payoff investments. A poor memory capacity coefficient allows defectors to change their behaviors but produces some opportunists. A large memory length results in a high cooperator fraction but is not suggested to be too large.

Cooperation without punishment

A fundamental question in social and biological sciences is whether self-governance is possible when individual and collective interests are in conflict. Free riding poses a major challenge to self-governance, and a prominent solution to this challenge has been altruistic punishment. However, this solution is ineffective when counter-punishments are possible and when social interactions are noisy. We set out to address these shortcomings, motivated by the fact that most people behave like conditional cooperators-individuals willing to cooperate if a critical number of others do so. In our evolutionary model, the population contains heterogeneous conditional cooperators whose decisions depend on past cooperation levels. The population plays a repeated public goods game in a moderately noisy environment where individuals can occasionally commit mistakes in their cooperative decisions and in their imitation of the role models' strategies. We show that, under moderate levels of noise, injecting a few altruists into the population triggers positive reciprocity among conditional cooperators, thereby providing a novel mechanism to establish stable cooperation. More broadly, our findings indicate that self-governance is possible while avoiding the detrimental effects of punishment, and suggest that society should focus on creating a critical amount of trust to harness the conditional nature of its members.

A Strategy Adaptive Evolution Approach Based on the Public Goods Game

Cluster behavior is prevalent in nature. Many individuals change their behavior to adapt to a dynamically changing environment by following simple rules of behavior and interacting with information from neighboring individuals. In this study, the traditional public goods game model is improved by combining the advantages of game theory and interactive learning. A strategy adaptive evolution method based on a public goods game is proposed. The emergence of cooperative behavior in weighted networks under the co-evolution of game strategies and node weights is explored in conjunction with multi-agent interactive learning. The results show that in a public goods game with strategic adaptation, a person’s influence becomes greater if their level of adaptation exceeds the desired level, and less otherwise. This weight adjustment is defined by the intensity parameter δ. A moderate δ value can effectively facilitate the occurrence of cooperative evolution. The level of cooperation depends mainly on the weight distribution of participants, which leads to the formation of cooperative clusters controlled by high-weighted cooperators. Even with the great temptation to defect, these cooperators can prevail over defectors. The adjustment of node weights increases the heterogeneity of individuals. This research provides a viable pathway to solve social dilemmas and will further promote the application of multi-agent intelligent decision making.

The probabilistic pool punishment proportional to the difference of payoff outperforms previous pool and peer punishment

The public goods game is a multiplayer version of the prisoner’s dilemma game. In the public goods game, punishment on defectors is necessary to encourage cooperation. There are two types of punishment: peer punishment and pool punishment. Comparing pool punishment with peer punishment, pool punishment is disadvantageous in comparison with peer punishment because pool punishment incurs fixed costs especially if second-order free riders (those who invest in public goods but do not punish defectors) are not punished. In order to eliminate such a flaw of pool punishment, this study proposes the probabilistic pool punishment proportional to the difference of payoff. In the proposed pool punishment, each punisher pays the cost to the punishment pool with the probability proportional to the difference of payoff between his/her payoff and the average payoff of his/her opponents. Comparing the proposed pool punishment with previous pool and peer punishment, in pool punishment of previous studies, cooperators who do not punish defectors become dominant instead of pool punishers with fixed costs. However, in the proposed pool punishment, more punishers and less cooperators coexist, and such state is more robust against the invasion of defectors due to mutation than those of previous pool and peer punishment. The average payoff is also comparable to peer punishment of previous studies.

Game dynamics of emotion evolution based on the Moran process

In this paper, emotions are classified into four types, namely, respect for the strong, envying the strong, sympathy for the weak, and bullying the weak. The corresponding relationship between the four emotion types and the two behaviors of competition and cooperation is then defined. The payoff matrices of the game based on emotions are obtained and the evolutionary dynamics of the four emotion types in a finite population based on the Moran process are studied. Next, we derive the absorption probabilities of a 4×4 symmetric evolutionary game of the population. The influence of the payoff parameters and the natural selection intensity on the result of the group evolution are then analyzed. The calculations indicate that there are differences in the absorption probabilities of the four absorption states of the system. At a steady state, individuals of the types envying the strong and bullying the weak have the highest probability of occupying the entire population, and individuals of the type respect for the strong and sympathy for the weak have the lowest one. By comparing the level of cooperation and average payoffs at a steady state, we observe that the level of cooperation and average payoffs based on the proposed model are better than those of the prisoner's dilemma game with two behaviors. Therefore, emotional evolution can promote cooperation and achieve better group fitness.

Evolution of cooperation with interactive identity and diversity

Interactive identity and interactive diversity are generally regarded as two typical interaction patterns in living systems. The former describes that in each generation every individual behaves identically to all of its opponents, and the latter allows each individual to behave diversely to its distinct opponents. Most traditional research on the evolution of cooperation, however, has been confined to populations with a uniform interaction pattern. Here we study the cooperation conundrum in a diverse population comprising players with interactive identity and with interactive diversity. We find that in homogeneous networks a small fraction of players taking interactive diversity are enough to stabilize cooperation for a wide range of payoff values even in a noisy environment. When assigned to heterogeneous networks, players in high-degree nodes taking interactive diversity significantly strengthen systems' resilience against the shifty environment and enlarge the survival region of cooperation. However, they fail to establish a homogeneous strategy 'cloud' in the neighborhood and thus can not coordinate players in low-degree nodes to reach a socially optimal cooperation level. The most favorable outcome emerges when players in high-degree nodes take interactive identity and meanwhile others adopt interactive diversity. Our findings reveal the significance of the two typical interaction patterns and could be a good heuristic in coordinating them to achieve the social optimum in cooperation.

A remarkable effect of the combination of probabilistic peer-punishment and coevolutionary mechanism on the evolution of cooperation

In the previous studies, the author has proposed the probabilistic peer-punishment based on the difference of payoff, and presented that the proposed peer-punishment utilizes its mechanism for preventing antisocial punishment like retaliation of a defector on a cooperator, effectively enhances the evolution of cooperation, and greatly increases the average payoff of all players in various parameters regarding static three types of topology of connections. Here, this study introduces both activities of breaking and creating connections of every player based on his/her preference to the model of the proposed peer-punishment. Every player will keep connections with his/her preferable players, whereas he/she will frequently break connections with his/her dissatisfied other players. Therefore, the new model of this study is the combination of probabilistic peer-punishment and coevolutionary mechanism that not only strategy of players but also connections between players evolve. This study discovers new knowledge that such combination induces high-level evolution of cooperation and great increase of the average payoff of all players in the condition where cooperation is hard to evolve.

Impact of interaction style and degree on the evolution of cooperation on Barabási-Albert scale-free network

In this work, we study an evolutionary prisoner's dilemma game (PDG) on Barabási-Albert scale-free networks with limited player interactions, and explore the effect of interaction style and degree on cooperation. The results show that high-degree preference interaction, namely the most applicable interaction in the real world, is less beneficial for emergence of cooperation on scale-free networks than random interaction. Besides, cooperation on scale-free networks is enhanced with the increase of interaction degree regardless whether the interaction is high-degree preference or random. If the interaction degree is very low, the cooperation level on scale-free networks is much lower than that on regular ring networks, which is against the common belief that scale-free networks must be more beneficial for cooperation. Our analysis indicates that the interaction relations, the strategy and the game payoff of high-connectivity players play important roles in the evolution of cooperation on scale-free networks. A certain number of interactions are necessary for scale-free networks to exhibit strong capability of facilitating cooperation. Our work provides important insight for members on how to interact with others in a social organization.

The coevolution of overconfidence and bluffing in the resource competition game

Resources are often limited, therefore it is essential how convincingly competitors present their claims for them. Beside a player’s natural capacity, here overconfidence and bluffing may also play a decisive role and influence how to share a restricted reward. While bluff provides clear, but risky advantage, overconfidence, as a form of self-deception, could be harmful to its user. Still, it is a long-standing puzzle why these potentially damaging biases are maintained and evolving to a high level in the human society. Within the framework of evolutionary game theory, we present a simple version of resource competition game in which the coevolution of overconfidence and bluffing is fundamental, which is capable to explain their prevalence in structured populations. Interestingly, bluffing seems apt to evolve to higher level than corresponding overconfidence and in general the former is less resistant to punishment than the latter. Moreover, topological feature of the social network plays an intricate role in the spreading of overconfidence and bluffing. While the heterogeneity of interactions facilitates bluffing, it also increases efficiency of adequate punishment against overconfident behavior. Furthermore, increasing the degree of homogeneous networks can trigger similar effect. We also observed that having high real capability may accommodate both bluffing ability and overconfidence simultaneously.

Bluffing promotes overconfidence on social networks

The overconfidence, a well-established bias, in fact leads to unrealistic expectations or faulty assessment. So it remains puzzling why such psychology of self-deception is stabilized in human society. To investigate this problem, we draw lessons from evolutionary game theory which provides a theoretical framework to address the subtleties of cooperation among selfish individuals. Here we propose a spatial resource competition model showing that, counter-intuitively, moderate values rather than large values of resource-to-cost ratio boost overconfidence level most effectively. In contrast to theoretical results in infinite well-mixed populations, network plays a role both as a “catalyst” and a “depressant” in the spreading of overconfidence, especially when resource-to-cost ratio is in a certain range. Moreover, when bluffing is taken into consideration, overconfidence evolves to a higher level to counteract its detrimental effect, which may well explain the prosperity of this “erroneous” psychology.

Emotion regulation moderates the association between empathy and prosocial behavior

Theory and evidence suggest that empathy is an important motivating factor for prosocial behaviour and that emotion regulation, i.e. the capacity to exert control over an emotional response, may moderate the degree to which empathy is associated with prosocial behaviour. However, studies to date have not simultaneously explored the associations between different empathic processes and prosocial behaviour, nor whether different types of emotion regulation strategies (e.g. cognitive reappraisal and expressive suppression) moderate associations between empathy and prosocial behaviour. One hundred-and-ten healthy adults completed questionnaire measures of empathy, emotion regulation and prosocial tendencies. In this sample, both affective and cognitive empathy predicted self-reported prosocial tendencies. In addition, cognitive reappraisal moderated the association between affective empathy and prosocial tendencies. Specifically, there was a significant positive association between empathy and prosocial tendencies for individuals with a low or average tendency to reappraise but not for those with a high tendency to reappraise. Our findings suggest that, in general, empathy is positively associated with prosocial behaviour. However, this association is not significant for individuals with a high tendency for cognitive reappraisal.

Effects of adaptive dynamical linking in networked games

The role of dynamical topologies in the evolution of cooperation has received considerable attention, as some studies have demonstrated that dynamical networks are much better than static networks in terms of boosting cooperation. Here we study a dynamical model of evolution of cooperation on stochastic dynamical networks in which there are no permanent partners to each agent. Whenever a new link is created, its duration is randomly assigned without any bias or preference. We allow the agent to adaptively adjust the duration of each link during the evolution in accordance with the feedback from game interactions. By Monte Carlo simulations, we find that cooperation can be remarkably promoted by this adaptive dynamical linking mechanism both for the game of pairwise interactions, such as the Prisoner's Dilemma game (PDG), and for the game of group interactions, illustrated by the public goods game (PGG). And the faster the adjusting rate, the more successful the evolution of cooperation. We also show that in this context weak selection favors cooperation much more than strong selection does. What is particularly meaningful is that the prosperity of cooperation in this study indicates that the rationality and selfishness of a single agent in adjusting social ties can lead to the progress of altruism of the whole population.

A bio-inspired methodology of identifying influential nodes in complex networks

How to identify influential nodes is a key issue in complex networks. The degree centrality is simple, but is incapable to reflect the global characteristics of networks. Betweenness centrality and closeness centrality do not consider the location of nodes in the networks, and semi-local centrality, leaderRank and pageRank approaches can be only applied in unweighted networks. In this paper, a bio-inspired centrality measure model is proposed, which combines the Physarum centrality with the K-shell index obtained by K-shell decomposition analysis, to identify influential nodes in weighted networks. Then, we use the Susceptible-Infected (SI) model to evaluate the performance. Examples and applications are given to demonstrate the adaptivity and efficiency of the proposed method. In addition, the results are compared with existing methods.