Network Reciprocity Research Articles

Cooperative evolution and symmetry breaking in interdependent networks based on alliance mechanisms

In real life, alliance organizations are common. Cross-border alliances and cross-industry cooperation are very popular business models where entities can achieve a win-win situation by leveraging each other’s strengths. To reveal how cooperation evolves under a cross-layer alliance, we introduce the prisoner’s dilemma game to depict the social dilemma, the interdependent two-layer network to depict the interaction structure. Eventually, the experimental results show that the alliance of individuals between layers can effectively inhibit network defective behavior and enhance the activity of cooperative behavior. As alliance strength increases, spontaneous symmetry breaking occurs and the breaking strength roughly tends to increase first and then decrease. This phenomenon is mainly caused by the asynchronous expansion of heterogeneous strategy coupling among two-layer networks, while the difference in time scales is another important factor in breaking the symmetry, thus further enriching the study of network reciprocity.

Reputation-based asymmetric comparison of fitness promotes cooperation on complex networks

Reputation is elaborated in society and has a great effect on individual fitness, under which each player acquires a special fitness. An asymmetric comparison will appear when players update their strategies based on fitness and imitation dynamics. To explore the impact of the above asymmetry on the evolution of cooperation, we present a new strategy updating rule. More precisely, a player compares his/her own fitness with neighbor’s payoff when he/she updates strategy. In this paper, individual payoff is dependent on both his/her strategy and partner’s strategy; and individual fitness is calculated according to individual payoff and reputation value. Extensive simulation results illustrate that in spatial evolutionary prisoner’s dilemma game, with the help of this new strategy updating rule, the proportion of cooperators increases significantly within a wide range of parameter value. During the evolution of cooperation, asymmetric comparison of fitness can enhance network reciprocity effectively. Furthermore, a discussion on micro dynamics from the perspective of fitness is presented. To test the generality of this mechanism, we also use this new updating rule to simulate the evolution of spatial snowdrift game. In addition, the results obtained on Barabási–Albert Scale-Free network and Erdős–Rényi random graph are also shown. Our work helps to understand the evolution of cooperation and reputation.

Comparing Egocentric and Sociocentric Centrality Measures in Directed Networks

Egocentric networks represent a popular research design for network research. However, to what extent and under what conditions egocentric network centrality can serve as reasonable substitutes for their sociocentric counterparts are important questions to study. The answers to these questions are uncertain simply because of the large variety of networks. Hence, this paper aims to provide exploratory answers to these questions by analyzing both empirical and simulated data. Through analyses of various empirical networks (including some classic albeit small ones), this paper shows that egocentric betweenness approximates sociocentric betweenness quite well (the correlation is high across almost all the networks being examined) while egocentric closeness approximates sociocentric closeness only reasonably well (the correlation is a bit lower on average with a larger variance across networks). Simulations also confirm this finding. Analyses further show that egocentric approximations of betweenness and closeness seem to work well in different types of networks (as featured by network size, density, centralization, reciprocity, transitivity, and geodistance). Lastly, the paper briefly presents three ideas to help improve egocentric approximations of centrality measures.

Evaluating households’ community participation: Does community trust play any role in sustainable development?

Traditional community support, prevention from disasters, and mitigation depend on the top-down mode of management regulated by the government. This study aims to analyze the association between social networks and its structure on the decision of households’ participation in community. A households survey was conducted in Yanliang district of Shaanxi province of China and 393 households were targeted. An ordered multi classification logistic regression model was utilized to empirically analyze the association between the variables. The results showed that social networks have a significant positive impact on the households’ participation in cooperatives/communities. Among other variables, network interaction, network learning, network trust, and households’ participation in green energy technologies and cooperatives/community showed significant and positive correlation, but the variable network reciprocity was found to be negatively correlated to the adoption of green energy technologies. Study findings further revealed that, there is an interaction effect in the participation of households’ behavioral decision-making and joining cooperatives. Furthermore, the social experience of the head of the household and the source of income of the family showed a significant positive association with households’ participation in cooperatives/communities. Based on the study findings, it is suggested that the utilization and cultivation of households’ social network, service level of cooperatives need to be improved.

Options for mobility and network reciprocity to jointly yield robust cooperation in social dilemmas

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.

Small world can alleviate the social dilemmas originating from self-regulation or community policing issues

Self-regulation and government regulation, community policing and external powerful forces, respectively, form vital part of today’s global economy and social management. The implementation of regulation from self-regulation or community policing requires considerable disciplined members to share the costs of execution, while government or external powerful forces are more likely to make an strong intervention as the industry or community is being widely eroded, which are thus two definitely different feedback regulation schemes. Together with those wrong-doers, the organizations of the two feedback regulation schemes consist of both first-order and novel second-order social dilemma. It still remains a significant challenge to identify an optimal structure to simultaneously alleviate the two dilemmas, and even to additionally favor the altruistic individuals. To address this issue, in this paper we adopt an evolutionary game model within the framework of the public good model, by considering defector-driven and cooperator-driven punishment to map the two feedback regulation schemes, respectively. Through a series of extensive Monte Carlo simulation experiments and mean-field analysis based on replicator dynamics, we finally uncover the combination of clustering and shortcuts, say the small-world structure, is required to largely alleviate both first-order and novel second-order dilemma, which can not only yield optimal public goods by successfully eliminating defectors through strong network reciprocity from dense local connections, but also provide sufficient shortcuts to promote the dominance of defector-driven punishers. Our findings can be beneficial for improving self-regulation or community policing systems by constructing novel monitoring networks.

Identifying oil market states based on structure and evolution of the international crude oil trade networks

With the growing demand for energy, the importance of oil as a major energy resource is increasingly evident, and trade has become the key to balancing energy supply and demand. We construct the evolving international oil trade network (iOTN) and analyze the structure and evolution characteristics of the network. Meanwhile, we identify different oil market states by applying the sequential clustering method, combined with relevant network indicators. We find an increase in bilateral cooperation among economies in the oil market, closer trade ties and an upward trend in network reciprocity. The iOTN is heterogeneous, and economies with widely differing trade positions are more likely to cooperate. Trade cooperation with significant trade volumes is more irreplaceable and stable. The changes of oil market state in 1990, 2004 and 2014 indicate that major international events significantly impact the structure of energy systems and trade networks. The division of the oil trade market state by sequential clustering can reflect the reality. Our study clarifies the structural attributes of the iOTN, explores the evolution of the oil trade pattern from the network level, and accurately identifies the state changes in the international oil market.

Community detection and reciprocity in networks by jointly modelling pairs of edges

Abstract To unravel the driving patterns of networks, the most popular models rely on community detection algorithms. However, these approaches are generally unable to reproduce the structural features of the network. Therefore, attempts are always made to develop models that incorporate these network properties beside the community structure. In this article, we present a probabilistic generative model and an efficient algorithm to both perform community detection and capture reciprocity in networks. Our approach jointly models pairs of edges with exact two-edge joint distributions. In addition, it provides closed-form analytical expressions for both marginal and conditional distributions. We validate our model on synthetic data in recovering communities, edge prediction tasks and generating synthetic networks that replicate the reciprocity values observed in real networks. We also highlight these findings on two real datasets that are relevant for social scientists and behavioural ecologists. Our method overcomes the limitations of both standard algorithms and recent models that incorporate reciprocity through a pseudo-likelihood approximation. The inference of the model parameters is implemented by the efficient and scalable expectation–maximization algorithm, as it exploits the sparsity of the dataset. We provide an open-source implementation of the code online.

Involution game with spatio-temporal heterogeneity of social resources

When group members claim a portion of limited resources, it is tempting to invest more effort to get a larger share. However, if everyone acts similarly, they all get the same piece they would obtain without extra effort. This is the involution game dilemma that can be detected in several real-life situations. It is also a realistic assumption that resources are not uniform in space and time, which may influence the system’s resulting involution level. We here introduce spatio-temporal heterogeneity of social resources and explore their consequences on involution. When spatial heterogeneity is applied, network reciprocity can mitigate the involution for rich resources, which would be critical otherwise in a homogeneous population. Interestingly, when the resource level is modest, spatial heterogeneity causes more intensive involution in a system where most cooperator agents, who want to keep investment at a low level, are present. This picture is partly the opposite in the extreme case when more investment is less effective. Spatial heterogeneity can also produce a counterintuitive effect when the presence of alternative resource levels cannot explain the emergence of involution. If we apply temporal heterogeneity additionally, then the impact of spatial heterogeneity practically vanishes, and we turn back to the behavior observed in a homogeneous population earlier. Our observations are also supported by solving the corresponding replicator equations numerically.

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.

Childlessness, personal social networks and wellbeing at advanced ages: a cross-sectional study in a Southern European familistic welfare state

AbstractDuring the past decades, childless old age has attracted a considerable amount of scholarly interest. However, few studies address this phenomenon in Southern European familistic welfare states, where there is a pervading expectation that family members, especially spouses and children, care for their older relatives. The present cross-sectional study aims to analyse the relationship between childlessness, social networks and wellbeing in a sample of 612 Portuguese individuals aged 65 and over, comprising two sub-samples: parents (N = 540) and childless (N = 72). Data were collected through a research protocol that included a sociodemographic questionnaire, a personal social network assessment inventory, and several validated psychometric measures of psychological wellbeing focusing on mental health, loneliness, depression and satisfaction with life. Childless older adults' social networks are smaller but more diverse, including a more significant proportion of friends and neighbours. No differences were found in perceived support from significant others, but network reciprocity was lower among non-parents. The childless subsample also reported more feelings of loneliness and less life satisfaction, but regression analysis showed that parenthood status, per se, is not significantly related to any outcome measures. Besides the central role of sociodemographic characteristics and personal functioning measures in explaining psychological wellbeing variance, several network factors were also identified as influential predictors. Implications for micro-level network intervention and macro-level social policy making are discussed.

Psychological Distance Impacts Subgroup Reciprocity in Technological Innovation Networks: The Mediating Role of Divisive Faultlines.

As information flows at ever-increasing speeds across technological innovation networks, it is crucial to optimize reciprocity among partnering enterprises. However, the impact of psychological distance on subgroup reciprocity in such networks has not yet been investigated. To address this gap, the current study drew on theories of faultlines and cohesive subgroups to model the relationship between psychological distance and subgroup reciprocity within technological innovation networks. Our hypotheses were tested using data from 174 respondents working in Yunnan Province, China. The results were as follows: first, psychological distance had negative effects on subgroup reciprocity in technological innovation networks; second, relationship-divisive and innovation-divisive faultlines negatively impacted reciprocity within and between subgroups; third, the faultlines partially mediated the negative relationship between psychological distance and intra-subgroup reciprocity; and fourth, the negative relationship between psychological distance and subgroup reciprocity was not mediated by the faultlines. The findings uncover the psychological mechanism of subgroup reciprocity within technological innovation networks. They will inform the decision-making process of enterprises when selecting partners within their technological innovation networks and support the development of effective reciprocal relationships with other innovators.

Reciprocity, community detection, and link prediction in dynamic networks

Many complex systems change their structure over time, in these cases dynamic networks can provide a richer representation of such phenomena. As a consequence, many inference methods have been generalized to the dynamic case with the aim to model dynamic interactions. Particular interest has been devoted to extend the stochastic block model and its variant, to capture community structure as the network changes in time. While these models assume that edge formation depends only on the community memberships, recent work for static networks show the importance to include additional parameters capturing structural properties, as reciprocity for instance. Remarkably, these models are capable of generating more realistic network representations than those that only consider community membership. To this aim, we present a probabilistic generative model with hidden variables that integrates reciprocity and communities as structural information of networks that evolve in time. The model assumes a fundamental order in observing reciprocal data, that is an edge is observed, conditional on its reciprocated edge in the past. We deploy a Markovian approach to construct the network’s transition matrix between time steps and parameters’ inference is performed with an expectation-maximization algorithm that leads to high computational efficiency because it exploits the sparsity of the dataset. We test the performance of the model on synthetic dynamical networks, as well as on real networks of citations and email datasets. We show that our model captures the reciprocity of real networks better than standard models with only community structure, while performing well at link prediction tasks.

The effect of perceptions competition and learning costs on cooperation in spatial evolutionary multigames

It is a great challenge to correctly understand the evolution and incentives of cooperation. In recent years, the spatial evolutionary multigames have attracted extensive attention from researchers. Actually, for players, not only themselves but also their neighbors will affect their perceptions, which has not been considered in previous works. In addition, changing perceptions has a learning process, which will cause some costs. Inspired by the above facts, we explore the impact of perceptions competition mechanisms and learning costs on the evolution of cooperation in the multigames dilemma, which consists of prisoner game and snowdrift game. Especially, we further explore how different groups can coexist in such a setting. It is found that the heterogeneity of payoffs contributes to network reciprocity and can maintain cooperative behaviors even under unfavorable conditions. Compared with the static multigames mechanism, our perceptions competition mechanism has a higher proportion of cooperators under the same temptation value b and sucker payoff θ, and the cooperators can survive within a larger range of parameters. At the same time, a small cost can effectively maintain a high proportion of cooperators, while an appropriate cost will keep players at a high level of both the proportion of cooperators and the coexistence range. The continuous increase of costs will make our evolutionary mechanism ineffective and turn to static multigames. We also find that the introduction of costs will help different types of players coexist, and with the increase of costs, the coexistence area will first decrease and then increase. Moreover, our main findings are equally applicable to complex networks such as BA networks and random networks.

Eliminating poverty through social mobility promotes cooperation in social dilemmas

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.

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.

Coupling group selection and network reciprocity in social dilemmas through multilayer networks

Group selection and network reciprocity are two well-known mechanisms for cooperation. And while they have separately received ample attention for their ability to promote cooperation in social dilemmas, their joint effects in this regard are much less explored. Here we propose a multilayer network model that takes into account that not only individuals are connected by means of networks, but that also groups can be connected in much the same way. The model thus couples together network reciprocity and group selection, and it allows us to study their joint effect on the evolution of cooperation. We use the prisoner’s dilemma game as the paradigmatic social dilemma example, showing that the fine-tuning of evolution frequency and the imitation rate in the group network play key roles in determining the survival thresholds of cooperators. We also explore the importance of deterministic and stochastic updating rules, showing that the former provides more options to further promote cooperation. We discuss the importance of our findings for cooperation in structured interactions among groups and in higher-order networks.

Neighborhood size effects on the evolution of cooperation under myopic dynamics.

We study the evolution of cooperation in 2×2 social dilemma games in which players are located on a two-dimensional square lattice. During the evolution, each player modifies her strategy by means of myopic update dynamic to maximize her payoff while composing neighborhoods of different sizes, which are characterized by the corresponding radius, r. An investigation of the sublattice-ordered spatial structure for different values of r reveals that some patterns formed by cooperators and defectors can help the former to survive, even under untoward conditions. In contrast to individuals who resist the invasion of defectors by forming clusters due to network reciprocity, innovators spontaneously organize a socially divisive structure that provides strong support for the evolution of cooperation and advances better social systems.

The Role of Opinion Leaders in the Sustainable Development of Corporate-Led Consumer Advice Networks: Evidence from a Chinese Travel Content Community

Online community marketing and social media influencer marketing have aroused the interest of many researchers and practitioners around the world. Companies building online content communities to implement community marketing and influencer marketing has become a new corporate strategy, especially in the tourism and hotel industries in which experiential products are sold. However, based on the content community, maintaining the sustainable development of a consumer advice network composed of opinion leaders and consumers is a major challenge. This paper selects the travel content community of Qunar.com as the research object to study the role of opinion leaders in the sustainable development of corporate-led consumer advice networks (CANs). Empirical evidence based on network evolution data from 1356 “Hotel Sleep Testers” across 11 years shows that: (1) the creation and provision of information can obviously increase the probability of the relationship construction and increase the number of relationships, thus facilitating the formation of opinion leadership (OL); (2) active participation in interactions and withhigh-quality information brings greater effects; (3) the network structure variables, such as preferential attachment, structural equivalence, and similarity, can also better predict the probability of a potential relationship; and (4) reciprocity in consumer advice networks has no significant impact on the establishment of network relationships.

Bilateral costly expulsions resolve the public goods dilemma.

Expulsion has been found to promote cooperation in social dilemmas, but only if it does not incur costs or is applied unilaterally. Here, we show that removing both conditions leads to a spontaneous resolution of the costly expulsion problem. Namely, by studying the public goods game where cooperators and defectors can expel others at a personal cost, we find that public cooperation thrives as expulsion costs increase. This is counterintuitive, as the cost of other-regarding behaviour typically places an additional burden on cooperation, which is in itself costly. Such scenarios are referred to as second-order free-rider problems, and they typically require an additional mechanism, such as network reciprocity, to be resolved. We perform a mean field analysis of the public goods game with bilateral costly expulsion, showing analytically that the expected payoff difference between cooperators and defectors increases with expulsion costs as long as players with the same strategy have, on average, a higher frequency to interact with each other. As the latter condition is often satisfied in social networks, our results thus reveal a fascinating new path to public cooperation, and they show that the costs of well-intended actions need not be low for them to be effective.