Prisoner's Dilemma Game on Two Types of Positively Correlated Networks

We study the effects of degree correlations on the evolution of cooperation in the prisoner＇s dilemma game with individuals located on two types of positively correlated networks. It is shown that the positive degree correlation can either promote or inhibit the emergence of cooperation depending on network configurations. Furthermore, we investigate the probability to cooperate as a function of connectivity degree, and find that high-degree individuals generally have a higher tendency to cooperate. Finally, it is found that small-degree individuals usually change their strategy more frequently, and such change is shown to be unfavourable to cooperation for both kinds of networks.     

Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network

Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency (wave number) of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.     

Cooperative Dynamics in Lattice-Embedded Scale-Free Networks

We investigate cooperative behaviors of lattice-embedded scale-free networking agents in the prisoner＇s dilemma game model by employing two initial strategy distribution mechanisms, which are specific distribution to the most connected sites （hubs） and random distribution. Our study indicates that the game dynamics crucially depends on the underlying spatial network structure with different strategy distribution mechanism. The cooperators＇ specific distribution contributes to an enhanced level of cooperation in the system compared with random one, and cooperation is robust to cooperators＇ specific distribution but fragile to defectors＇ specific distribution. Especially, unlike the specific case, increasing heterogeneity of network does not always favor the emergence of cooperation under random mechanism. Furthermore, we study the geographical effects and find that the graphically constrained network structure tends to improve the evolution of cooperation in random case and in specific one for a large temptation to defect.     

Prisoner＇s Dilemma Game with Nonlinear Attractive Effect on Regular Small-World Networks

We investigate a spatial Prisoner＇s Dilemma game with nonlinear attractive effect on regular small-world networks. The players located on the sites of networks can either cooperate with their neighbours or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbours with a probability proportional to .A^α denoting the attractiveness of the neighbour, where .4 is the collected payoff and ^α （-〉0） is a free parameter characterizing the extent of nonlinear effect. Then each player adopts its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density pc of cooperators in the stationary state for various values of α and the rewiring probability q of the network. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect for the same network structures. We also point out that long-range connections either enhance or inhibit the cooperation, which depends on the value of α and the payoff parameter b.     

Prisoner's Dilemma on Co-Evolving Networks without Strategy Update

We investigate the game theory in a structured population with the assumption that the evolution of network structure is far faster than that of strategy update. We find that the degree distribution for the finM network consists of two distinct parts： the low degree part which is contributed to by defectors and a broadband in the regime with high degree which is formed by cooperators. The structure of the final network and the final strategy pattern have also been numerically proved to be independent of the game parameters.     

Co-evolution of the brand effect and competitiveness in evolving networks

The principle that ‘the brand effect is attractive’ underlies the preferential attachment. Here we show that the brand effect is just one dimension of attractiveness. Another dimension is competitiveness. We firstly introduce a general framework that allows us to investigate the competitive aspect of real networks, instead of simply preferring popular nodes. Our model accurately describes the evolution of social and technological networks. The phenomenon that more competitive nodes become richer can help us to understand the evolution of many competitive systems in nature and society. In general,the paper provides an explicit analytical expression of degree distributions of the network. In particular, the model yields a nontrivial time evolution of nodes’ properties and the scale-free behavior with exponents depending on the microscopic parameters characterizing the competition rules. Secondly, through theoretical analyses and numerical simulations, we reveal that our model has not only the universality for the homogeneous weighted network, but also the character for the heterogeneous weighted network. Thirdly, we also develop a model based on the profit-driven mechanism. It can better describe the observed phenomenon in enterprise cooperation networks. We show that the standard preferential attachment,the growing random graph, the initial attractiveness model, the fitness model, and weighted networks can all be seen as degenerate cases of our model.     

Clustering Effect on the Evolution of Cooperation in a Herding Snowdrift Game

We study the evolution of cooperation for two cluster breaking mechanisms in a herding snowdrift game. The cooperative behavior is observed to be related to the duster size. A negative dependence of the payoff parameter r on cooperative behavior is discovered. For a low r, herding helps promote the cooperation, whereas for a high r, herding tends to prevent cooperative behavior.     

Evolutionary Prisoners' Dilemma Game on Scale-Free Networks with Degree-Degree Correlation

Degree-degree correlation and heterogeneity in degree are important topological properties characterizing scale-free networks. We consider an evolutionary prisoners＇ dilemma game on scale-free networks and investigate how degree-degree correlation influences cooperation. It is found that the cooperator frequency displays resonance-like behavior with the variation of Pearson correlation coefficient. A measure on local heterogeneity in a network is proposed and it is realized that cooperation is proportional to the local heterogeneity.     

Evolutionary snowdrift game on heterogeneous Newman--Watts small-world network

We study the evolutionary snowdrift game in a heterogeneous Newman-Watts small-world network. The heterogeneity of the network is controlled by the number of hubs. It is found that the moderate heterogeneity of the network can promote the cooperation best. Besides, we study how the hubs affect the evolution of cooperative behaviours of the heterogeneous Newman-Watts small-world network. Simulation results show that both the initial states of hubs and the connections between hubs can play an important role. Our work gives a further insight into the effect of hubs on the heterogeneous networks.     

Evolutionary prisoner’s dilemma game on highly clustered community networks

This paper studies the evolutionary prisoner's dilemma game on a highly clustered community network in which the clustering coefficient and the community size can be tuned. It finds that the clustering coefficient in such a degree-homogeneous network inhibits the emergence of cooperation for the entire range of the payoff parameter. Moreover, it finds that the community size can also have a marked influence on the evolution of cooperation, with a larger community size leading to not only a lower cooperation level but also a smaller threshold of the payoff parameter above which cooperators become extinct.     

Load-dependent random walks on complex networks

Load-dependent random walks are used to investigate the evolution of load distribution in transportation network systems. The walkers hop to a node according to node load of the last time step. The preference of walks leads to a change in the load distribution. It changes from degree-dependent distribution in the case of non-preference walks to eigenvector-centrality-dependent distribution. By numerical simulations, it is shown that the network heterogeneity has a influence on the effect of walk preference. In the cascading failure phenomenon, an appropriate degree correlation can guarantee a low risk of cascading failures.     

Diversity of reproduction rate supports cooperation in the prisoner's dilemma game on complex networks

In human societies the probability of strategy adoption from a given person may be affected by the personal features. Now we investigate how an artificially imposed restricted ability to reproduce, overruling ones fitness, affects an evolutionary process. For this purpose we employ the evolutionary prisoner's dilemma game on different complex graphs. Reproduction restrictions can have a facilitative effect on the evolution of cooperation that sets in irrespective of particularities of the interaction network. Indeed, an appropriate fraction of less fertile individuals may lead to full supremacy of cooperators where otherwise defection would be widespread. By studying cooperation levels within the group of individuals having full reproduction capabilities, we reveal that the recent mechanism for the promotion of cooperation is conceptually similar to the one reported previously for scale-free networks. Our results suggest that the diversity in the reproduction capability, related to inherently different attitudes of individuals, can enforce the emergence of cooperative behavior among selfish competitors.     

Evolution of Cooperation in Continuous Prisoner's Dilemma Games on Barabasi-Albert Networks with Degree-Dependent Guilt Mechanism

This paper studies the continuous prisoner's dilemma games (CPDG) on Barabasi-Albert (BA) networks. In the model, each agent on a vertex of the networks makes an investment and interacts with all of his neighboring agents. Making an investment is costly, but which benefits its neighboring agents, where benefit and cost depend on the level of investment made. The payoff of each agent is given by the sum of payoffs it receives in its interactions with all its neighbors. Not only payoff, individual's guilty emotion in the games has also been considered. The negative guilty emotion produced in comparing with its neighbors can reduce the utility of individuals directly. We assume that the reduction amount depends on the individual's degree and a baseline level parameter. The group's cooperative level is characterized by the average investment of the population. Each player makes his investment in the next step based on a convex combination of the investment of his best neighbors in the last step, his best history strategies in the latest steps which number is controlled by a memory length parameter, and a uniformly distributed random number. Simulation results show that this degree-dependent guilt mechanism can promote the evolution of cooperation dramatically comparing with degree-independent guilt or no guilt cases. Imitation, memory, uncertainty coefficients and network structure also play determinant roles in the cooperation level of the population. All our results may shed some new light on studying the evolution of cooperation based on network reciprocity mechanisms.     

Spatial Games Based on Pursuing the Highest Average Payoff

We propose a strategy updating mechanism based on pursuing the highest average payoff to investigate the prisoner＇s dilemma game and the snowdrift game. We apply the new rule to investigate cooperative behaviours on regular, small-world, scale-free networks, and find spatial structure can maintain cooperation for the prisoner＇s dilemma game. fn the snowdrift game, spatial structure can inhibit or promote cooperative behaviour which depends on payoff parameter. We further study cooperative behaviour on scale-free network in detail. Interestingly, non-monotonous behaviours observed on scale-free network with middle-degree individuals have the lowest cooperation level. We also find that large-degree individuals change their strategies more frequently for both games.     

Promoting cooperation in social dilemmas via simple coevolutionary rules

We study the evolution of cooperation in structured populations within popular models of social dilemmas, whereby simple coevolutionary rules are introduced that may enhance players abilities to enforce their strategy on the opponent. Coevolution thus here refers to an evolutionary process affecting the teaching activity of players that accompanies the evolution of their strategies. Particularly, we increase the teaching activity of a player after it has successfully reproduced, yet we do so depending on the disseminated strategy. We separately consider coevolution affecting either only the cooperators or only the defectors, and show that both options promote cooperation irrespective of the applied game. Opposite to intuitive reasoning, however, we reveal that the coevolutionary promotion of players spreading defection is, in the long run, more beneficial for cooperation than the likewise promotion of cooperators. We explain the contradictive impact of the two considered coevolutionary rules by examining the differences between resulting heterogeneities that segregate participating players, and furthermore, demonstrate that the influential individuals completely determine the final outcome of the games. Our findings are immune to changes defining the type of considered social dilemmas and highlight that the heterogeneity of players, resulting in a positive feedback mechanism, is a fundamental property promoting cooperation in groups of selfish individuals.     

Competition-driven network dynamics: emergence of a scale-free leadership structure and collective efficiency

Using the minority game as a model for competition dynamics, we investigate the effects of interagent communications across a network on the global evolution of the game. Agent communication across this network leads to the formation of an influence network, which is dynamically coupled to the evolution of the game, and it is responsible for the information flow driving the agents' actions. We show that the influence network spontaneously develops hubs with a broad distribution of in-degrees, defining a scale-free robust leadership structure. Furthermore, in realistic parameter ranges, facilitated by information exchange on the network, agents can generate a high degree of cooperation making the collective almost maximally efficient.     

Influence of the variance of degree distributions on the evolution of cooperation in complex networks

We study how initial network structure affects the evolution of cooperation in a spatial prisoner’s dilemma game. The network structure is characterized by various statistical properties. Among those properties, we focus on the variance of the degree distribution, and inquire how it affects the evolution of cooperation by three methods of imitation. For every method, it was found that a scale-free network does not always promote the evolution of cooperation, and that there exists an appropriate value of the variance, at which cooperation is optimal.     

Evolutionary Prisoner's Dilemma Game Based on Pursuing Higher Average Payoff

We investigate the prisoner＇s dilemma game based on a new rule： players will change their current strategies to opposite strategies with some probability if their neighbours＇ average payoffs are higher than theirs. Compared with the cases on regular lattices （RL） and Newman-Watts small world network （NW）, cooperation can be best enhanced on the scale-free Barabasi-Albert network （BA）. It is found that cooperators are dispersive on RL network, which is different from previously reported results that cooperators will form large clusters to resist the invasion of defectors. Cooperative behaviours on the BA network are discussed in detail. It is found that large-degree individuals have lower cooperation level and gain higher average payoffs than that of small-degree individuals. In addition, we find that small-degree individuals more frequently change strategies than do large- degree individuals.     

Cooperation and charity in spatial public goods game under different strategy update rules

Human cooperation can be influenced by other human behaviors and recent years have witnessed the flourishing of studying the coevolution of cooperation and punishment, yet the common behavior of charity is seldom considered in game-theoretical models. In this article, we investigate the coevolution of altruistic cooperation and egalitarian charity in spatial public goods game, by considering charity as the behavior of reducing inter-individual payoff differences. Our model is that, in each generation of the evolution, individuals play games first and accumulate payoff benefits, and then each egalitarian makes a charity donation by payoff transfer in its neighborhood. To study the individual-level evolutionary dynamics, we adopt different strategy update rules and investigate their effects on charity and cooperation. These rules can be classified into two global rules: random selection rule in which individuals randomly update strategies, and threshold selection rule where only those with payoffs below a threshold update strategies. Simulation results show that random selection enhances the cooperation level, while threshold selection lowers the threshold of the multiplication factor to maintain cooperation. When charity is considered, it is incapable in promoting cooperation under random selection, whereas it promotes cooperation under threshold selection. Interestingly, the evolution of charity strongly depends on the dispersion of payoff acquisitions of the population, which agrees with previous results. Our work may shed light on understanding human egalitarianism.