We propose a simple mechanism for generating scale-free networks with degree exponent γ=3, where the new node is connected to the existing nodes by step-by-step random walk. It is found that the clique-degree distrib...We propose a simple mechanism for generating scale-free networks with degree exponent γ=3, where the new node is connected to the existing nodes by step-by-step random walk. It is found that the clique-degree distribution based on our model obeys a power-law form, which is in agreement with the recently empirical evidences. In addition, our model displays the small-world effect and the hierarchical structure.展开更多
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 ne...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.展开更多
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 ...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.展开更多
In this paper, we introduce an asymmetric payoff distribution mechanism into the evolutionary prisoner＇s dilemma game （PDG） on Newman Watts social networks, and study its effects on the evolution of cooperation. Th...In this paper, we introduce an asymmetric payoff distribution mechanism into the evolutionary prisoner＇s dilemma game （PDG） on Newman Watts social networks, and study its effects on the evolution of cooperation. The asymmetric payoff distribution mechanism can be adjusted by the parameter α： if α〉 0, the rich will exploit the poor to get richer; if α 〈 0, the rich are forced to offer part of their income to the poor. Numerical results show that the cooperator frequency monotonously increases with c~ and is remarkably promoted when c~ 〉 0. The effects of updating order and self-interaction are also investigated. The co-action of random updating and self-interaction can induce the highest cooperation level. Moreover, we employ the Gini coefficient to investigate the effect of asymmetric payoff distribution on the the system＇s wealth distribution. This work may be helpful for understanding cooperative behaviour and wealth inequality in society.展开更多
We propose a new two-type-player prisoner＇s dilemma game based on the division of work on a square lattice, in which a fraction of the population μ are assigned type A and the rest B. In a one-shot two-player game, ...We propose a new two-type-player prisoner＇s dilemma game based on the division of work on a square lattice, in which a fraction of the population μ are assigned type A and the rest B. In a one-shot two-player game, we let both of their original payoffs be scaled by a same multiplicative factor α 〉 1, if two neighboring players are of different types; however we leave the payoffs unchanged if they are of the same type. Then we show that combined with the two-type setup, the square lattice can assist to induce different social ranks according to players＇ abilities to collect payoffs. Simulation results show that the density of cooperation is significantly promoted for a wide range of the temptation to defection parameters and that there are optimal values for both α and μ leading to the maximal cooperation level. We reach these results by analyzing the distribution of the players in the social ranks and we also show some typical snapshots of the system.展开更多
We investigate the naming game on geometric networks. The geometric networks are constructed by adding geometric links to two-dimensional regular lattices. It is found that the agreement time is a non-monotonic functi...We investigate the naming game on geometric networks. The geometric networks are constructed by adding geometric links to two-dimensional regular lattices. It is found that the agreement time is a non-monotonic function of the geometric distance and there exists an optimal value of the geometric distance resulting in the shortest agreement time. All these results show that the geometric distance plays an important role in the evolutionary process of the language game. Our results also show that the convergence time strongly depends on the number of adding links.展开更多
Based on previous works, we give further investigations on the Prisoners＇ Dilemma Game （PDG） on two different types of homogeneous networks, i.e. the homogeneous small-world network （HSWN） and the regular ring gr...Based on previous works, we give further investigations on the Prisoners＇ Dilemma Game （PDG） on two different types of homogeneous networks, i.e. the homogeneous small-world network （HSWN） and the regular ring graph. We find that the so-called resonance-like character can occur on both the networks. Different from the viewpoint in previous publications, we think the small-world effect may be unnecessary to produce this character. Therefore, over these two types of networks, we suggest a common understanding in the viewpoint of clustering coefficient. Detailed simulation results can sustain our viewpoint quite well. Furthermore, we investigate the Snowdrift Game （SG） on the same networks. The difference between the outputs of the PDG and the SG can also sustain our viewpoint.展开更多
The naming game is a model of nonequilibrium dynamics for the self-organized emergence of a language or a communication system. We study a modified version of the minimal naming game in which the speaker selects a wor...The naming game is a model of nonequilibrium dynamics for the self-organized emergence of a language or a communication system. We study a modified version of the minimal naming game in which the speaker selects a word from its inventory with a probability proportional to exp（Rs ＊ α）, where Rs is the success ratio of the name and α is a tunable parameter. By investigating the effects of α on the evolutionary processes for both square lattice and scale-free networks, we find that the convergence time decreases with the increasing α on both two networks, which indicates that preferential selection of successful words can accelerate the reaching of consensus. More interestingly, for α 〉 0, we find that the relation between convergence time and α exhibits a power-law form.展开更多
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....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.展开更多
基金Supported by the National Basic Research Programme of China under Grant No 2006CB705500, the National Natural Science Foundation of China under Grant Nos 60744003, 10635040, 10532060 and 10472116, the Special Research Funds for Theoretical Physics Frontier Problems （NSFC Nos 10547004 and A0524701）, the President Funding of Chinese Academy of Sciences, and the Specialized Research Fund for the Doctoral Programme of Higher Education of China.
文摘We propose a simple mechanism for generating scale-free networks with degree exponent γ=3, where the new node is connected to the existing nodes by step-by-step random walk. It is found that the clique-degree distribution based on our model obeys a power-law form, which is in agreement with the recently empirical evidences. In addition, our model displays the small-world effect and the hierarchical structure.
基金supported by the National Basic Research Program of China (No 2006CB705500)the National Natural Science Foundation of China (Grant Nos 60744003, 10635040, 10532060 and 10472116)the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘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.
基金Supported by the National Basic Research Programme of China under Grant No 2006CB705500, the National Natural Science Foundation of China under Grant Nos 60744003, 10635040, 10532060, and 10472116, by the Special Research Funds for Theoretical Physics Frontier Problems （NSFC No 10547004 and A0524701）, the President Funding of Chinese Academy of Sciences, and the Specialized Research Fund for the Doctoral Programme of Higher Education of China.
文摘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.
基金Project supported by the Major State Basic Research Development Program of China (Grant No. 2004CB318109)Program for New Century Excellent Talents in University of China (Grant No. NCET-07-0787)the National Natural Science Foundation of China (Grant No. 70601026)
文摘In this paper, we introduce an asymmetric payoff distribution mechanism into the evolutionary prisoner＇s dilemma game （PDG） on Newman Watts social networks, and study its effects on the evolution of cooperation. The asymmetric payoff distribution mechanism can be adjusted by the parameter α： if α〉 0, the rich will exploit the poor to get richer; if α 〈 0, the rich are forced to offer part of their income to the poor. Numerical results show that the cooperator frequency monotonously increases with c~ and is remarkably promoted when c~ 〉 0. The effects of updating order and self-interaction are also investigated. The co-action of random updating and self-interaction can induce the highest cooperation level. Moreover, we employ the Gini coefficient to investigate the effect of asymmetric payoff distribution on the the system＇s wealth distribution. This work may be helpful for understanding cooperative behaviour and wealth inequality in society.
基金Supported by the National Basic Research Program of China under Grant No 2006CB705500, the National Natural Science Foundation of China under Grant Nos 60744003, 10635040 and 10532060, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No 20060358065, and the National Science Fund for Fostering Talents in Basic Science （J0630319）.
文摘We propose a new two-type-player prisoner＇s dilemma game based on the division of work on a square lattice, in which a fraction of the population μ are assigned type A and the rest B. In a one-shot two-player game, we let both of their original payoffs be scaled by a same multiplicative factor α 〉 1, if two neighboring players are of different types; however we leave the payoffs unchanged if they are of the same type. Then we show that combined with the two-type setup, the square lattice can assist to induce different social ranks according to players＇ abilities to collect payoffs. Simulation results show that the density of cooperation is significantly promoted for a wide range of the temptation to defection parameters and that there are optimal values for both α and μ leading to the maximal cooperation level. We reach these results by analyzing the distribution of the players in the social ranks and we also show some typical snapshots of the system.
基金Supported by the National Basic Research Program of China under Grant No 2006CB705500, the National Natural Science Foundation of China under Grant Nos 10975126 and 10635040, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No 20093402110032, and the Scientific Research Fund of Sichuan Provincial Education Department （08ZA037, 09ZA103）.
文摘We investigate the naming game on geometric networks. The geometric networks are constructed by adding geometric links to two-dimensional regular lattices. It is found that the agreement time is a non-monotonic function of the geometric distance and there exists an optimal value of the geometric distance resulting in the shortest agreement time. All these results show that the geometric distance plays an important role in the evolutionary process of the language game. Our results also show that the convergence time strongly depends on the number of adding links.
基金Supported by the National Basic Research Programme of China under Grant No 2006CB705500, the National Natural Science Foundation of China under Grant Nos 60744003, 10635040, 10532060, 10472116 and 10404025, and the Specialized Research Fund for the Doctoral Programme of Higher Education of China.
文摘Based on previous works, we give further investigations on the Prisoners＇ Dilemma Game （PDG） on two different types of homogeneous networks, i.e. the homogeneous small-world network （HSWN） and the regular ring graph. We find that the so-called resonance-like character can occur on both the networks. Different from the viewpoint in previous publications, we think the small-world effect may be unnecessary to produce this character. Therefore, over these two types of networks, we suggest a common understanding in the viewpoint of clustering coefficient. Detailed simulation results can sustain our viewpoint quite well. Furthermore, we investigate the Snowdrift Game （SG） on the same networks. The difference between the outputs of the PDG and the SG can also sustain our viewpoint.
基金Supported by the National Basic Research Program of China under Grant No 2006CB705500, the National Natural Science Foundation of China under Grant Nos 10975126 and 10635040, and the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No 20093402110032.
文摘The naming game is a model of nonequilibrium dynamics for the self-organized emergence of a language or a communication system. We study a modified version of the minimal naming game in which the speaker selects a word from its inventory with a probability proportional to exp（Rs ＊ α）, where Rs is the success ratio of the name and α is a tunable parameter. By investigating the effects of α on the evolutionary processes for both square lattice and scale-free networks, we find that the convergence time decreases with the increasing α on both two networks, which indicates that preferential selection of successful words can accelerate the reaching of consensus. More interestingly, for α 〉 0, we find that the relation between convergence time and α exhibits a power-law form.
基金Supported by the National Basic Research Programme of China under Grant No 2006CB705500, the National Natural Science Foundation of China under Grant Nos 60744003, 10635040, 10532060 and 10472116, the Special Research Funds for Theoretical Physics Frontier Problems （NSFC 10547004 and A0524701）, the President Funding of Chinese Academy of Sciences, and by the Specialized Research Fund for the Doctoral Programme of Higher Education of China.
文摘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.
