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 investigate an evolutionary snowdrift game on a square N ： L × L lattice with periodic boundary conditions, where a population of no （no ≤ N） players located on the sites of this lattice can either coopera...We investigate an evolutionary snowdrift game on a square N ： L × L lattice with periodic boundary conditions, where a population of no （no ≤ N） players located on the sites of this lattice can either cooperate with or defect from their nearest neighbours. After each generation, every player moves with a certain probability p to one of the player＇s nearest empty sites. It is shown that, when p = 0, the cooperative behaviour can be enhanced in disordered structures. When p 〉 0, the effect of mobility on cooperation remarkably depends on the payoff parameter r and the density of individuals ρ （ρ = no/N）. Compared with the results of p = 0, for small r, the persistence of cooperation is enhanced at not too small values of p; whereas for large r, the introduction of mobility inhibits the emergence of cooperation at any p 〈 1; for the intermediate value of r, the cooperative behaviour is sometimes enhanced and sometimes inhibited, depending on the values of p and p. In particular, the cooperator density can reach its maximum when the values of p and p reach their respective optimal values. In addition, two absorbing states of all cooperators and all defectors can emerge respectively for small and large r in the case of p 〉 0.展开更多
We propose an evolutionary snowdrift game model for heterogeneous systems with two types of agents, in which the inner-directed agents adopt the memory-based updating rule while the copycat-like ones take the uncondit...We propose an evolutionary snowdrift game model for heterogeneous systems with two types of agents, in which the inner-directed agents adopt the memory-based updating rule while the copycat-like ones take the unconditional imitation rule; moreover, each＇agent can change his type to adopt another updating rule once the number he sequentially loses the game at is beyond his upper limit of tolerance. The cooperative behaviors of such heterogeneous systems are then investigated by Monte Carlo simulations. The numerical results show the equilibrium cooperation frequency and composition as functions of the cost-to-benefit ratio r are both of plateau structures with discontinuous steplike jumps, and the number of plateaux varies non-monotonically with the upper limit of tolerance VT as well as the initial composition of agents faO. Besides, the quantities of the cooperation frequency and composition are dependent crucially on the system parameters including VT, faO, and r. One intriguing observation is that when the upper limit of tolerance is small, the cooperation frequency will be abnormally enhanced with the increase of the cost-to-benefit ratio in the range of 0 〈 r 〈 1/4. We then probe into the relative cooperation frequencies of either type of agents, which are also of plateau structures dependent on the system parameters. Our results may be helpful to understand the cooperative behaviors of heterogenous agent systems.展开更多
In this paper,we study the influence of the size of interaction neighbors(k) on the evolution of cooperation in the spatial snowdrift game.At first,we consider the effects of noise K and cost-to-benefit ratio r,the si...In this paper,we study the influence of the size of interaction neighbors(k) on the evolution of cooperation in the spatial snowdrift game.At first,we consider the effects of noise K and cost-to-benefit ratio r,the simulation results indicate that the evolution of cooperation depends on the combined action of noise and cost-to-benefit ratio.For a lower r,the cooperators are multitudinous and the cooperation frequency ultimately increases to 1 as the increase of noise.However,for a higher r,the defectors account for the majority of the game and dominate the game if the noise is large enough.Then we mainly investigate how k influences the evolution of cooperation by varying the noise in detail.We find that the frequency of cooperators is closely related to the size of neighborhood and cost-to-benefit ratio r.In the case of lower r,the augmentation of k plays no positive role in promoting the cooperation as compared with that of k = 4,while for higher r the cooperation is improved for a growing size of neighborhood.At last,based on the above discussions,we explore the cluster-forming mechanism among the cooperators.The current results are beneficial to further understand the evolution of cooperation in many natural,social and biological systems.展开更多
We investigate the cooperative behavior and the phase separation in a coevolving system. Agents in the system constructed by a regular random network initially play the snowdrift game with their neighbors. They try to...We investigate the cooperative behavior and the phase separation in a coevolving system. Agents in the system constructed by a regular random network initially play the snowdrift game with their neighbors. They try to obtain a better competing environment by imitating a neighbor＇s more successful strategy or cutting the connection to a defective neighbor and randomly rewiring to another agent so as to seek a better neighborhood. The dynamic process of strategy imitation and relationship among agents due to rewiring neighbors may drive the system into different states. The simulation results show that there are three different phases in the q-r plane, where q is the rewiring probability and r is the cost-to-benefit ratio. One is a static phase of a pure cooperative cluster with a few isolated defectors. The other two belong to active phases with one of a main mixed-strategy cluster and the other of a pure defective state. We find that a simple mean field theory can predict correctly the static phase and the active phase of the main mixed-strategy cluster. The theoretical boundary line between the two phases is in good agreement with the simulation result.展开更多
Traffic issues have always received enthusiastic attention from the society.To better simulate the traffic environment,we use the well-known snowdrift game(SDG).Punishment has been regarded as a significant method to ...Traffic issues have always received enthusiastic attention from the society.To better simulate the traffic environment,we use the well-known snowdrift game(SDG).Punishment has been regarded as a significant method to promote cooperation.We propose a novel punishment mechanism and discuss its influence on the cooperation of the SDG.Considering that the snowball causes traffic jam,we add the role of the traffic police in the SDG.When the traffic police choose to cooperate,they have the right to punish the defectors.The scope of jurisdiction,the record of punishment and the method of deployment are decisive factors in deciding whether or not to punish the defectors and the severity of the punishment.Whether to sanction the defector and the severity of the punishment is jointly determined by the traffic police’s punishment record,jurisdiction,and deployment method.Through extensive simulation,we found that the difference between the two distribution methods becomes smaller as the jurisdiction becomes smaller.We need to choose the dominant distribution method based on the jurisdiction and the neighbor pattern.The results demonstrate that the punitive record,jurisdiction and distribution method all have an important impact on the SDG and traffic governance.展开更多
We propose a novel snowdrift game model with edge weighting mechanism to explore the cooperative behaviors among the players on the square lattice. Based on the assumption of three types of weight distribution includi...We propose a novel snowdrift game model with edge weighting mechanism to explore the cooperative behaviors among the players on the square lattice. Based on the assumption of three types of weight distribution including uniform, exponential and power-law schemes, the cooperation level is largely boosted in contrast with the traditional snowdrift game on the unweighted square lattice. Exten- sive numerical simulations indicate that the fraction of cooperators greatly augments, especially for the intermediate range of cost-to-benefit ratio r. Furthermore, we investigate how the cooperative behaviors are affected by the undulation amplitude of weight distribution and noise strength of strat- egy selection, respectively. The simulation results will be conducive to further understanding and analyzing the emergence of cooperation, which is a ubiquitous phenomenon in social and biological science.展开更多
Among complex network models,the hierarchical network model is the one most close to such real networks as world trade web,metabolic network,WWW,actor network,and so on.It has not only the property of power-law degree...Among complex network models,the hierarchical network model is the one most close to such real networks as world trade web,metabolic network,WWW,actor network,and so on.It has not only the property of power-law degree distribution,but also the scaling clustering coefficient property which Barabási-Albert(BA)model does not have.BA model is a model of network growth based on growth and preferential attachment,showing the scale-free degree distribution property.In this paper,we study the evolution of cooperation on a hierarchical network model,adopting the prisoner's dilemma(PD)game and snowdrift game(SG)as metaphors of the interplay between connected nodes.BA model provides a unifying framework for the emergence of cooperation.But interestingly,we found that on hierarchical model,there is no sign of cooperation for PD game,while the fre-quency of cooperation decreases as the common benefit decreases for SG.By comparing the scaling clustering coefficient prop-erties of the hierarchical network model with that of BA model,we found that the former amplifies the effect of hubs.Considering different performances of PD game and SG on complex network,we also found that common benefit leads to cooperation in the evolution.Thus our study may shed light on the emergence of cooperation in both natural and social environments.展开更多
We combine the Fermi and Moran update rules in the spatial prisoner＇s dilemma and snowdrift games to investigate the behavior of collective cooperation among agents on the regular lattice. Large-scale simulations ind...We combine the Fermi and Moran update rules in the spatial prisoner＇s dilemma and snowdrift games to investigate the behavior of collective cooperation among agents on the regular lattice. Large-scale simulations indicate that, compared to the model with only one update rule, the the role of update dynamics should be paid more attention in cooperation behavior exhibits the richer phenomena, and the evolutionary game theory. Meanwhile, we also observe that the introduction of Moran rule, which needs to consider all neighbor＇s information, can markedly promote the aggregate cooperation level, that is, randomly selecting the neighbor proportional to its payoff to imitate will facilitate the cooperation among agents. Current results will contribute to further understand the cooperation dynamics and evolutionary behaviors within many biological, economic and social systems.展开更多
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Project supported by the National Natural Science Foundation of China （Grant No 10775060）.
文摘We investigate an evolutionary snowdrift game on a square N ： L × L lattice with periodic boundary conditions, where a population of no （no ≤ N） players located on the sites of this lattice can either cooperate with or defect from their nearest neighbours. After each generation, every player moves with a certain probability p to one of the player＇s nearest empty sites. It is shown that, when p = 0, the cooperative behaviour can be enhanced in disordered structures. When p 〉 0, the effect of mobility on cooperation remarkably depends on the payoff parameter r and the density of individuals ρ （ρ = no/N）. Compared with the results of p = 0, for small r, the persistence of cooperation is enhanced at not too small values of p; whereas for large r, the introduction of mobility inhibits the emergence of cooperation at any p 〈 1; for the intermediate value of r, the cooperative behaviour is sometimes enhanced and sometimes inhibited, depending on the values of p and p. In particular, the cooperator density can reach its maximum when the values of p and p reach their respective optimal values. In addition, two absorbing states of all cooperators and all defectors can emerge respectively for small and large r in the case of p 〉 0.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11175131 and 10875086)
文摘We propose an evolutionary snowdrift game model for heterogeneous systems with two types of agents, in which the inner-directed agents adopt the memory-based updating rule while the copycat-like ones take the unconditional imitation rule; moreover, each＇agent can change his type to adopt another updating rule once the number he sequentially loses the game at is beyond his upper limit of tolerance. The cooperative behaviors of such heterogeneous systems are then investigated by Monte Carlo simulations. The numerical results show the equilibrium cooperation frequency and composition as functions of the cost-to-benefit ratio r are both of plateau structures with discontinuous steplike jumps, and the number of plateaux varies non-monotonically with the upper limit of tolerance VT as well as the initial composition of agents faO. Besides, the quantities of the cooperation frequency and composition are dependent crucially on the system parameters including VT, faO, and r. One intriguing observation is that when the upper limit of tolerance is small, the cooperation frequency will be abnormally enhanced with the increase of the cost-to-benefit ratio in the range of 0 〈 r 〈 1/4. We then probe into the relative cooperation frequencies of either type of agents, which are also of plateau structures dependent on the system parameters. Our results may be helpful to understand the cooperative behaviors of heterogenous agent systems.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 60904063 and 60673046Tianjin municipal Natural Science Foundation under Grant No. 11JCYBJC06600the Development Fund of Science and Technology for the Higher Education in Tianjin under Grant No. 20090813
文摘In this paper,we study the influence of the size of interaction neighbors(k) on the evolution of cooperation in the spatial snowdrift game.At first,we consider the effects of noise K and cost-to-benefit ratio r,the simulation results indicate that the evolution of cooperation depends on the combined action of noise and cost-to-benefit ratio.For a lower r,the cooperators are multitudinous and the cooperation frequency ultimately increases to 1 as the increase of noise.However,for a higher r,the defectors account for the majority of the game and dominate the game if the noise is large enough.Then we mainly investigate how k influences the evolution of cooperation by varying the noise in detail.We find that the frequency of cooperators is closely related to the size of neighborhood and cost-to-benefit ratio r.In the case of lower r,the augmentation of k plays no positive role in promoting the cooperation as compared with that of k = 4,while for higher r the cooperation is improved for a growing size of neighborhood.At last,based on the above discussions,we explore the cluster-forming mechanism among the cooperators.The current results are beneficial to further understand the evolution of cooperation in many natural,social and biological systems.
文摘We investigate the cooperative behavior and the phase separation in a coevolving system. Agents in the system constructed by a regular random network initially play the snowdrift game with their neighbors. They try to obtain a better competing environment by imitating a neighbor＇s more successful strategy or cutting the connection to a defective neighbor and randomly rewiring to another agent so as to seek a better neighborhood. The dynamic process of strategy imitation and relationship among agents due to rewiring neighbors may drive the system into different states. The simulation results show that there are three different phases in the q-r plane, where q is the rewiring probability and r is the cost-to-benefit ratio. One is a static phase of a pure cooperative cluster with a few isolated defectors. The other two belong to active phases with one of a main mixed-strategy cluster and the other of a pure defective state. We find that a simple mean field theory can predict correctly the static phase and the active phase of the main mixed-strategy cluster. The theoretical boundary line between the two phases is in good agreement with the simulation result.
基金the National Natural Science Foundation of China(No.62073270)the State Ethnic Affairs Commission Innovation Research Team and Innovative Research Team of the Education Department of Sichuan Province(No.15TD0050)the Fundamental Research Funds for the Central Universities,Southwest Minzu University(No.2021NYYXS38)。
文摘Traffic issues have always received enthusiastic attention from the society.To better simulate the traffic environment,we use the well-known snowdrift game(SDG).Punishment has been regarded as a significant method to promote cooperation.We propose a novel punishment mechanism and discuss its influence on the cooperation of the SDG.Considering that the snowball causes traffic jam,we add the role of the traffic police in the SDG.When the traffic police choose to cooperate,they have the right to punish the defectors.The scope of jurisdiction,the record of punishment and the method of deployment are decisive factors in deciding whether or not to punish the defectors and the severity of the punishment.Whether to sanction the defector and the severity of the punishment is jointly determined by the traffic police’s punishment record,jurisdiction,and deployment method.Through extensive simulation,we found that the difference between the two distribution methods becomes smaller as the jurisdiction becomes smaller.We need to choose the dominant distribution method based on the jurisdiction and the neighbor pattern.The results demonstrate that the punitive record,jurisdiction and distribution method all have an important impact on the SDG and traffic governance.
文摘We propose a novel snowdrift game model with edge weighting mechanism to explore the cooperative behaviors among the players on the square lattice. Based on the assumption of three types of weight distribution including uniform, exponential and power-law schemes, the cooperation level is largely boosted in contrast with the traditional snowdrift game on the unweighted square lattice. Exten- sive numerical simulations indicate that the fraction of cooperators greatly augments, especially for the intermediate range of cost-to-benefit ratio r. Furthermore, we investigate how the cooperative behaviors are affected by the undulation amplitude of weight distribution and noise strength of strat- egy selection, respectively. The simulation results will be conducive to further understanding and analyzing the emergence of cooperation, which is a ubiquitous phenomenon in social and biological science.
基金Project supported by the Natural Science Foundation of ZhejiangProvince, China (No. Y105697)the Ningbo Natural ScienceFoundation,China (No. 2005A610004)
文摘Among complex network models,the hierarchical network model is the one most close to such real networks as world trade web,metabolic network,WWW,actor network,and so on.It has not only the property of power-law degree distribution,but also the scaling clustering coefficient property which Barabási-Albert(BA)model does not have.BA model is a model of network growth based on growth and preferential attachment,showing the scale-free degree distribution property.In this paper,we study the evolution of cooperation on a hierarchical network model,adopting the prisoner's dilemma(PD)game and snowdrift game(SG)as metaphors of the interplay between connected nodes.BA model provides a unifying framework for the emergence of cooperation.But interestingly,we found that on hierarchical model,there is no sign of cooperation for PD game,while the fre-quency of cooperation decreases as the common benefit decreases for SG.By comparing the scaling clustering coefficient prop-erties of the hierarchical network model with that of BA model,we found that the former amplifies the effect of hubs.Considering different performances of PD game and SG on complex network,we also found that common benefit leads to cooperation in the evolution.Thus our study may shed light on the emergence of cooperation in both natural and social environments.
基金Supported by the National Natural Science Foundation of China under Grant No.60904063Tianjin Municipal Natural Science Foundation under Grant No.11JCYBJC06600+1 种基金the Development Fund of Science and Technology for the Higher Education in Tianjin under Grant No.20090813the 7th Overseas Training Project for the Young and Middle Teachers in Tianjin Municipal Universities
文摘We combine the Fermi and Moran update rules in the spatial prisoner＇s dilemma and snowdrift games to investigate the behavior of collective cooperation among agents on the regular lattice. Large-scale simulations indicate that, compared to the model with only one update rule, the the role of update dynamics should be paid more attention in cooperation behavior exhibits the richer phenomena, and the evolutionary game theory. Meanwhile, we also observe that the introduction of Moran rule, which needs to consider all neighbor＇s information, can markedly promote the aggregate cooperation level, that is, randomly selecting the neighbor proportional to its payoff to imitate will facilitate the cooperation among agents. Current results will contribute to further understand the cooperation dynamics and evolutionary behaviors within many biological, economic and social systems.
