Self-serving,rational agents sometimes cooperate to their mutual benefit.The two-player iterated prisoner′s dilemma game is a model for including the emergence of cooperation.It is generally believed that there is no...Self-serving,rational agents sometimes cooperate to their mutual benefit.The two-player iterated prisoner′s dilemma game is a model for including the emergence of cooperation.It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants.The zero-determinant strategy in the iterated prisoner′s dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents.However,strategies in the prisoner′s dilemma game are only two strategies.Are there these results for general multi-strategy games?To address this question,the paper develops a theory for zero-determinant strategies for multi-strategy games,with any number of strategies.The analytical results exhibit a similar yet different scenario to the case of two-strategy games.The results are also applied to the Snowdrift game,the Hawk-Dove game and the Chicken game.展开更多
In our society, it is a major issue to enhance cooperative behaviors. Without this, our society fall into social dilemma situations, and gets worse and worse. Such a situation in an organization leads to violation of ...In our society, it is a major issue to enhance cooperative behaviors. Without this, our society fall into social dilemma situations, and gets worse and worse. Such a situation in an organization leads to violation of social or organizational rules, and at the worst case it suffers from serious accidents or scandals. Therefore, it is important for organizational managers to make efforts and take measures to enhance cooperative behaviors. Although there seem to be many ways to constantly elicit cooperative behaviors, the punishment is one of the most effective measures for enhancing cooperation. This study focused on the effects of penalty and probability of the revelation of defection on the cooperation, and getting insight into how punishment strategy should be used to get rid of social dilemmas and enhance cooperation. This study conducted a simulation experiment to find the proper penal regulations condition that can suppress violations （defective behavior） in a 2-person prisoner＇s dilemma situation. The effects of probability of the revelation of defection and penalty to revelation on the cooperative behavior were identified with the interactive effect of both experimental factors. The defection （uncooperative behavior） decreased when the penalty to the defection was heavy and the probability of the revelation of defection was low than that when the penalty to the defection was light and the probability of the revelation of the defection was high.展开更多
In this work, we consider an evolutionary prisoner＇s dilemma game on a homogeneous random network with the richest-following strategy adoption rule. By constructing homogeneous random networks from a regular ring gra...In this work, we consider an evolutionary prisoner＇s dilemma game on a homogeneous random network with the richest-following strategy adoption rule. By constructing homogeneous random networks from a regular ring graph, we investigate the effects of topologicaJ randomness on cooperation. In contrast to the ordinary view that the presence of smaJ1 amount of shortcuts in ring graphs favors cooperation, we find the cooperation inhibition by weak topological randomness. The explanations on the observations are presented.展开更多
We investigate the evolutionary prisoner＇s dilemma game in structured populations by introducing dimers, which are defined as that two players in each dimer always hold a same strategy. We find that influences of dim...We investigate the evolutionary prisoner＇s dilemma game in structured populations by introducing dimers, which are defined as that two players in each dimer always hold a same strategy. We find that influences of dimets on cooperation depend on the type of dimers and the population structure. For those dimers in which players interact with each other, the cooperation level increases with the number of dimers though the cooperation improvement level depends on the type of network structures. On the other hand, the dimers, in which there are not mutual interactions, will not do any good to the cooperation level in a single community, but interestingly, will improve the cooperation level in a population with two communities. We explore the relationship between dimers and self-interactions and find that the effects of dimers are similar to that of self-interactions. Also, we find that the dimers, which are established over two communities in a multi-community network, act as one type of interaction through which information between communities is communicated by the requirement that two players in a dimer hold a same strategy.展开更多
We study a spectrum sharing problem where multiple systems coexist and interfere with each other. First, an analysis is proposed for distributed spectrum sharing based on Prisoners' Dilemma (PD) in Cognitive Radio...We study a spectrum sharing problem where multiple systems coexist and interfere with each other. First, an analysis is proposed for distributed spectrum sharing based on Prisoners' Dilemma (PD) in Cognitive Radios (CRs). In one-shot game, selfish and rational CRs greedily full spread their own spectrum space in order to maximize their own rates, which leads to Nash Equilibrium (N.E.). But with long term interaction, i.e., Iterated Prisoner's Dilemma (IPD), CRs can come to cooperate and acquire the social optimal point by using different evolutionary strategies such as Tit For Tat (TFT), Generous TFT (GTFT), etc. Also we compare the performances of the different evolutionary strategies in noise-free and noisy environments for two-player games. Finally, N-player IPD (N-IPD) is simulated to verify our conclusions that TFT is a good strategy for spectrum sharing in CRs.展开更多
As a basic study to prevent accidents or concealment caused by violation of rules or regulations （which are regarded as uncooperative behavior）, an attempt was made to clarify the condition necessary for promoting c...As a basic study to prevent accidents or concealment caused by violation of rules or regulations （which are regarded as uncooperative behavior）, an attempt was made to clarify the condition necessary for promoting cooperation when the tit-for-tat strategy is adopted in the finite and repeated prisoner＇s dilemma situations. A mathematical model, in which three different strategies （tit-for-tat, all defection （individualism）, and all cooperation （altruism）） exist, was constructed in order to demonstrate the condition that can promote cooperative behaviors. As a result of an agent-agent computer simulation, it was shown that the tit-for-tat strategy promoted more cooperation than other strategies when the number of agents adopting the tit-for-tat strategy was dominant in the population and the discount parameter was larger. Next, it was explored how the tit-for-tat strategy in the finite and repeated prisoner＇s dilemma promotes cooperation using a human-agent computer simulation. In other words, the condition under which cooperative behavior is encouraged was clarified. In the simulation experiment, the discount rate was controlled as an experimental variable. As well as the first experiment above, the dominant occupation of the tit-for-tat strategy was found to lead to the promoted cooperation. Concerning the effect of discount parameter on the cooperative behavior, the cooperation rate tended to increase with the increase of discount parameter only when the t-t-for-tat strategy is dominant. As a whole, the type of change of discount parameter did not affect the cooperation rate.展开更多
The aim of this paper is to reveal the mechanism of compromise and change in coordination where players agree in general but disagree on coordination methods. When players agree on the need to collaborate but are in c...The aim of this paper is to reveal the mechanism of compromise and change in coordination where players agree in general but disagree on coordination methods. When players agree on the need to collaborate but are in conflict regarding the specific method, one player must always compromise. This situation is known as the Battle of the Sexes in game theory. It has ever been believed that if an agreement is reached under such circumstances, the players do not have the incentive to withdraw from the agreement. However, this study shows that this belief is not always true if the players were able to revise the outcome of their negotiations later. The wide-ranging fields use game theories for their analysis frameworks to analyze the success or failure of coordination. However, comparing with the possibility of betrayal illustrated as a well-known Prisoner Dilemma, it has been rare to discuss conflict regarding the specific method of coordination, although such situations are often observed in today＇s interdependent real world. The repeated Battle of the Sexes games presented in this study would be a useful framework to analyze conflict regarding the specific method of coordination.展开更多
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 ...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.展开更多
Considering the inertia of individuals in real inertia of players is introduced into evolutionary prisoner＇s life, we propose a modified Fermi updating rule, where the dilemma game （PDG） on square lattices. We main...Considering the inertia of individuals in real inertia of players is introduced into evolutionary prisoner＇s life, we propose a modified Fermi updating rule, where the dilemma game （PDG） on square lattices. We mainly focus on how the inertia affects the cooperative behavior of the system. Interestingly, we find that the cooperation level has a nonmonotonic dependence on the inertia： with small inertia, cooperators will soon be invaded by defectors; with large inertia, players are unwilling to change their strategies and the cooperation level remains the same as the initial state; while a moderate inertia can induce the highest cooperation level. Moreover, effects of environmental noise and individual inertia are studied. Our work may be helpful in understanding the emergence and persistence of cooperation in nature and society.展开更多
To deeply understand the emergence of cooperation in natural,social and economical systems,we present an improved fitness evaluation mechanism with memory in spatial prisoner's dilemma game on regular lattices.In ...To deeply understand the emergence of cooperation in natural,social and economical systems,we present an improved fitness evaluation mechanism with memory in spatial prisoner's dilemma game on regular lattices.In our model,the individual fitness is not only determined by the payoff in the current game round,but also by the payoffs in previous round bins.A tunable parameter,termed as the memory strength(μ),which lies between 0 and 1,is introduced into the model to regulate the ratio of payoffs of current and previous game rounds in the individual fitness calculation.When μ = 0,our model is reduced to the standard prisoner's dilemma game;while μ = 1 represents the case in which the payoff is totally determined by the initial strategies and thus it is far from the realistic ones.Extensive numerical simulations indicate that the memory effect can substantially promote the evolution of cooperation.For μ < 1,the stronger the memory effect,the higher the cooperation level,but μ = 1 leads to a pathological state of cooperation,but can partially enhance the cooperation in the very large temptation parameter.The current results are of great significance for us to account for the role of memory effect during the evolution of cooperation among selfish players.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
This paper considers optimization problems for a new kind of control systems based on non-equilibrium dynamic games.To be precise,the authors consider the infinitely repeated games between a human and a machine based ...This paper considers optimization problems for a new kind of control systems based on non-equilibrium dynamic games.To be precise,the authors consider the infinitely repeated games between a human and a machine based on the generic 2×2 game with fixed machine strategy of finite k-step memory.By introducing and analyzing the state transfer graphes(STG),it will be shown that the system state will become periodic after finite steps under the optimal strategy that maximizes the human’s averaged payoff,which helps us to ease the task of finding the optimal strategy considerably. Moreover,the question whether the optimizer will win or lose is investigated and some interesting phenomena are found,e.g.,for the standard Prisoner’s Dilemma game,the human will not lose to the machine while optimizing her own averaged payoff when k = 1;however,when k≥2,she may indeed lose if she focuses on optimizing her own payoff only The robustness of the optimal strategy and identification problem are also considered.It appears that both the framework and the results are beyond those in the classical control theory and the traditional game theory.展开更多
A prisoner's dilemma game model is studied using complex networks with a fixed strategy. The strategy of the player is updated according to not only the payoff differences between players and the neighbors, but al...A prisoner's dilemma game model is studied using complex networks with a fixed strategy. The strategy of the player is updated according to not only the payoff differences between players and the neighbors, but also the majority of neighbors (noted as conformist mentality strategy). According to our results of the simulations we found that the players which select the conformist mentality strategy, the density of cooperators markedly improves. The variation trend is slower on the square lattice and small-world networks, but a different phenomenon is noted for scale-free networks. A range of conformist mentality probability is seen on BA networks which conforms to a higher density of cooperators.展开更多
文摘Self-serving,rational agents sometimes cooperate to their mutual benefit.The two-player iterated prisoner′s dilemma game is a model for including the emergence of cooperation.It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants.The zero-determinant strategy in the iterated prisoner′s dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents.However,strategies in the prisoner′s dilemma game are only two strategies.Are there these results for general multi-strategy games?To address this question,the paper develops a theory for zero-determinant strategies for multi-strategy games,with any number of strategies.The analytical results exhibit a similar yet different scenario to the case of two-strategy games.The results are also applied to the Snowdrift game,the Hawk-Dove game and the Chicken game.
文摘In our society, it is a major issue to enhance cooperative behaviors. Without this, our society fall into social dilemma situations, and gets worse and worse. Such a situation in an organization leads to violation of social or organizational rules, and at the worst case it suffers from serious accidents or scandals. Therefore, it is important for organizational managers to make efforts and take measures to enhance cooperative behaviors. Although there seem to be many ways to constantly elicit cooperative behaviors, the punishment is one of the most effective measures for enhancing cooperation. This study focused on the effects of penalty and probability of the revelation of defection on the cooperation, and getting insight into how punishment strategy should be used to get rid of social dilemmas and enhance cooperation. This study conducted a simulation experiment to find the proper penal regulations condition that can suppress violations （defective behavior） in a 2-person prisoner＇s dilemma situation. The effects of probability of the revelation of defection and penalty to revelation on the cooperative behavior were identified with the interactive effect of both experimental factors. The defection （uncooperative behavior） decreased when the penalty to the defection was heavy and the probability of the revelation of defection was low than that when the penalty to the defection was light and the probability of the revelation of the defection was high.
基金Supported by the Project of NECT-07-0112 the National Natural Science Foundation of China under Grant Nos. 10775022 and 90921015
文摘In this work, we consider an evolutionary prisoner＇s dilemma game on a homogeneous random network with the richest-following strategy adoption rule. By constructing homogeneous random networks from a regular ring graph, we investigate the effects of topologicaJ randomness on cooperation. In contrast to the ordinary view that the presence of smaJ1 amount of shortcuts in ring graphs favors cooperation, we find the cooperation inhibition by weak topological randomness. The explanations on the observations are presented.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10775022, 90921015the Fundamental Research Funds for the Central Universities
文摘We investigate the evolutionary prisoner＇s dilemma game in structured populations by introducing dimers, which are defined as that two players in each dimer always hold a same strategy. We find that influences of dimets on cooperation depend on the type of dimers and the population structure. For those dimers in which players interact with each other, the cooperation level increases with the number of dimers though the cooperation improvement level depends on the type of network structures. On the other hand, the dimers, in which there are not mutual interactions, will not do any good to the cooperation level in a single community, but interestingly, will improve the cooperation level in a population with two communities. We explore the relationship between dimers and self-interactions and find that the effects of dimers are similar to that of self-interactions. Also, we find that the dimers, which are established over two communities in a multi-community network, act as one type of interaction through which information between communities is communicated by the requirement that two players in a dimer hold a same strategy.
基金Supported by the "863" Program (No.2009AA01Z241)the National Natural Science Foundation of China (No.60772062)+2 种基金Key Scientific Research Project of Office of Education in Jiangsu Province (No.06KJA51001)Scientific Research Project of Office of Education in Jiangsu Province (No.8KJB510015)Startup Funding (No.NY208048)
文摘We study a spectrum sharing problem where multiple systems coexist and interfere with each other. First, an analysis is proposed for distributed spectrum sharing based on Prisoners' Dilemma (PD) in Cognitive Radios (CRs). In one-shot game, selfish and rational CRs greedily full spread their own spectrum space in order to maximize their own rates, which leads to Nash Equilibrium (N.E.). But with long term interaction, i.e., Iterated Prisoner's Dilemma (IPD), CRs can come to cooperate and acquire the social optimal point by using different evolutionary strategies such as Tit For Tat (TFT), Generous TFT (GTFT), etc. Also we compare the performances of the different evolutionary strategies in noise-free and noisy environments for two-player games. Finally, N-player IPD (N-IPD) is simulated to verify our conclusions that TFT is a good strategy for spectrum sharing in CRs.
文摘As a basic study to prevent accidents or concealment caused by violation of rules or regulations （which are regarded as uncooperative behavior）, an attempt was made to clarify the condition necessary for promoting cooperation when the tit-for-tat strategy is adopted in the finite and repeated prisoner＇s dilemma situations. A mathematical model, in which three different strategies （tit-for-tat, all defection （individualism）, and all cooperation （altruism）） exist, was constructed in order to demonstrate the condition that can promote cooperative behaviors. As a result of an agent-agent computer simulation, it was shown that the tit-for-tat strategy promoted more cooperation than other strategies when the number of agents adopting the tit-for-tat strategy was dominant in the population and the discount parameter was larger. Next, it was explored how the tit-for-tat strategy in the finite and repeated prisoner＇s dilemma promotes cooperation using a human-agent computer simulation. In other words, the condition under which cooperative behavior is encouraged was clarified. In the simulation experiment, the discount rate was controlled as an experimental variable. As well as the first experiment above, the dominant occupation of the tit-for-tat strategy was found to lead to the promoted cooperation. Concerning the effect of discount parameter on the cooperative behavior, the cooperation rate tended to increase with the increase of discount parameter only when the t-t-for-tat strategy is dominant. As a whole, the type of change of discount parameter did not affect the cooperation rate.
文摘The aim of this paper is to reveal the mechanism of compromise and change in coordination where players agree in general but disagree on coordination methods. When players agree on the need to collaborate but are in conflict regarding the specific method, one player must always compromise. This situation is known as the Battle of the Sexes in game theory. It has ever been believed that if an agreement is reached under such circumstances, the players do not have the incentive to withdraw from the agreement. However, this study shows that this belief is not always true if the players were able to revise the outcome of their negotiations later. The wide-ranging fields use game theories for their analysis frameworks to analyze the success or failure of coordination. However, comparing with the possibility of betrayal illustrated as a well-known Prisoner Dilemma, it has been rare to discuss conflict regarding the specific method of coordination, although such situations are often observed in today＇s interdependent real world. The repeated Battle of the Sexes games presented in this study would be a useful framework to analyze conflict regarding the specific method of coordination.
基金Supported by the National Natural Science Foundation of China under Grant Nos.71071119 and 60574071supported by Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology)
文摘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.
基金Supported by the National Basic Research Program of China under Grant No.2011CB707004the Foundation for Innovative Research Groups of the NNSFC under Grant No.60921001+1 种基金the National Key Technologies R&D Program of China under Grant No.2011BAH24B02the State Science and Technology Support Program under Grant No.2012BAG04B01
文摘Considering the inertia of individuals in real inertia of players is introduced into evolutionary prisoner＇s life, we propose a modified Fermi updating rule, where the dilemma game （PDG） on square lattices. We mainly focus on how the inertia affects the cooperative behavior of the system. Interestingly, we find that the cooperation level has a nonmonotonic dependence on the inertia： with small inertia, cooperators will soon be invaded by defectors; with large inertia, players are unwilling to change their strategies and the cooperation level remains the same as the initial state; while a moderate inertia can induce the highest cooperation level. Moreover, effects of environmental noise and individual inertia are studied. Our work may be helpful in understanding the emergence and persistence of cooperation in nature and society.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 61203138,60904063Innovation Fund for Technology Based Firms in Tianjin
文摘To deeply understand the emergence of cooperation in natural,social and economical systems,we present an improved fitness evaluation mechanism with memory in spatial prisoner's dilemma game on regular lattices.In our model,the individual fitness is not only determined by the payoff in the current game round,but also by the payoffs in previous round bins.A tunable parameter,termed as the memory strength(μ),which lies between 0 and 1,is introduced into the model to regulate the ratio of payoffs of current and previous game rounds in the individual fitness calculation.When μ = 0,our model is reduced to the standard prisoner's dilemma game;while μ = 1 represents the case in which the payoff is totally determined by the initial strategies and thus it is far from the realistic ones.Extensive numerical simulations indicate that the memory effect can substantially promote the evolution of cooperation.For μ < 1,the stronger the memory effect,the higher the cooperation level,but μ = 1 leads to a pathological state of cooperation,but can partially enhance the cooperation in the very large temptation parameter.The current results are of great significance for us to account for the role of memory effect during the evolution of cooperation among selfish players.
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.
基金supported by the National Natural Science Foundation of China under Grant No.60821091 by the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No.KJCX3-SYW-S01
文摘This paper considers optimization problems for a new kind of control systems based on non-equilibrium dynamic games.To be precise,the authors consider the infinitely repeated games between a human and a machine based on the generic 2×2 game with fixed machine strategy of finite k-step memory.By introducing and analyzing the state transfer graphes(STG),it will be shown that the system state will become periodic after finite steps under the optimal strategy that maximizes the human’s averaged payoff,which helps us to ease the task of finding the optimal strategy considerably. Moreover,the question whether the optimizer will win or lose is investigated and some interesting phenomena are found,e.g.,for the standard Prisoner’s Dilemma game,the human will not lose to the machine while optimizing her own averaged payoff when k = 1;however,when k≥2,she may indeed lose if she focuses on optimizing her own payoff only The robustness of the optimal strategy and identification problem are also considered.It appears that both the framework and the results are beyond those in the classical control theory and the traditional game theory.
文摘A prisoner's dilemma game model is studied using complex networks with a fixed strategy. The strategy of the player is updated according to not only the payoff differences between players and the neighbors, but also the majority of neighbors (noted as conformist mentality strategy). According to our results of the simulations we found that the players which select the conformist mentality strategy, the density of cooperators markedly improves. The variation trend is slower on the square lattice and small-world networks, but a different phenomenon is noted for scale-free networks. A range of conformist mentality probability is seen on BA networks which conforms to a higher density of cooperators.
