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Zero-determinant strategies in iterated multi-strategy games
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作者 GUO Jinli 《纯粹数学与应用数学》 2024年第3期381-393,共13页
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
关键词 prisoner′s dilemma zero-determinant strategy multi-strategy game symmetric game
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Defection or Cooperation—Richard Power’s Moral Insights in Prisoner’s Dilemma
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作者 梁渊 宋祝 +1 位作者 陈益 周永胜 《海外英语》 2021年第4期239-241,共3页
Prisoner’s Dilemma is a master trope for relaying the permanent impasse or dilemma of cooperation versus defection.In Prisoner’s Dilemma Richard Powers narrates a multiform of dilemma mainly narrating Eddie Hobson’... Prisoner’s Dilemma is a master trope for relaying the permanent impasse or dilemma of cooperation versus defection.In Prisoner’s Dilemma Richard Powers narrates a multiform of dilemma mainly narrating Eddie Hobson’s traumatic history,along with Eddie’s attempt to carry out a strategy—Eddie’s ideal Hobstown which is supposed to cope with the confused dilemma.Pow⁃ers’strategic moral insights are revealed by assuming that each player feels sympathy for the other and a moral cooperative instead of antagonistic solution to the Prisoner’s Dilemma will be found. 展开更多
关键词 DEFECTION COOPERATION MoralInsights Prisoner’s dilemma
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Richard Power’s Philosophical Thoughts in Prisoner’s Dilemma
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作者 梁渊 陈益 魏澜 《海外英语》 2020年第11期213-214,220,共3页
The“prisoner’s dilemma”illustrates that everyone is rationally thinking about maximizing their own interests and taking their own best strategies,but the end result is counterproductive.In Prisoner’s Dilemma Richa... The“prisoner’s dilemma”illustrates that everyone is rationally thinking about maximizing their own interests and taking their own best strategies,but the end result is counterproductive.In Prisoner’s Dilemma Richard Powers describes multiformareas of dilemma;to lose balance;to make choices;and ask each other:what to do next?It is a master trope for relaying the permanent impasse or dilemma of cooperation versus defection.In most cases,the prisoner's dilemma is more about the number of defeats in the game,and even a major loss of society.Individual rationality is likely to be a collective disregard,and if everyone is acting on the principle of self-interest,it is often the result that everyone is lost.Powers expresses his philosophical insight:Until a cooperative instead of antagonistic solution is collectively agreed upon,we still remain imprisoned in an interminable and oppressive struggle and conflict decided by self-interest and rational control,which is also a moral response to historical consciousness of postmodernism. 展开更多
关键词 Prisoner’s dilemma DEFECTION COOPERATION Philosophical Thoughts
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An Adaptive Strategy via Reinforcement Learning for the Prisoner's Dilemma Game 被引量:8
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作者 Lei Xue Changyin Sun +2 位作者 Donald Wunsch Yingjiang Zhou Fang Yu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第1期301-310,共10页
The iterated prisoner's dilemma(IPD) is an ideal model for analyzing interactions between agents in complex networks. It has attracted wide interest in the development of novel strategies since the success of tit-... The iterated prisoner's dilemma(IPD) is an ideal model for analyzing interactions between agents in complex networks. It has attracted wide interest in the development of novel strategies since the success of tit-for-tat in Axelrod's tournament. This paper studies a new adaptive strategy of IPD in different complex networks, where agents can learn and adapt their strategies through reinforcement learning method. A temporal difference learning method is applied for designing the adaptive strategy to optimize the decision making process of the agents. Previous studies indicated that mutual cooperation is hard to emerge in the IPD. Therefore, three examples which based on square lattice network and scale-free network are provided to show two features of the adaptive strategy. First, the mutual cooperation can be achieved by the group with adaptive agents under scale-free network, and once evolution has converged mutual cooperation, it is unlikely to shift. Secondly, the adaptive strategy can earn a better payoff compared with other strategies in the square network. The analytical properties are discussed for verifying evolutionary stability of the adaptive strategy. 展开更多
关键词 Complex network prisoner’s dilemma reinforcement learning temporal differences learning
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THE OPTIMAL CONTROL FOR PROMOTING THE COOPERATION IN EVOLUTION GAME GENERATED BY PRISONER'S DILEMMA 被引量:2
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作者 王先甲 董瑞 陈琳 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期73-92,共20页
Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner's Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optima... Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner's Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optimal control is designed for promoting cooperation based on the recent advances in mechanisms for the evolution of cooperation. Two con- trol strategies are proposed: compensation control strategy for the cooperator when playing against a defector and reward control strategy for cooperator when playing against a coop- erator. The feasibility and effectiveness of these control strategies for promoting cooperation in different stages are analyzed. The reward for cooperation can't prevent defection from being evolutionary stable strategy (ESS). On the other hand, compensation for the coopera- tor can't prevent defection from emerging and sustaining. By considering the effect and the cost, an optimal control scheme with constraint on the admissible control set is put forward. By analyzing the special nonlinear system of replicator dynamics, the exact analytic solution of the optimal control scheme is obtained based on the maximum principle. Finally, the effectiveness of the proposed method is illustrated by examples. 展开更多
关键词 evolutionary games Prisoner's dilemma evolution of cooperation promoting cooperation control optimal control
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Evolutionary prisoner's dilemma game on highly clustered community networks 被引量:1
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作者 刘永奎 李智 +1 位作者 陈小杰 王龙 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第7期2623-2628,共6页
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... 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. 展开更多
关键词 prisoner's dilemma COOPERATION clustering coefficient community structure
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Effects of Probability of Revelation of Defection and Penalty to Defection on Cooperative Behavior in 2-Person Prisoner's Dilemma Game 被引量:3
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作者 Atsuo Murata Takuma Kanagawa Naoki Hata 《Computer Technology and Application》 2012年第11期749-755,共7页
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
关键词 Prisoner's dilemma cooperation defect punishment model violation-based accident.
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Evolutionary prisoner’s dilemma on Newman-Watts social networks with an asymmetric payoff distribution mechanism 被引量:1
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作者 杜文博 曹先彬 +1 位作者 杨涵新 胡茂彬 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第1期17-21,共5页
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
关键词 prisoner's dilemma game COOPERATION complex social networks
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Payoff-based accumulative effect promotes cooperation in spatial prisoner’s dilemma
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作者 刘永奎 李智 +1 位作者 陈小杰 王龙 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第9期53-58,共6页
We study the effect of accumulative payoff on the evolution of cooperation in the evolutionary prisoner's dilemma on a square lattice. We introduce a decaying factor for the accumulative payoff, which characterizes t... We study the effect of accumulative payoff on the evolution of cooperation in the evolutionary prisoner's dilemma on a square lattice. We introduce a decaying factor for the accumulative payoff, which characterizes the extent that the historical payoff is accumulated. It is shown that for fixed values of the temptation to defect, the density of cooperators increases with the value of the decaying factor. This indicates that the more the historical payoff is involved, the more favourable cooperators become. In the critical region where the cooperator density converges to zero, cooperators vanish according to a power-law-like behaviour. The associated exponents agree approximately with the two-dimensional directed percolation and depend weakly on the value of the decaying factor. 展开更多
关键词 payoff accumulative effect prisoner's dilemma COOPERATION
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Adaptive co-evolution of strategies and network leading to optimal cooperation level in spatial prisoner's dilemma game
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作者 陈含爽 侯中怀 +1 位作者 张季谦 辛厚文 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第5期25-30,共6页
We study evolutionary prisoner's dilemma game on adaptive networks where a population of players co-evolves with their interaction networks. During the co-evolution process, interacted players with opposite strategie... We study evolutionary prisoner's dilemma game on adaptive networks where a population of players co-evolves with their interaction networks. During the co-evolution process, interacted players with opposite strategies either rewire the link between them with probability p or update their strategies with probability 1 - p depending on their payoffs. Numerical simulation shows that the final network is either split into some disconnected communities whose players share the same strategy within each community or forms a single connected network in which all nodes are in the same strategy. Interestingly, the density of cooperators in the final state can be maximised in an intermediate range of p via the competition between time scale of the network dynamics and that of the node dynamics. Finally, the mean-field analysis helps to understand the results of numerical simulation. Our results may provide some insight into understanding the emergence of cooperation in the real situation where the individuals' behaviour and their relationship adaptively co-evolve. 展开更多
关键词 prisoner's dilemma game adaptive network CO-EVOLUTION COOPERATION
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PREFERENCE AND EVOLUTION IN THE ITERATED PRISONER'S DILEMMA
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作者 王先甲 刘伟兵 《Acta Mathematica Scientia》 SCIE CSCD 2009年第2期456-464,共9页
Game theory is extensively used to study strategy-making and actions of play- ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated priso... Game theory is extensively used to study strategy-making and actions of play- ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated prisoner's dilemma. In this article, a preference parameter k was introduced in the payoff matrix, wherein the value of k denotes the player's degree of egoism and altruism (preference). Then, a game-theoretic dynamical model was formulated using Birth-and-Death process. The authors studied how preference influences the evolutionary equilibrium and behaviors of players. The authors get the general results: egoism leads to defection, and altruism can make players build trust and maintain cooperation, and so, the hope of the Pareto optimal solution. In the end, the simulation experiments proved the efficiency of the method. 展开更多
关键词 Game theory evolutionary game prisoner's dilemma Birth-and-Death process PREFERENCE
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Effects of Dimers on Cooperation in the Spatial Prisoner's Dilemma Game
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作者 李海红 程洪艳 +3 位作者 代琼琳 鞠萍 章梅 杨俊忠 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第11期813-818,共6页
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
关键词 prisoner's dilemma game cooperation frequency NETWORKs
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Cooperation influenced by the correlation degree of two-layered complex networks in evolutionary prisoner’s dilemma games
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作者 关剑月 吴枝喜 +1 位作者 黄子罡 汪映海 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第2期13-18,共6页
An evolutionary prisoner's dilemma game is investigated on two-layered complex networks respectively representing interaction and learning networks in one and two dimensions. A parameter q is introduced to denote the... An evolutionary prisoner's dilemma game is investigated on two-layered complex networks respectively representing interaction and learning networks in one and two dimensions. A parameter q is introduced to denote the correlation degree between the two-layered networks. Using Monte Carlo simulations we studied the effects of the correlation degree on cooperative behaviour and found that the cooperator density nontrivially changes with q for different payoff parameter values depending on the detailed strategy updating and network dimension. An explanation for the obtained results is provided. 展开更多
关键词 prisoner's dilemma game two-layered complex networks COOPERATION
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A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game
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作者 方祥圣 朱平 +2 位作者 刘润然 刘恩钰 魏贵义 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第10期555-562,共8页
In this study,we propose a spatial prisoner's dilemma game model with a 2-stage strategy updating rule,and focus on the cooperation behavior of the system.In the first stage,i.e.,the pre-learning stage,a focal player... In this study,we propose a spatial prisoner's dilemma game model with a 2-stage strategy updating rule,and focus on the cooperation behavior of the system.In the first stage,i.e.,the pre-learning stage,a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors.If the player makes up his mind to update,he enters into the second stage,i.e.,the learning stage,and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule.The simulation results show that the cooperation level has a non-trivial dependence on the pre-learning factor.Generally,the cooperation frequency decreases as the pre-learning factor increases;but a high cooperation level can be obtained in the intermediate region of- 3〈 β 〈-1.We then give some explanations via studying the co-action of pre-learning and learning.Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games. 展开更多
关键词 evolutionary game theory strategy updating social cooperation prisoner's dilemma game
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SPECTRUM SHARING IN ITERATED PRISONER'S DILEMMA GAME BASED ON EVOLUTIONARY STRATEGIES FOR COGNITIVE RADIOS
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作者 Tian Feng Yang Zhen 《Journal of Electronics(China)》 2009年第5期588-599,共12页
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
关键词 Cognitive Radio (CR) Iterated Prisoner's dilemma (IPD) spectrum sharing Evolutionary strategies Gaussian interference channel
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Condition to Gain More Profits and Promote Cooperation by Tit-for-Tat Strategy in Finite and Repeated Prisoner's Dilemma
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作者 Atsuo Murata Naoki Hata 《Computer Technology and Application》 2013年第1期23-33,共11页
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
关键词 Prisoner's dilemma COOPERATION defect tit-for-tat strategy discount parameter violation-based accident.
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Effect of Strategy-Homogeneity on the Prisoner’s Dilemma Game in a Square Lattice
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作者 Mengqin Yang Hedong Xu +1 位作者 Cong Li Suohai Fan 《Journal of Applied Mathematics and Physics》 2021年第2期295-305,共11页
We investigate the effect of strategy-homogeneity on the prisoner’s dilemma game in a square lattice. Strategy-homogeneity means that the population contains at least one connected group in which individuals maintain... We investigate the effect of strategy-homogeneity on the prisoner’s dilemma game in a square lattice. Strategy-homogeneity means that the population contains at least one connected group in which individuals maintain the same strategy at each iteration and may update according to updating rule at next iteration. The simulation results show that the introduction of strategy-homogeneity increases the cooperation in the evolutionary stable state. For any value of temptation to defect, the density of cooperators in equilibrium state increases firstly and then decreases as the level of strategy-homogeneity increases constantly, and there exists an appropriate level of strategy-homogeneity, maximizing the density of cooperators. The results may be favorable for comprehending cooperative behaviors in societies composed of connected groups with coherent strategy. 展开更多
关键词 strategy-Homogeneity Prisoner’s dilemma Game square Lattice Cooperative Behavior
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The Female Dilemma in The Grass Is Singing
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作者 WANG Qiu-pei 《Journal of Literature and Art Studies》 2021年第4期222-225,共4页
Doris Lessing,a British female writer,published her first work,The Grass is Singing in 1950,which has attracted the attention of literary critics since its publication.From the perspectives of postcolonialism,ecology ... Doris Lessing,a British female writer,published her first work,The Grass is Singing in 1950,which has attracted the attention of literary critics since its publication.From the perspectives of postcolonialism,ecology and ecofeminism,the critics interpret the racial oppression and conflicts in the African colonies and the tragic story of Mary,which is the heroine under the influence of racial discrimination.From the perspective of feminist criticism theory,this paper mainly discusses the survival and spiritual dilemma faced by Mary,the heroine who is oppressed and bound in the patriarchal society,the reasons behind Mary’s dilemma,and Mary’s behavior and measures when facing the dilemma.It reveals the survival status of women in patriarchal society,which is the author’s criticism and irony of the patriarchal society.It is of positive significance for the development of feminist literature to cry out about women’s miserable situation. 展开更多
关键词 The Grass is singing FEMINIsM women’s dilemma patriarchal society racial discrimination
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Hempel' s Dilemma and the Threat of Being Misjudged
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作者 Li Nan 《学术界》 CSSCI 北大核心 2013年第9期249-254,共6页
Recently P.Bokulich suggests a newway to grab the first horn of Hempel’s Dilemma.His strategy is to define "the physical" with "the stuff recognized by currently well-understood parts of physics",... Recently P.Bokulich suggests a newway to grab the first horn of Hempel’s Dilemma.His strategy is to define "the physical" with "the stuff recognized by currently well-understood parts of physics",such as Quantum electrodynamics,as far as the mindbody problem is concerned.I argue that the physicalism doctrine formulated following Bokulich’s suggestion is still under the threat of being misjudged and also will not be welcomed by the physicalists.After considering some potential objections,I conclude that Bokulich’s strategy fails. 展开更多
关键词 威胁 量子电动力学 物理
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Egypt’s Dilemma Continues
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《ChinAfrica》 2013年第8期11-11,共1页
Egyptian President Mohamed Morsi was overthrown and de- tained by the nation's army in July, just one year after he be- came the country's first demo- cratically elected president. Egypt is now again at a cross- roa... Egyptian President Mohamed Morsi was overthrown and de- tained by the nation's army in July, just one year after he be- came the country's first demo- cratically elected president. Egypt is now again at a cross- roads, as it was one year ago. 展开更多
关键词 Egypt’s dilemma Continues
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