从经典博弈论到量子博弈论
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摘要
博弈论是一门研究理性人策略选择的学科,在经济学,社会学等领域有着广泛的应用,被誉为“社会科学的数学”。近年来随着量子理论研究的发展,出现了博弈论与量子物理的新兴交叉学科——量子博弈论。本文首先介绍经典博弈论,并由此引入量子化的博弈模型,结合近年来国内外对量子博弈研究的最新成果对量子博弈作了较全面的介绍。通过比较的方法体现出量子博弈的优越性,进而对量子博弈在哲学上所带来的新问题进行探讨。全文分为引言,四个篇章和结束语六个部分。
引言部分中对博弈论的研究对象,内容,目的和方法作了介绍,说明了量子博弈论研究的基本依据和所带来的进步。
第一章全面介绍了经典博弈论的相关概念,简要回顾了博弈论的发展历史,对博弈的种类进行了划分,介绍了博弈论中的纳什均衡和囚徒困境等重要概念和问题。
第二章介绍了量子信息论,量子纠缠等量子博弈论所需的背景知识,介绍了量子博弈论的由来。
第三章对量子博弈作了详细的介绍,讨论了PQ翻硬币模型中量子博弈所带来的优越性。之后对经典的囚徒困境作了量子化模型的分析。本章的最后部分简要总结了量子博弈论的研究意义。说明量子博弈论并非仅仅是经典博弈论的量子形式描述,而是一种全新的博弈形式。
第四章讨论博弈问题的哲学意义,结合囚徒困境从理性与道德,合作与进化方面对博弈论的哲学意义作了分析,之后对量子博弈论做出了哲学反思。
结束语对于全文作了简要回顾,指出量子博弈论目前的研究仍在起步阶段,对其面临的问题和今后的发展趋势作了简要的陈述。
Game theory is a subject studies on the rational strategy movement, it is widely used in economics, sociology and many other areas, regarded as "the mathematics of social science". In recent years, for the development of quantum physics, a new intercross area of game theory and quantum physics had born, that is quantum game theory. This thesis will give a presentation of game theory and quantum game theory, and incarnate the advantages of quantum game by compare them in some classical game model. Moreover, a discussion of philosophy meaning in game theory and quantum game theory will be given in the last part.
In preface part, there will be a presentation of the aims, main ideas, objects and research approaches of game theory, explain how would quantum game theory came into been and the possible progress made by it.
In chapter one, it will be a brief look back into the history of game theory, define the types of different games in several point of view, introduce Nash Equilibrium and Prisoner Dilemma, which are quite important in game theory.
In chapter two, there will be an introduction of quantum information theory and quantum entanglement, which is background knowledge of quantum game theory. It will also present how the original ideas of quantum game theory came into been.
In chapter three, there will be some details of quantum game theory. The advantage brought by quantum strategy in PQ penny flip model will be discussed. And the analysis of quantumize the model of prisoner dilemma will be presented. A summarization will be given for the last part of this chapter, indicate that quantum game is not just quantumization of classical game, but a new kind of game.
In chapter four, it will present some philosophy thinking over game theory; discuss the philosophy meaning of quantum game theory.
In the ending part, there is a short summarize of the whole article, present the problems of quantum game theory, and talk about the future direction of it.
引言部分中对博弈论的研究对象,内容,目的和方法作了介绍,说明了量子博弈论研究的基本依据和所带来的进步。
第一章全面介绍了经典博弈论的相关概念,简要回顾了博弈论的发展历史,对博弈的种类进行了划分,介绍了博弈论中的纳什均衡和囚徒困境等重要概念和问题。
第二章介绍了量子信息论,量子纠缠等量子博弈论所需的背景知识,介绍了量子博弈论的由来。
第三章对量子博弈作了详细的介绍,讨论了PQ翻硬币模型中量子博弈所带来的优越性。之后对经典的囚徒困境作了量子化模型的分析。本章的最后部分简要总结了量子博弈论的研究意义。说明量子博弈论并非仅仅是经典博弈论的量子形式描述,而是一种全新的博弈形式。
第四章讨论博弈问题的哲学意义,结合囚徒困境从理性与道德,合作与进化方面对博弈论的哲学意义作了分析,之后对量子博弈论做出了哲学反思。
结束语对于全文作了简要回顾,指出量子博弈论目前的研究仍在起步阶段,对其面临的问题和今后的发展趋势作了简要的陈述。
Game theory is a subject studies on the rational strategy movement, it is widely used in economics, sociology and many other areas, regarded as "the mathematics of social science". In recent years, for the development of quantum physics, a new intercross area of game theory and quantum physics had born, that is quantum game theory. This thesis will give a presentation of game theory and quantum game theory, and incarnate the advantages of quantum game by compare them in some classical game model. Moreover, a discussion of philosophy meaning in game theory and quantum game theory will be given in the last part.
In preface part, there will be a presentation of the aims, main ideas, objects and research approaches of game theory, explain how would quantum game theory came into been and the possible progress made by it.
In chapter one, it will be a brief look back into the history of game theory, define the types of different games in several point of view, introduce Nash Equilibrium and Prisoner Dilemma, which are quite important in game theory.
In chapter two, there will be an introduction of quantum information theory and quantum entanglement, which is background knowledge of quantum game theory. It will also present how the original ideas of quantum game theory came into been.
In chapter three, there will be some details of quantum game theory. The advantage brought by quantum strategy in PQ penny flip model will be discussed. And the analysis of quantumize the model of prisoner dilemma will be presented. A summarization will be given for the last part of this chapter, indicate that quantum game is not just quantumization of classical game, but a new kind of game.
In chapter four, it will present some philosophy thinking over game theory; discuss the philosophy meaning of quantum game theory.
In the ending part, there is a short summarize of the whole article, present the problems of quantum game theory, and talk about the future direction of it.
引文
[1] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J], 2003, 22(12): 3~9
[2] 施锡铨. 博弈论[M]. 上海: 上海财经大学出版社, 2000
[3] 弗登伯格. 博弈论[M]. 姚洋译. 北京: 中国人民大学出版社, 2002
[4] 弗登伯格. 博弈论[M]. 姚洋译. 北京: 中国人民大学出版社, 2002
[5] 纳什. 纳什博弈论论文集[M]. 张良桥, 王晓刚译. 北京: 首都经济贸易大学出版社, 2000
[6] 纳什. 纳什博弈论论文集[M]. 张良桥, 王晓刚译. 北京: 首都经济贸易大学出版社, 2000
[7] 潘天群. 博弈生存[M]. 北京: 中央编译出版社, 2001
[8] 潘天群. 博弈生存[M]. 北京: 中央编译出版社, 2001
[9] 潘天群. 博弈生存[M]. 北京: 中央编译出版社, 2001
[10] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J], 2003, 22(12): 3~9
[11] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J], 2003, 22(12): 3~9
[12] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J], 2003, 22(12): 3~9
[13] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J], 2003, 22(12): 3~9
[14] 杜江峰, 李卉, 许晓栋等. 量子“囚徒困境”的混合量子对策. 广西师范大学学报(自然科学版)[J]. 2002, 20(2): 19~24
[15] Zellinger, A., The quantum centennial, Nature [J]. 2000
[16] Schaden, M., Quantum finance, Physia A [J]. 2002
[17] Adrian P. Flitney. Aspects of Quantum Game Theory:[Thesis submitted for the degree of Doctor of Philosophy]. Department of Electrical and Electronic Engineering, Faculty of Engineering, Computer and Mathematical Sciences. The University of Adelaide, Australia,2005
[18] Adrian P. Flitney. Aspects of Quantum Game Theory:[Thesis submitted for the degree of Doctor of Philosophy]. Department of Electrical and Electronic Engineering, Faculty of Engineering, Computer and Mathematical Sciences. The University ofAdelaide, Australia,2005
[19] Adrian P. Flitney. Aspects of Quantum Game Theory:[Thesis submitted for the degree of Doctor of Philosophy]. Department of Electrical and Electronic Engineering, Faculty of Engineering, Computer and Mathematical Sciences. The University of Adelaide, Australia,2005
[20] Holevo, A., Statistical Structure of Quantum Theory [M]. Berlin: Springer Verlag, 2001
[21] Meyer, D. A., Quantum strategies, Physical Review Letters [J]. 1999
[22] S. J. van Enk, R. Pike. Classical rules in quantum games. Physical Review A [J]. 2002
[23] Eisert, J., Wilkens, M., Lewenstein, M., Quantum Games and Quantum Strategies, Physical Review Letters [J]. 1999
[24] S. J. van Enk, R. Pike. Classical rules in quantum games. Physical Review A [J]. 2002
[25] 赵汀阳. 博弈问题的哲学分析. 北京行政学院学报[J]. 2005, 3
[26] 赵汀阳. 博弈问题的哲学分析. 北京行政学院学报[J]. 2005, 3
[27] R.Campbel, L.Sowden. Paradoxes of Rationality and Cooperation, Prisoner’s Dilemma and Newcomb’s Problem[M]. Vancouver: The University of British Columbia Press, 1995
[28] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[29] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[30] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[31] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[32] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[33] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[34] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[35] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[36] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[37] 郝宁湘. 量子计算机的本质特征及其哲学意义. 自然辩证法研究[J]. 2001, 17(9): 12~16
[1] 万小龙. 范·弗拉森的量子理论的解释思想. 华中科技大学学报(人文社会学版)[J]. 2002, 2: 14~20
[2] 万小龙. 范·弗拉森的量子力学解释理论. 自然辩证法研究[J]. 2002, 18(3): 14~17
[3] 万小龙. 范·弗拉森对 EPR 关联的分析. 自然辩证法研究[J]. 2004, 20(4): 1~4
[4] 万小龙. 范·弗拉森对量子概率的模态解释. 华中科技大学学报(人文社会科学版)[J]. 2004, 3: 16~21
[5] 万小龙. 范·弗拉森关于量子测量的模态解释. 自然辩证法通讯[J]. 2002, 24(6): 21~27
[6] 万小龙. 表征主义: 当代科学哲学与量子力学哲学的一个新动向. 哲学动态[J]. 2004, 3: 42~46
[7] 吕增建. 爱因斯坦与现代物理学. 洛阳师范学院学报[J]. 2001, 2: 39~43
[8] 楚文章. 波尔“互补原理”哲学评述. 沈阳师范学院学报(社会科学版)[J]. 1997, 21(3): 56~60
[9] 韩锋, 朱云江. 波粒二象性的信息熵解释. 新疆师范大学学报(自然科学版)[J]. 1996, 15(3): 32~37
[10] 赵国求. 波粒二象性的有机统一. 武钢职工大学学报[J]. 2000, 12(2): 1~7
[11] 洪定国. 波粒二象性的哲学思考. 中南民族学院学报(自然科学版)[J]. 2000, 19(9): 1~6
[12] 杜江峰, 李卉, 许晓栋等. 量子“囚徒困境”. 广西师范大学学报(自然科学版)[J]. 2001, 19(4): 1~7
[13] 杜江峰, 李卉, 许晓栋等. 量子“囚徒困境”的混合量子对策. 广西师范大学学报(自然科学版)[J]. 2002, 20(2): 19~24
[14] 张鲁殷, 张广剑, 周森林等. 量子博弈的优越性分析. 山东科技大学学报(社会科学版)[J]. 2005, 7(4): 19~21
[15] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J]. 2003, 22(12): 3~9
[16] 施锡铨. 博弈论[M]. 上海: 上海财经大学出版社, 2000
[17] 潘天群. 博弈生存[M]. 北京: 中央编译出版社, 2001
[18] 纳什. 纳什博弈论论文集[M]. 张良桥, 王晓刚译. 北京: 首都经济贸易大学出版社, 2000
[19] 弗登伯格. 博弈论[M]. 姚洋译. 北京: 中国人民大学出版社, 2002
[20] 赵汀阳. 博弈问题的哲学分析. 北京行政学院学报[J]. 2005, 3
[21] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[22] 郝宁湘. 量子计算机的本质特征及其哲学意义. 自然辩证法研究[J]. 2001, 17(9): 12~16
[23] Adrian P. Flitney. Aspects of Quantum Game Theory: [Thesis submitted for the degree of Doctor of Philosophy]. Department of Electrical and Electronic Engineering, Faculty of Engineering, Computer and Mathematical Sciences. The University of Adelaide, Australia, 2005
[24] Zellinger, A., The quantum centennial, Nature [J]. 2000
[25] Wiesner, S., Conjugate coding, SIGACT News [J]. 1983, 78
[26] Baaquie, B. E., Quantum field theory of treasury bonds, Physical Review [J]. 2001
[27] Schaden, M., Quantum finance, Physia A [J]. 2002
[28] Waite, S., Quantum investing [M]. London :Texere Publishing, 2002
[29] Piotrowski, E. W., S adkowski, J., Quantum Market Games, Physica A[J]. 2002
[30] Piotrowski, E. W., S adkowski, J., Quantum solution to the Newcomb's paradox, International Journal of Quantum Information [J]. 2003
[31] Penrose, R., Shadows of the Mind [M]. Cambridge: Cambridge University Press,1994
[32] Wallace, D., Quantum theory of probability and decision theory, Revisited. Quantum physics [J]. 2002
[33] Nielsen, M. A., Chuang, I. L., Quantum Computation and Quantum Information [M], Cambridge: Cambridge University Press, 2000
[34] Holevo, A., Statistical Structure of Quantum Theory [M]. Berlin: Springer Verlag, 2001
[35] Piotrowski, E. W., S adkowski, J., An invitation to quantum game theory, International Journal of Theoretical Physics [J]. 2003
[36] Meyer, D. A., Quantum strategies, Physical Review Letters [J]. 1999
[37] Eisert, J., Wilkens, M., Lewenstein, M., Quantum Games and Quantum Strategies, Physical Review Letters [J]. 1999
[38] Iqbal A., Toor A.H., Backwards: Conduction outcome in a quantum game, Physical Review [J]. 2002
[39] Iqbal A., Toor A. H., Quantum mechanics gives stability to a Nash equilibrium, Physical Review A [J]. 2002
[40] Piotrowski, E. W., S adkowski, J., Quantum English auctions, Physica A [J]. 2003
[41] Piotrowski, E. W., S adkowski, J., Quantum bargaining games, Physica A [J]. 2002
[42] S adkowski, J., Gi en paradoxes in quantum market games, Physica A [J]. 2003
[43] Wigner, E., On the quantum correction for thermodynamic equilibrium, Physical Review[J]. 1932
[44] Fischer, M. C., Gutierrez-Medina, B., Raizen, M. G., Observation of the quantum Zeno and anti-Zeno e ects in an unstable system, Physical Review Letters[J]. 2001
[45] S. J. van Enk, R. Pike. Classical rules in quantum games. Physical Review A [J]. 2002
[46] Simon C. Benjamin and Patrick M. Hayden. Multiplayer quantum games. Physical Review A [J]. 2001
[2] 施锡铨. 博弈论[M]. 上海: 上海财经大学出版社, 2000
[3] 弗登伯格. 博弈论[M]. 姚洋译. 北京: 中国人民大学出版社, 2002
[4] 弗登伯格. 博弈论[M]. 姚洋译. 北京: 中国人民大学出版社, 2002
[5] 纳什. 纳什博弈论论文集[M]. 张良桥, 王晓刚译. 北京: 首都经济贸易大学出版社, 2000
[6] 纳什. 纳什博弈论论文集[M]. 张良桥, 王晓刚译. 北京: 首都经济贸易大学出版社, 2000
[7] 潘天群. 博弈生存[M]. 北京: 中央编译出版社, 2001
[8] 潘天群. 博弈生存[M]. 北京: 中央编译出版社, 2001
[9] 潘天群. 博弈生存[M]. 北京: 中央编译出版社, 2001
[10] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J], 2003, 22(12): 3~9
[11] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J], 2003, 22(12): 3~9
[12] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J], 2003, 22(12): 3~9
[13] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J], 2003, 22(12): 3~9
[14] 杜江峰, 李卉, 许晓栋等. 量子“囚徒困境”的混合量子对策. 广西师范大学学报(自然科学版)[J]. 2002, 20(2): 19~24
[15] Zellinger, A., The quantum centennial, Nature [J]. 2000
[16] Schaden, M., Quantum finance, Physia A [J]. 2002
[17] Adrian P. Flitney. Aspects of Quantum Game Theory:[Thesis submitted for the degree of Doctor of Philosophy]. Department of Electrical and Electronic Engineering, Faculty of Engineering, Computer and Mathematical Sciences. The University of Adelaide, Australia,2005
[18] Adrian P. Flitney. Aspects of Quantum Game Theory:[Thesis submitted for the degree of Doctor of Philosophy]. Department of Electrical and Electronic Engineering, Faculty of Engineering, Computer and Mathematical Sciences. The University ofAdelaide, Australia,2005
[19] Adrian P. Flitney. Aspects of Quantum Game Theory:[Thesis submitted for the degree of Doctor of Philosophy]. Department of Electrical and Electronic Engineering, Faculty of Engineering, Computer and Mathematical Sciences. The University of Adelaide, Australia,2005
[20] Holevo, A., Statistical Structure of Quantum Theory [M]. Berlin: Springer Verlag, 2001
[21] Meyer, D. A., Quantum strategies, Physical Review Letters [J]. 1999
[22] S. J. van Enk, R. Pike. Classical rules in quantum games. Physical Review A [J]. 2002
[23] Eisert, J., Wilkens, M., Lewenstein, M., Quantum Games and Quantum Strategies, Physical Review Letters [J]. 1999
[24] S. J. van Enk, R. Pike. Classical rules in quantum games. Physical Review A [J]. 2002
[25] 赵汀阳. 博弈问题的哲学分析. 北京行政学院学报[J]. 2005, 3
[26] 赵汀阳. 博弈问题的哲学分析. 北京行政学院学报[J]. 2005, 3
[27] R.Campbel, L.Sowden. Paradoxes of Rationality and Cooperation, Prisoner’s Dilemma and Newcomb’s Problem[M]. Vancouver: The University of British Columbia Press, 1995
[28] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[29] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[30] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[31] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[32] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[33] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[34] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[35] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[36] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[37] 郝宁湘. 量子计算机的本质特征及其哲学意义. 自然辩证法研究[J]. 2001, 17(9): 12~16
[1] 万小龙. 范·弗拉森的量子理论的解释思想. 华中科技大学学报(人文社会学版)[J]. 2002, 2: 14~20
[2] 万小龙. 范·弗拉森的量子力学解释理论. 自然辩证法研究[J]. 2002, 18(3): 14~17
[3] 万小龙. 范·弗拉森对 EPR 关联的分析. 自然辩证法研究[J]. 2004, 20(4): 1~4
[4] 万小龙. 范·弗拉森对量子概率的模态解释. 华中科技大学学报(人文社会科学版)[J]. 2004, 3: 16~21
[5] 万小龙. 范·弗拉森关于量子测量的模态解释. 自然辩证法通讯[J]. 2002, 24(6): 21~27
[6] 万小龙. 表征主义: 当代科学哲学与量子力学哲学的一个新动向. 哲学动态[J]. 2004, 3: 42~46
[7] 吕增建. 爱因斯坦与现代物理学. 洛阳师范学院学报[J]. 2001, 2: 39~43
[8] 楚文章. 波尔“互补原理”哲学评述. 沈阳师范学院学报(社会科学版)[J]. 1997, 21(3): 56~60
[9] 韩锋, 朱云江. 波粒二象性的信息熵解释. 新疆师范大学学报(自然科学版)[J]. 1996, 15(3): 32~37
[10] 赵国求. 波粒二象性的有机统一. 武钢职工大学学报[J]. 2000, 12(2): 1~7
[11] 洪定国. 波粒二象性的哲学思考. 中南民族学院学报(自然科学版)[J]. 2000, 19(9): 1~6
[12] 杜江峰, 李卉, 许晓栋等. 量子“囚徒困境”. 广西师范大学学报(自然科学版)[J]. 2001, 19(4): 1~7
[13] 杜江峰, 李卉, 许晓栋等. 量子“囚徒困境”的混合量子对策. 广西师范大学学报(自然科学版)[J]. 2002, 20(2): 19~24
[14] 张鲁殷, 张广剑, 周森林等. 量子博弈的优越性分析. 山东科技大学学报(社会科学版)[J]. 2005, 7(4): 19~21
[15] 李威, 赵红敏, 林家逖. 量子博弈论及其应用[J]. 大学物理[J]. 2003, 22(12): 3~9
[16] 施锡铨. 博弈论[M]. 上海: 上海财经大学出版社, 2000
[17] 潘天群. 博弈生存[M]. 北京: 中央编译出版社, 2001
[18] 纳什. 纳什博弈论论文集[M]. 张良桥, 王晓刚译. 北京: 首都经济贸易大学出版社, 2000
[19] 弗登伯格. 博弈论[M]. 姚洋译. 北京: 中国人民大学出版社, 2002
[20] 赵汀阳. 博弈问题的哲学分析. 北京行政学院学报[J]. 2005, 3
[21] 李伯聪, 李军. 关于囚徒困境的几个问题. 自然辩证法通讯[J]. 1996, 4
[22] 郝宁湘. 量子计算机的本质特征及其哲学意义. 自然辩证法研究[J]. 2001, 17(9): 12~16
[23] Adrian P. Flitney. Aspects of Quantum Game Theory: [Thesis submitted for the degree of Doctor of Philosophy]. Department of Electrical and Electronic Engineering, Faculty of Engineering, Computer and Mathematical Sciences. The University of Adelaide, Australia, 2005
[24] Zellinger, A., The quantum centennial, Nature [J]. 2000
[25] Wiesner, S., Conjugate coding, SIGACT News [J]. 1983, 78
[26] Baaquie, B. E., Quantum field theory of treasury bonds, Physical Review [J]. 2001
[27] Schaden, M., Quantum finance, Physia A [J]. 2002
[28] Waite, S., Quantum investing [M]. London :Texere Publishing, 2002
[29] Piotrowski, E. W., S adkowski, J., Quantum Market Games, Physica A[J]. 2002
[30] Piotrowski, E. W., S adkowski, J., Quantum solution to the Newcomb's paradox, International Journal of Quantum Information [J]. 2003
[31] Penrose, R., Shadows of the Mind [M]. Cambridge: Cambridge University Press,1994
[32] Wallace, D., Quantum theory of probability and decision theory, Revisited. Quantum physics [J]. 2002
[33] Nielsen, M. A., Chuang, I. L., Quantum Computation and Quantum Information [M], Cambridge: Cambridge University Press, 2000
[34] Holevo, A., Statistical Structure of Quantum Theory [M]. Berlin: Springer Verlag, 2001
[35] Piotrowski, E. W., S adkowski, J., An invitation to quantum game theory, International Journal of Theoretical Physics [J]. 2003
[36] Meyer, D. A., Quantum strategies, Physical Review Letters [J]. 1999
[37] Eisert, J., Wilkens, M., Lewenstein, M., Quantum Games and Quantum Strategies, Physical Review Letters [J]. 1999
[38] Iqbal A., Toor A.H., Backwards: Conduction outcome in a quantum game, Physical Review [J]. 2002
[39] Iqbal A., Toor A. H., Quantum mechanics gives stability to a Nash equilibrium, Physical Review A [J]. 2002
[40] Piotrowski, E. W., S adkowski, J., Quantum English auctions, Physica A [J]. 2003
[41] Piotrowski, E. W., S adkowski, J., Quantum bargaining games, Physica A [J]. 2002
[42] S adkowski, J., Gi en paradoxes in quantum market games, Physica A [J]. 2003
[43] Wigner, E., On the quantum correction for thermodynamic equilibrium, Physical Review[J]. 1932
[44] Fischer, M. C., Gutierrez-Medina, B., Raizen, M. G., Observation of the quantum Zeno and anti-Zeno e ects in an unstable system, Physical Review Letters[J]. 2001
[45] S. J. van Enk, R. Pike. Classical rules in quantum games. Physical Review A [J]. 2002
[46] Simon C. Benjamin and Patrick M. Hayden. Multiplayer quantum games. Physical Review A [J]. 2001