多人量子博弈若干问题的研究
发布时间：2018-09-16 20:30
【摘要】：量子博弈论是应用数学的一个分支,是经典博弈论与量子信息论结合的产物,相对经典博弈有明显的优势。它作为独立的学科在政治、经济、文化、军事领域等领域有广泛的应用。在现实研究中,许多过程都可以看作是竞争博弈,而博弈不单单涉及两人博弈,更多的是多人博弈,因此对多人量子博弈的研究更具有实际应用价值。 本论文主要从两方面讨论分析多人量子博弈,一是博弈的最佳结果：有唯一Nash均衡和达到上限值的期望收益。二是多人非合作博弈中的合谋。本文的主要研究工作和创新点具体如下： 在非合作博弈方面,我们主要研究了少数者博弈。第一,计算了N人少数者博弈期望收益的最小值和上限值,并给出严格的数学证明过程。第二,提出了control-target协议,并用该协议设计了两选择少数者博弈和多选择少数者博弈过程,使得博弈有最佳结果。第三,分析了少数者博弈中的量子合谋,找到了最佳量子合谋策略——“n均分”组合策略,使得合谋者有最大期望收益。第四,分析了合谋与博弈初态的关系,为博弈初态的选择提供了理论依据,并指出部分玩家总可以通过合谋提高期望收益。在合作博弈方面,我们主要研究了完全协调博弈。我们用control-target协议设计了博弈过程,而且将其扩展到多人多选择的完全协调博弈,并用类control-target协议设计该博弈过程,使得两个博弈均有最佳结果。
[Abstract]:Quantum game theory is a branch of applied mathematics. It is the result of the combination of classical game theory and quantum information theory. It has obvious advantages over classical game theory. As an independent subject, it is widely used in political, economic, cultural, military and other fields. In practical research, many processes can be regarded as competitive game, and game is not only involved in two-person game, but also multi-player game, so the study of multi-person quantum game has more practical application value. This paper mainly discusses and analyzes the multiplayer quantum game from two aspects. One is the best result of the game: there is a unique Nash equilibrium and the expected income reaches the upper limit. The second is the collusion in multi-person non-cooperative game. The main research work and innovation of this paper are as follows: in non-cooperative game, we mainly study minority game. First, we calculate the minimum and upper limit of the expected return of N-person minority game, and give a strict mathematical proof process. Secondly, the control-target protocol is proposed, and the two-choice minority game and the multi-selection minority game process are designed with this protocol, so that the game has the best result. Thirdly, the quantum collusion in minority game is analyzed, and the optimal quantum collusion strategy, "n-equal partition" combination strategy, is found, so that the collusion has the maximum expected return. Fourthly, the relationship between collusion and initial game is analyzed, which provides a theoretical basis for the selection of initial game, and points out that some players can always increase the expected income by collusion. In the cooperative game, we mainly study the fully coordinated game. We design the game process with control-target protocol, and extend it to the fully coordinated game with many people and many choices. We design the game process with control-target protocol, so that the two games have the best results.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O225
本文编号：2244708
[Abstract]:Quantum game theory is a branch of applied mathematics. It is the result of the combination of classical game theory and quantum information theory. It has obvious advantages over classical game theory. As an independent subject, it is widely used in political, economic, cultural, military and other fields. In practical research, many processes can be regarded as competitive game, and game is not only involved in two-person game, but also multi-player game, so the study of multi-person quantum game has more practical application value. This paper mainly discusses and analyzes the multiplayer quantum game from two aspects. One is the best result of the game: there is a unique Nash equilibrium and the expected income reaches the upper limit. The second is the collusion in multi-person non-cooperative game. The main research work and innovation of this paper are as follows: in non-cooperative game, we mainly study minority game. First, we calculate the minimum and upper limit of the expected return of N-person minority game, and give a strict mathematical proof process. Secondly, the control-target protocol is proposed, and the two-choice minority game and the multi-selection minority game process are designed with this protocol, so that the game has the best result. Thirdly, the quantum collusion in minority game is analyzed, and the optimal quantum collusion strategy, "n-equal partition" combination strategy, is found, so that the collusion has the maximum expected return. Fourthly, the relationship between collusion and initial game is analyzed, which provides a theoretical basis for the selection of initial game, and points out that some players can always increase the expected income by collusion. In the cooperative game, we mainly study the fully coordinated game. We design the game process with control-target protocol, and extend it to the fully coordinated game with many people and many choices. We design the game process with control-target protocol, so that the two games have the best results.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O225
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