多人量子博弈若干問題的研究
發(fā)布時間：2018-09-16 20:30
【摘要】：量子博弈論是應(yīng)用數(shù)學的一個分支,是經(jīng)典博弈論與量子信息論結(jié)合的產(chǎn)物,相對經(jīng)典博弈有明顯的優(yōu)勢。它作為獨立的學科在政治、經(jīng)濟、文化、軍事領(lǐng)域等領(lǐng)域有廣泛的應(yīng)用。在現(xiàn)實研究中,許多過程都可以看作是競爭博弈,而博弈不單單涉及兩人博弈,更多的是多人博弈,因此對多人量子博弈的研究更具有實際應(yīng)用價值。 本論文主要從兩方面討論分析多人量子博弈,一是博弈的最佳結(jié)果：有唯一Nash均衡和達到上限值的期望收益。二是多人非合作博弈中的合謀。本文的主要研究工作和創(chuàng)新點具體如下： 在非合作博弈方面,我們主要研究了少數(shù)者博弈。第一,計算了N人少數(shù)者博弈期望收益的最小值和上限值,并給出嚴格的數(shù)學證明過程。第二,提出了control-target協(xié)議,并用該協(xié)議設(shè)計了兩選擇少數(shù)者博弈和多選擇少數(shù)者博弈過程,使得博弈有最佳結(jié)果。第三,分析了少數(shù)者博弈中的量子合謀,找到了最佳量子合謀策略——“n均分”組合策略,使得合謀者有最大期望收益。第四,分析了合謀與博弈初態(tài)的關(guān)系,為博弈初態(tài)的選擇提供了理論依據(jù),并指出部分玩家總可以通過合謀提高期望收益。在合作博弈方面,我們主要研究了完全協(xié)調(diào)博弈。我們用control-target協(xié)議設(shè)計了博弈過程,而且將其擴展到多人多選擇的完全協(xié)調(diào)博弈,并用類control-target協(xié)議設(shè)計該博弈過程,使得兩個博弈均有最佳結(jié)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.
【學位授予單位】：北京郵電大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O225
本文編號：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.
【學位授予單位】：北京郵電大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O225
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