量子策略及量子纠缠对合作联盟特征函数的影响

发布时间：2018-04-02 21:11

本文选题：量子博弈　切入点：特征函数　出处：《武汉大学》2017年硕士论文

【摘要】：近年来,博弈论作为经济学的分支在现实社会中应用越来越广泛。加之近几年几次诺贝尔经济学奖都授予了博弈论学者,对于博弈论的研究也越来越多。量子博弈则是量子理论应用于博弈中来研究博弈行为的一种新的研究方法,通过对策略空间进行扩展,引入纠缠,叠加的性质成功地解决了非合作博弈中的诸如"囚徒困境"、"寡头垄断"等问题,拓展了博弈论的研究方式,得到了越来越多的学者关注。本文主要基于量子博弈的发展特点、以及博弈中相关问题,对量子博弈的发展历程进行划分,对所涉及的量子博弈模型进行归纳,然后对量子博弈优势进行总结。考虑到量子博弈主要研究的是非合作博弈的问题,而对合作博弈的研究较少,又加之特征函数的描述是和联盟策略相关的,因此在合作博弈中选定特征函数作为研究对象,在一个三人的产量竞争模型分别使用量子策略和经典策略求得联盟的特征函数,对比分析得到量子博弈下的特征函数的性质。然后用状态空间的描述形式给出量子策略下特征函数的定义,通过一个算例验证该性质的合理性。最后,考虑到了状态空间和密度矩阵都可以描述系统的状态,运用MW模型对这个产量竞争模型进行一般化描述,然后思考初始状态处于最大纠缠态时联盟的特征函数与经典情况下的差异,给出密度算子描述下的联盟特征函数的定义。文章为量子合作博弈中特征函数的描述提供了一种新的方法,分别从状态向量和密度算子两个角度对产量竞争下的特征函数进行重新描述,有利于合作博弈的量子化研究,为后续的合作博弈提供借鉴。
[Abstract]:In recent years, as a branch of economics, game theory is more and more widely used in real society.In addition, several Nobel prizes in economics have been awarded to game theorists in recent years, and more and more researches have been made on game theory.Quantum game is a new method to study the behavior of game by applying quantum theory to game. By expanding the strategy space, the entanglement is introduced.The superposition has successfully solved the problems such as "prisoner's dilemma" and "oligopoly" in non-cooperative games, expanded the research methods of game theory, and attracted more and more scholars' attention.Based on the development characteristics of quantum game and the related problems in the game, this paper divides the development course of quantum game, sums up the quantum game model involved, and then summarizes the advantages of quantum game.Considering that quantum game mainly studies the problem of non-cooperative game, but the research of cooperative game is less, and the description of characteristic function is related to the strategy of alliance, so the characteristic function is selected as the object of study in cooperative game.In a three-person production competition model, the characteristic functions of the alliance are obtained by using quantum strategy and classical strategy, respectively, and the properties of the eigenfunctions under quantum game are obtained by comparison and analysis.Then the definition of the eigenfunction under the quantum strategy is given in the form of the state space, and the rationality of the property is verified by an example.Finally, considering that both the state space and the density matrix can describe the state of the system, the MW model is used to describe the production competition model.Then consider the difference between the characteristic function of the alliance when the initial state is in the maximal entangled state and the classical case, and give the definition of the characteristic function of the alliance described by the density operator.This paper provides a new method for describing the characteristic function in quantum cooperative game. It is beneficial to the quantization research of cooperative game by redescribing the characteristic function in production competition from the point of view of state vector and density operator respectively.For the subsequent cooperative game to provide reference.
【学位授予单位】：武汉大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O413;F224.32

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