量子博弈论研究
Studies in the Theory of Quantum Games
摘要：
量子博弈论是近年来发展迅速的一个新的研究领域。在量子世界中玩游戏的最初动机来自于重新制定量子通信协议和算法的可能性，即量子和经典玩家之间的游戏。这种可能性导致了这样一种观点，即量子游戏有可能为量子算法的工作提供有益的见解，甚至在寻找新算法方面。本文分析和比较了经典博弈和量子博弈中的一些有趣的博弈。论文的很大一部分涉及调查的纳什均衡概念的细化概念。这种改进被称为进化稳定策略（ESS），最初是由数学生物学家在20世纪70年代引入的，用于使用借鉴博弈论的技术来模拟进化中的种群。分析是围绕一种情况时，量化改变ESS，而不影响相应的纳什均衡。量化的解决方案的概念以外的纳什均衡的影响，并进行了讨论。为此，选择了联盟价值、后向归纳结果和子博弈完美结果的概念。重复博弈的信息结构不同于一次性博弈。调查提出了一种可能的方式，量化改变了重复游戏的结果。最后，提出了两个新的建议，发挥量子版本的经典矩阵游戏。第一种方法利用德布罗意波与移动的物质物体的关联，作为玩量子游戏的资源。第二个建议涉及EPR类型设置直接利用贝尔不等式中的相关性来玩双矩阵游戏。
英文摘要：
Theory of quantum games is a new area of investigation that has gone through rapid development during the last few years. Initial motivation for playing games, in the quantum world, comes from the possibility of re-formulating quantum communication protocols, and algorithms, in terms of games between quantum and classical players. The possibility led to the view that quantum games have a potential to provide helpful insight into working of quantum algorithms, and even in finding new ones. This thesis analyzes and compares some interesting games when played classically and quantum mechanically. A large part of the thesis concerns investigations into a refinement notion of the Nash equilibrium concept. The refinement, called an evolutionarily stable strategy (ESS), was originally introduced in 1970s by mathematical biologists to model an evolving population using techniques borrowed from game theory. Analysis is developed around a situation when quantization changes ESSs without affecting corresponding Nash equilibria. Effects of quantization on solution-concepts other than Nash equilibrium are presented and discussed. For this purpose the notions of value of coalition, backwards-induction outcome, and subgame-perfect outcome are selected. Repeated games are known to have different information structure than one-shot games. Investigation is presented into a possible way where quantization changes the outcome of a repeated game. Lastly, two new suggestions are put forward to play quantum versions of classical matrix games. The first one uses the association of De Broglie's waves, with travelling material objects, as a resource for playing a quantum game. The second suggestion concerns an EPR type setting exploiting directly the correlations in Bell's inequalities to play a bi-matrix game.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
