量子博弈中的几个问题
Some Topics in Quantum Games
摘要：
本文在作者硕士论文的基础上，研究了两个玩家同时行动的量子博弈。基于最佳反应函数法，构造了一个求解量子博弈纯策略纳什均衡的数值算法。然后，它被用来表明，有一个临界程度的纠缠以上的纯策略纳什均衡不存在。这两种支付的行为接近合作的经典行为。定义了贝叶斯量子博弈，证明了在一定条件下，即使纠缠最大，这种博弈也存在{ \it}纯策略纳什均衡.给出了基于两人{ \it 3}决策经典博弈的量子博弈的基本组成。这需要定义三位数（而不是比特）和量子三位数（而不是量子比特）。结果表明，在这个量子博弈中，不存在经典可解性，即经典策略不是量子策略的特例。构造了一个将纯二量子态转变为最大纠缠态的纠缠算符。
英文摘要：
This work, based on the author's MA thesis, concentrates on simultaneous move quantum games of two players. A numerical algorithm based on the method of best response functions, designed to search for pure strategy Nash equilibrium in quantum games is constructed. It is then used show that there is a critical degree of entanglement above which a pure strategy Nash Equilibrium does not exist. The behavior of the two payoffs approach the cooperative classical ones. Bayesian quantum games are defined, and it is shown that under certain conditions, there {\it is} a pure strategy Nash equilibrium in such games even when entanglement is maximal. The basic ingredients of a quantum game based on a two-players {\it three} decisions classical games are presented. This requires the definition of trits (instead of bits) and quantum trits (instead of quantum bits). It is shown that in this quantum game, there is no classical commensurability in the sense that the classical strategies are not obtained as a special case of the quantum strategies. An entanglement operator transforming a pure two qutrit state into a maximally entangled one is explicitly constructed.
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