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研究了量子博弈中的“PQ”问题, 重点探讨了参与者策略制定、收益分配和量子效应对博弈结果的影响. 首先回顾了量子博弈理论的发展, 并对经典博弈与量子博弈进行了对比, 详细定义了参与者和策略空间, 并利用收益矩阵和量子操作符进行了建模. 为解决“PQ”问题, 提出了量子策略选择和优化算法, 并设计了针对该问题的量子算法. 在实际应用和案例研究方面, 通过评述经典双人博弈—“PQ翻硬币”问题, 表明当其中一个参与人采用量子策略时, 他可以打败他的经典对手, 获得更高的收益. 通过量化手段, 把整个“PQ”问题放在一个更为普遍和公平的条件下, 对其推广并从多个方面和角度再次对其进行研究. 同时, 给出了“不完全公平博弈”和“完全公平博弈”的定义, 对量子硬币翻转博弈(Meyer
1999 Phys. Rev. lett. 821052 )进行了修改, 使博弈公平, 并研究了量子硬币翻转的多轮版本. 最后对“PQ”问题的局限性与扩展性进行了讨论, 并展望了量子博弈研究的未来发展方向.This paper reviews the coin flipping problem of “PQ” in a classical two-player game, and shows that when one player adopts quantum strategy, he can beat his classical opponent and gain higher returns. By using quantitative means, the whole “PQ” problem is put under a more general and fair condition, and it is generalized and studied again from many aspects and angles. Finally, we obtain some more essential and important conclusions, and explain the conclusions and its practical significance through some practical examples. At the same time, this paper gives the definition of imperfect fair game and the definition of perfect fair game, revises the quantum coin flipping game to make the game fair, and studies a multi-round version of quantum coin flipping. Some basic conclusions of fair quantum game are obtained, and the meaning of perfectly fair game is explained in practice.-
Keywords:
- quantum game/
- classical game/
- quantum computing/
- “PQ” problem
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