论文标题
无限重复的量子游戏和战略效率
Infinitely Repeated Quantum Games and Strategic Efficiency
论文作者
论文摘要
重复的量子游戏理论解决了选择量子策略的玩家之间的长期关系。在传统的量子游戏理论中，单圆量子游戏或最多有限重复的游戏已经被广泛研究，但是对于无限重复的量子游戏而闻名。调查无限重复的游戏至关重要，因为有限重复的游戏与单轮游戏没有太大差异。在这项工作中，我们建立了一般重复的量子游戏的概念，并向量子民间定理展示了，该定理声称，通过迭代游戏，可以找到游戏的平衡策略，并获得相应单圆量子游戏的NASH平衡而无法获得的奖励。反复的量子囚犯的困境与反复的古典囚犯困境之间的一个显着差异是，当纠缠足够强大时，经典的帕累托最佳解决方案并不总是反复量子游戏的平衡。当纠缠足够强大并且奖励很小时，相互合作不能成为重复量子游戏的平衡。此外，我们提出了重复的量子囚犯困境的几种具体平衡策略。
Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however less is known for infinitely repeated quantum games. Investigating infinitely repeated games is crucial since finitely repeated games do not much differ from single round games. In this work we establish the concept of general repeated quantum games and show the Quantum Folk Theorem, which claims that by iterating a game one can find an equilibrium strategy of the game and receive reward that is not obtained by a Nash equilibrium of the corresponding single round quantum game. A significant difference between repeated quantum prisoner's dilemma and repeated classical prisoner's dilemma is that the classical Pareto optimal solution is not always an equilibrium of the repeated quantum game when entanglement is sufficiently strong. When entanglement is sufficiently strong and reward is small, mutual cooperation cannot be an equilibrium of the repeated quantum game. In addition we present several concrete equilibrium strategies of the repeated quantum prisoner's dilemma.
