This work proposes an extension of the well-known Eisert–Wilkens–Lewenstein scheme for playing a twice repeated \(2\times 2\) game using a single quantum system with ten maximally entangled qubits. The proposed scheme is then applied to the Prisoner’s Dilemma game. Rational strategy profiles are examined in the presence of limited awareness of the players. In particular, the paper considers two cases of a classical player against a quantum player game: the first case when the classical player does not know that his opponent is a quantum one and the second case, when the classical player is aware of it. To this end, the notion of unawareness was used, and the extended Nash equilibria were determined.

中文翻译：

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二次重复$$ 2 \ times 2 $$ 2×2游戏的量子方法

这项工作提出了著名的Eisert–Wilkens–Lewenstein方案的扩展，该方案使用具有10个最大纠缠量子位的单量子系统玩两次重复的（2 × 2）游戏。拟议的方案然后应用于囚徒困境游戏。在参与者意识有限的情况下检查理性策略配置文件。特别是，本文考虑了古典玩家与量子玩家游戏的两种情况：一种是古典玩家不知道自己的对手是量子玩家的情况，另一种是古典玩家意识到它的情况。为此，使用了无意识的概念，并确定了扩展的纳什均衡。