量子博弈中纳什均衡的不动点保证
No fixed-point guarantee of Nash equilibrium in quantum games
摘要：
量子博弈理论允许参与者选择准备和测量量子态的策略。而传统的博弈论提供了非合作博弈的固定点稳定性的保证，所谓的纳什均衡，我们发现这种保证是不提供量子游戏。特别是，我们表明条件Glickberg的不动点定理不适用于纯量子游戏时的回报是一个物理观测。我们进一步表明，纳什均衡时，可以保证支付的状态准备。
英文摘要：
The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we find this guarantee is not provided for quantum games. In particular, we show the conditions for Glickberg's fixed-point theorem do not apply to pure quantum games when the payoff is a physical observable. We further show that Nash equilibrium can be guaranteed when the payoff is defined with respect to state preparation.
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