标题： 连续放松重复博弈中的零确定策略 显示英文标题

标题： Zero-determinant strategies in repeated continuously-relaxed games

摘要： 混合扩展在博弈论中发挥了重要作用，特别是在策略型博弈中纳什均衡存在性的证明中。 混合扩展可以被视为策略型博弈的连续松弛。 最近，在重复博弈中，引入了一类称为零决定策略的行为策略。 零决定策略单方面强制支付之间的线性关系，并用于控制玩家的支付。 有许多尝试扩展零决定策略，以便将其应用于更广泛的情况。 在这里，我们将零决定策略扩展到阶段博弈中玩家行动集被连续松弛的重复博弈。 我们发现，与原始的重复博弈相比，连续松弛扩大了可能的零决定策略的范围。 此外，我们引入了一种特殊的零决定策略，称为一点零决定策略，它在所有轮次中仅重复一个连续松弛的动作。 通过研究几个例子，我们表明混合策略纳什均衡的一些性质可以重新解释为一点零决定策略的支付控制特性。 显示英文摘要

摘要： Mixed extension has played an important role in game theory, especially in the proof of the existence of Nash equilibria in strategic form games. Mixed extension can be regarded as continuous relaxation of a strategic form game. Recently, in repeated games, a class of behavior strategies, called zero-determinant strategies, was introduced. Zero-determinant strategies unilaterally enforce linear relations between payoffs, and are used to control payoffs of players. There are many attempts to extend zero-determinant strategies so as to apply them to broader situations. Here, we extend zero-determinant strategies to repeated games where action sets of players in stage game are continuously relaxed. We see that continuous relaxation broadens the range of possible zero-determinant strategies, compared to the original repeated games. Furthermore, we introduce a special type of zero-determinant strategies, called one-point zero-determinant strategies, which repeat only one continuously-relaxed action in all rounds. By investigating several examples, we show that some property of mixed-strategy Nash equilibria can be reinterpreted as a payoff-control property of one-point zero-determinant strategies.