In repeated games with incomplete information, rational agents must carefully weigh the tradeoffs of advantageously exploiting their information to achieve a short-term gain versus carefully concealing their information so as not to give up a long-term informed advantage. The theory of infinitely-repeated two-player zero-sum games with incomplete information has been carefully studied, beginning with the seminal work of Aumann and Maschler. While this theoretical work has produced a characterization of optimal strategies, algorithms for solving for optimal strategies have not yet been studied. For the case where one player is informed about the true state of the world and the other player is uninformed, we provide a non-convex mathematical programming formulation for computing the value of the game, as well as optimal strategies for the informed player. We then describe an efficient algorithm for solving this difficult optimization problem to within arbitrary accuracy. We also discuss how to efficiently compute optimal strategies for the uninformed player using the output of our algorithm.
在重复的信息不完整的游戏中,理性的行为人必须谨慎权衡权衡利弊,以利于利用其信息来获得短期收益,而不是谨慎地隐藏其信息以免放弃长期的知情利益。从Aumann和Maschler的开创性工作开始,已经仔细研究了具有不完全信息的无限重复两人零和游戏的理论。虽然这项理论工作产生了最佳策略的表征 I>,但尚未研究用于最佳策略的求解 I>的算法。对于其中一个玩家了解了世界的真实状态而另一个玩家不了解 I>的情况,我们提供了一种非凸的数学编程公式来计算游戏,以及明智玩家的最佳策略。然后,我们描述了一种有效的算法,可以在任意精度内解决这一难题。我们还将讨论如何使用我们算法的输出为不知情的玩家有效地计算最佳策略。 P>
two-person zero-sum incomplete-information repeated games;
机译:信息不完整且持续时间不确定的两人零和重复游戏的价值
机译:重复的两人零和游戏,具有不平等的折扣和私人监控
机译:两人零和重复游戏中渐近值的连续时间方法
机译:解决一个不完整信息的双人零和重复游戏
机译:信息不完整的重复游戏中的声誉和有限记忆。
机译:零和思想的政治:政治意识形态与生活是零和游戏的信念之间的关系
机译:两人零和重复游戏的渐近值的连续时间方法