论文标题
多州游戏的专制策略
Autocratic Strategies of Multi-State Games
论文作者
论文摘要
在单州重复的游戏中，零确定的策略可以单方面强制收益的功能，以在特定的封闭间隔内采用值。当分析中不存在明确使用决定因素时，它们被称为专制。我们将他们的研究扩展到具有确定性过渡的有限州游戏的设置。对于给定的游戏，我们发现可执行值间隔的终点必须满足固定点方程。从这些极端可执行的值中，我们表明，始终有可能构建有限的内存策略来执行特定值。提出了一种算法，该算法将近似于每个状态中的可强制性值。最后，我们提出了可以从近似溶液中回收精确溶液的公式。
In a single-state repeated game, zero-determinant strategies can unilaterally force functions of the payoffs to take values in particular closed intervals. When the explicit use of a determinant is absent from the analysis, they are instead called autocratic. We extend their study to the setting of finite state games with deterministic transitions. For a given game we find that the endpoints of the intervals of enforceable values must satisfy fixed point equations. From these extreme enforceable values we show it is always possible to construct finite memory strategies to enforce a particular value. An algorithm is presented which will approximate the enforceable values in each state. Finally, we present formulas from which the exact solutions can be recovered from the approximate solution.
