论文标题
通过零确定的策略来控制有条件的期望
Controlling conditional expectations by zero-determinant strategies
论文作者
论文摘要
零确定的策略是重复游戏中的记忆策略，它们单方面地在玩家的预期收益之间执行线性关系。最近，将零确定策略的概念扩展到了以$ n \ geq 1 $的方式扩展到内存的类别 - $ n $ n $策略，这使一个玩家可以更复杂地控制收益。但是，我们可以通过内存来做的事情 - $ n $零确定的策略仍然不清楚。在这里，我们表明内存 - 重复游戏中的零确定性策略可用于控制收益的条件期望。同等地，它们可用于控制有偏见的合奏中的预期收益，在这种偏见的史轮廓具有较大价值的偏见功能的历史史。控制收益的有条件期望对于加强零确定策略很有用，因为玩家可以选择条件，以至于只有在条件下包含对一个玩家的不利动作概况。我们提供了几个记忆的例子 - $ n $零确定的策略在重复的囚犯的困境游戏中。我们还解释说，零确定策略的变形版本很容易扩展到内存 - $ n $情况。
Zero-determinant strategies are memory-one strategies in repeated games which unilaterally enforce linear relations between expected payoffs of players. Recently, the concept of zero-determinant strategies was extended to the class of memory-$n$ strategies with $n\geq 1$, which enables more complicated control of payoffs by one player. However, what we can do by memory-$n$ zero-determinant strategies is still not clear. Here, we show that memory-$n$ zero-determinant strategies in repeated games can be used to control conditional expectations of payoffs. Equivalently, they can be used to control expected payoffs in biased ensembles, where a history of action profiles with large value of bias function is more weighted. Controlling conditional expectations of payoffs is useful for strengthening zero-determinant strategies, because players can choose conditions in such a way that only unfavorable action profiles to one player are contained in the conditions. We provide several examples of memory-$n$ zero-determinant strategies in the repeated prisoner's dilemma game. We also explain that a deformed version of zero-determinant strategies is easily extended to the memory-$n$ case.
