策略无关游戏的最佳选择
Strategy-indifferent games of best choice
摘要：
最佳选择博弈（英语：Game of Best Choice）（或称秘书问题）是一个在固定数量的候选选择中做出不可撤销的决定的模型，这些候选选择以随机顺序依次呈现，一次一个。因为经典的最优解是已知的拒绝候选人的初始序列，一个悖论出现的事实，即候选人有一个激励，以定位自己立即在这个截止后，挑战的假设，候选人到达均匀随机顺序。解决这个问题的一种方法是考虑每个（合理的）策略都有相同成功概率的博弈。在这项工作中，我们将这些“策略无关”的最佳选择游戏。事实证明，赢得这样一个游戏的概率本质上是候选排序的完整集合中从左到右最大值的期望数量的倒数。我们提出了一些例子，这些游戏的基础上，避免排列模式的大小为3，其中涉及到计算分布的左到右的最大值在这些模式类。
英文摘要：
The game of best choice (or "secretary problem") is a model for making an irrevocable decision among a fixed number of candidate choices that are presented sequentially in random order, one at a time. Because the classically optimal solution is known to reject an initial sequence of candidates, a paradox emerges from the fact that candidates have an incentive to position themselves immediately after this cutoff which challenges the assumption that candidates arrive in uniformly random order. One way to resolve this is to consider games for which every (reasonable) strategy results in the same probability of success. In this work, we classify these "strategy-indifferent" games of best choice. It turns out that the probability of winning such a game is essentially the reciprocal of the expected number of left-to-right maxima in the full collection of candidate rank orderings. We present some examples of these games based on avoiding permutation patterns of size 3, which involves computing the distribution of left-to-right maxima in each of these pattern classes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
