随机淘汰赛
Random Knockout Tournaments
摘要：
我们考虑玩家$1, \ldots, n$之间的随机淘汰赛，其中每场比赛涉及两个玩家。比赛形式由每轮比赛的数量指定，其中每轮比赛的构成是随机的。假设存在$v_1, \ldots, v_n$使得$i$和$j$之间的比赛将由$i$以概率$\frac{v_i}{v_i+v_j}$获胜，我们获得了最佳玩家的锦标赛获胜概率的下界，以及所有玩家的上界和下界。我们还获得了额外的界限，考虑最好的和最坏的格式的球员$1$在特殊情况下$v_1 > v_2 = v_3 = \cdots = v_n.$
英文摘要：
We consider a random knockout tournament among players $1, \ldots, n$, in which each match involves two players. The match format is specified by the number of matches played in each round, where the constitution of the matches in a round is random. Supposing that there are numbers $v_1, \ldots, v_n$ such that a match between $i$ and $j$ will be won by $i$ with probability $\frac{v_i}{v_i+v_j}$, we obtain a lower bound on the tournament win probability for the best player, as well as upper and lower bounds for all the players. We also obtain additional bounds by considering the best and worst formats for player $1$ in the special case $v_1 > v_2 = v_3 = \cdots = v_n.$
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。
