论文标题
常规赛中每个球队的最佳策略在淘汰赛中赢得冠军
Best Strategy for Each Team in The Regular Season to Win Champion in The Knockout Tournament
论文作者
论文摘要
在J. Schwenk（2018）中[“播种淘汰赛的正确方法是什么？”从美国的数学月份中检索出来] Schwenk在播种单个消除（或淘汰赛）比赛的标准方法中发现了令人惊讶的弱点。他特别表明，对于游戏结果的一定概率模型，可能是顶级种子球队赢得比赛的可能性要比第二个种子球队少的可能性。这增加了在某些情况下，有可能在某些情况下故意失去一场比赛，以便在比赛中获得最佳（尽管可能较低）的种子可能是有利的。我们在四个团队联赛的背景下研究了这个问题，该联赛由循环的“常规赛”组成，然后是一次淘汰赛，并由常规赛的结果确定了种子[4]。使用与Schwenk相同的概率模型，我们表明，在某些情况下，确实使团队有意输球是最佳的。此外，我们展示了一个团队如何决定是否有意丢失。我们进行了两个详细的分析。一种是对于其他球队总是试图赢得每场比赛的情况。另一种是在其他团队足够聪明的情况下，即在必要时他们也可以故意失去一些游戏。该分析涉及概率和（多人）游戏理论中的计算。
In J. Schwenk.(2018) ['What is the Correct Way to Seed a Knockout Tournament?' Retrieved from The American Mathematical Monthly], Schwenk identified a surprising weakness in the standard method of seeding a single elimination (or knockout) tournament. In particular, he showed that for a certain probability model for the outcomes of games it can be the case that the top seeded team would be less likely to win the tournament than the second seeded team. This raises the possibility that in certain situations it might be advantageous for a team to intentionally lose a game in an attempt to get a more optimal (though possibly lower) seed in the tournament. We examine this question in the context of a four team league which consists of a round robin "regular season" followed by a single elimination tournament with seedings determined by the results from the regular season [4]. Using the same probability model as Schwenk we show that there are situations where it is indeed optimal for a team to intentionally lose. Moreover, we show how a team can make the decision as to whether or not it should intentionally lose. We did two detailed analysis. One is for the situation where other teams always try to win every game. The other is for the situation where other teams are smart enough, namely they can also lose some games intentionally if necessary. The analysis involves computations in both probability and (multi-player) game theory.
