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In J. Schwenk.(2018) ['What is the Correct Way to Seed a KnockoutTournament?' Retrieved from The American Mathematical Monthly], Schwenkidentified a surprising weakness in the standard method of seeding a singleelimination (or knockout) tournament. In particular, he showed that for acertain probability model for the outcomes of games it can be the case that thetop seeded team would be less likely to win the tournament than the secondseeded team. This raises the possibility that in certain situations it might beadvantageous for a team to intentionally lose a game in an attempt to get amore optimal (though possibly lower) seed in the tournament. We examine thisquestion in the context of a four team league which consists of a round robin"regular season" followed by a single elimination tournament with seedingsdetermined by the results from the regular season [4]. Using the sameprobability model as Schwenk we show that there are situations where it isindeed optimal for a team to intentionally lose. Moreover, we show how a teamcan make the decision as to whether or not it should intentionally lose. We didtwo detailed analysis. One is for the situation where other teams always try towin every game. The other is for the situation where other teams are smartenough, namely they can also lose some games intentionally if necessary. Theanalysis involves computations in both probability and (multi-player) gametheory.

Best Strategy for Each Team in The Regular Season to Win Champion in The Knockout Tournament