  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.
