We have two teams $a, b$ each containing $n$ players. Function $w(a_i, b_i)$ gives the chance of player $a_i$ beating $b_i$. This chance is (potentially) different for each pair of players, but each game must end in a win, thus $w(a_i, b_i) = 1 - w(b_i, a_i)$.
Now teams $a$ and $b$ will play a tournament. Each will field one player at a time.
- Initially both teams will have to field a player of their choice simultaneously.
- The player that loses this match is disqualified and can no longer play. The losing team will have to field another player of their choice, the winner has to stay.
- This continues, the first team to run out of players to field loses.
What is the optimal strategy in choosing the players, given full information about $w$?
I'm also interested in a variant where the winner of a match is disqualified (meaning they can't field that player again), and both teams simultaneously choose new players to field (the losing player can be fielded again). The first team to get every player on their team disqualified wins.