Alice and Bob are competing team managers in a gladiator competition. Alice's gladiators have strength a1, a2, a3...an and Bob's have strength b1, b2, b3...bm. Each round, Alice will select a gladiator from her team and then Bob will select one from his team and the chosen gladiators will fight.
If a gladiator of strength x fights a gladiator of strength y, the chance the one with strength x wins is given by x/(x+y). The losing gladiator is eliminated and then a new round begins with Alice and Bob selecting gladiators to fight. The competition ends when one of the teams has run out of gladiators.
What is the optimal play? In particular, suppose Alice always chooses to send in her strongest gladiator, how should Bob respond?
Its the exact same as last time, but this time the gladiators strengths are constant, rather than gaining confidence from the fights.
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