actually i disagree on the "wants to win" part - that opens itself to out of character behavior. like... if courage the cowardly dog were nominated, knowing he's in a fight would result in him bailing, not wanting to win. knowing there's a fight should be enough, especially when we're actually MAKING them after all. if a character is super powerful but doesn't want to actually fight then it lends itself to 'well, can the opponent win without fighting directly?' which i think is fine. of course that'd have its own set of problems - the issue of "Well, either they talk him out and win or they don't, pick a fight, and lose." but the idea is being forced to want to win always seemed... unnatural.
The problem with not including the part where the combatants will actually want to win is that its the same as not having the "knows they're in a fight" rule at all. The whole point is who would win in a fight, it doesn't really do anything if you have one person just not fight, they still need to lose a fight for the other person to win. Deliberate giving up defeats the purpose of the contest, it really does need to come down to an actual battle between the two, otherwise its pointless. At the very least, both sides should be assumed to know that nothing will happen until one of them beats the other.
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We clasped our hands, our hands in praise of a conquerors right to tyranny