= Solution
For a payoff set $A\subseteq M^\omega$, a <quasistrategy> for a player assigns a nonempty subset of $M$ to every finite position at which that player moves. A play is consistent with it when each of that player's moves belongs to the assigned set. The set $A$, or equivalently the <infinite game of perfect information> $G(A)$, is <quasidetermined infinite game>[quasidetermined] when one player has a quasistrategy under which every consistent play is won by that player.
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