# Question on the equivalence of behaviour strategy and mixed strategy for a player with a single information set

Prove that if a player in an extensive-form game has only one information set, then his set of mixed strategies equals his set of behavior strategies.

This is the exercise $6.4$ on page $246$ in Game Theory by Michael Maschler, Eilon Solan and Shmuel Zamir.

But I think the example game $A$(absent-minded driver game) in $6.3$ invalidate this claim, since Player I can't reach the payoff $10$ by a mixed strategy but it's not the case for a behavior stategy. What's wrong?