I wonder if a behavior strategy in an extensive form game has always an equivalent mixed strategy. There is no consensus in the literature I've read on this:
in the chapter in the Handbook of game theory vol. 1 on the page 32, there is written We will see below that a behavior strategy is essentially a (special kind of) mixed strategy. which is formally stated in lemma 7.3
However, in the book by Maschler, Solan and Zamir Game Theory on page 225 in the example 6.9, there is a sentence The Absent-Minded Driver: a game with a behavior strategy that has no equivalent mixed strategy. For the second source just type
"The Absent-Minded Driver: a game with a behavior strategy that has no equivalent mixed strategy."
into books.google.com and click on the first link. If you wish pdf of the handbook see here: https://ulozto.cz/!0NWHQRrhzNyb/r-j-aumann-s-hart-handbook-of-game-theory-witvol1-bookos-org-pdf AND click on "Stahnout pomalu".
How can go these two facts together?