Suppose you and a classmate are playing a game where your classmate proposes a division of $1.00. Then, you either accept or reject the offer. If you accept, then you and the classmate get the proposed portions of the dollar. However, if you reject the offer, then you and your classmate receive nothing. Suppose your classmate offers you

$0.23.

What is your optimal strategy? Your optimal strategy is to

accept the proposed division.

Now suppose instead that you propose the division of the dollar. Your classmate will then accept or reject your division. If the classmate accepts, then you each receive the portion of the dollar as you have proposed. However, if your classmate rejects, then you both get nothing. Your optimal strategy is to offer your classmate $ ?

(Enter a numeric response rounded to two decimal places.)

* note a pervious tutor suggested the answer $0.12 which was marked as incorrect.