Is not the following a Nash equillibrium?

Player 1: Offer x=0.1

Player: Accept if x=0.1. Reject otherwise, even if x is larger than 0.1.

Given these strategies it does not pay for player 1 to offer anything else since in that case he would get nothing. It does not matter what strategy player 2 has when x<> 0.1 since it never happens so he can keep the current strategy.

Of course it is not sub-game perfect.