True or false and explain.

In an ultimatum game, suppose the pie to be divided between the two players is infinitely divisible. We have been told the unique subgame perfect equilibrium(SPE) is for the proposer to claim the entire pie for herself and for the responder to accept any proposal made by the proposer. But this cannot be an SPE since the responder is indifferent between accepting and rejecting the proposer's (so-called) equilibrium proposal.