This lecture explores the ultimatum game when the proposer can make an offer from a continuum of possibilities.
- Offering any of the surplus to the receiver is never optimal for the proposer. This is because the proposer can always shave the offer down by a tiny fraction, still induce the receiver to accept, and keep more of the surplus for himself.
- The proposer can no longer shave down the offer by a tiny fraction if the offer gives none of the surplus to the receiver. (The receiver would reject such offers.)
- Thus, the proposer can capture the entire surplus.