Possibly-Final Offers

Abstract

A price-setting seller faces a buyer with unknown reservation value. We show that if the buyer is sufficiently risk averse, the seller can benefit from employing a Possibly-Final Offer (PFO) strategy. In a PFO, if the buyer rejects the seller's initial offer the seller sometimes terminates the interaction. If the seller does not terminate, he follows up with a subsequent, more attractive offer. As the buyer's risk aversion increases, the seller's expected profit under the optimal PFO approaches the full-information profit. These results extend to contexts with endogenous commitment, multiple types of buyers, multidimensional objects, and nonseparable utility functions.