First Cut is the Deepest: On Optimal Acceptance Strategies in Real Estate

We consider the problem of a seller who faces an unknown number of offers where each offer is a random draw from a known distribution. The objective of the seller is to maximize the probability that the highest offer is chosen. This is equivalent to maximizing expected utility when one assigns preferences to rankings of offers. We identify the optimal selling strategy using the technique of Porosiński (1987) and general optimal stopping theory. We show that the optimal strategy is characterized by a non-increasing stochastic set of reservation prices. This is in contrast to the classical search theory models where reservation prices are deterministic. Our analysis also provides theoretical support to the observation that first offers in residential real estate markets should be accepted more often since they tend to be higher than subsequent offers.