To accept or not to accept: Optimal strategy for sellers 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. We show that the optimal strategy is characterized by a nonincreasing stochastic set of reservation prices. We also provide numerical analysis to calibrate the model and provide support to the observation that first offers in residential real estate markets tend to be higher than subsequent offers. The model's prediction closely matches the empirical findings of Merlo and Ortalo-Magne that more than 70% of the properties sell to the buyer who makes the first offer.