Exploding Offers

A buyer seeks to purchase an asset from a seller who has a finite time T in which to sell his asset. Either the buyer's offer is permanent and remains available until time T, or it is an exploding offer and remains in effect only at the instant it is made. Our goal is to determine when an exploding offer maximizes the buyer's probability of purchasing the asset (at the given offer price). We embed our analysis in a standard continuous time finite horizon search model with recall in which only one buyer is strategic and considers making an exploding offer. Our analysis and examples reveal that the strategic buyer's choice of offer duration is complex: almost anything can occur. We obtain an explicit characterization of the optimal choice when the offer distribution is uniform.