Deadlines, Offer Timing, and the Search for Alternatives

We model two agents who can benefit from a mutual deal or partnership, yet are also searching for outside alternatives. This generic situation is observed in various settings (e.g., the job market for experts) and involves several decisions. The proposer decides not only on the timing, deadline, and value of her offer but also on how to handle her outside alternatives; the responder decides whether or not to accept the proposer's offer (if any) and how to handle his own outside alternatives. A responder holding an offer with a long deadline becomes more selective when evaluating outside alternatives, an effect we call acceptance deterrence. The strength of this effect depends on the information structure of the game as well as on the ways in which the proposer and the responder can interact. A practical prescription for the proposer is to use exploding offers in the settings where acceptance deterrence is weak (e.g., stationary search, search with recall). In contrast, longer deadlines are benefcial in the settings where acceptance deterrence is strong (e.g., perfect information)