Read the working paper
INSEAD Working Paper 2016/09/DSC
We model two agents who can benefit from a mutual deal or partnership yet are also involved in outside search. This generic situation is observed in various settings (e.g., the job market for experts) and involves several decisions.
The proposer decides when to make an offer to the responder, what deadline to set, and how to handle her outside alternatives; the responder decides whether to accept the proposer's offer (if any) and also how to handle his own outside alternatives. We find that the proposer's optimal strategy is to set the shortest possible deadline and that this conclusion is robust to different sets of assumptions. Across all variations of the game, we find that deals are made at a time preferred by the less eager agent (i.e., the one who would rather sign a mutual deal later) unless the more eager agent can make an ultimatum offer.