Size Matters, so Does Duration: The Interplay between Offer Size and Offer Deadline
45 Pages Posted: 22 Mar 2018
Date Written: March 19, 2018
This paper investigates the interplay between offer size and offer deadline in a Stackelberg game involving a proposer and responder. The proposer acts first by making an offer to the responder with a deadline, and the responder, concurrently following a continuous finite-horizon search for alternative offers, has to respond to the proposer's offer by the deadline. The responder's strategy is captured by a "reservation value policy" that depends on both the proposer's offer size and deadline and the distribution of alternative offers. Taking this into account, the proposer's optimal strategy can vary from an exploding offer—an offer that has to be accepted or rejected on the spot—to an offer with extended deadline under different market conditions, proxied by characteristics of the alternative offer distribution. In particular, the proposer should offer a non-exploding offer when the alternative offer market is favorable to the responder, and the more favorable it is, the smaller the offer size and the longer the deadline. When the alternative offer market is unfavorable to the responder, the proposer can profit from making an exploding offer with a smaller size in a harsher market. Finally, our analyses in cases where only the offer deadline or the offer size is at the proposer's disposal contribute additional insights into similar real-world practices. Interestingly, our results indicate that when the proposer is only allowed to manipulate offer size, the optimal offer size first decreases then increases in the given offer duration.
Keywords: search theory, ultimatum, offer size, offer deadline, mean residual life order
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