Sequences of Take-It-or-Leave-It Offers: Near-Optimal Auctions Without Full Valuation Revelation

Abstract

We introduce take-it-or-leave-it auctions (TLAs) as an allocation
mechanism that allows buyers to retain much of their private valuation
information, yet generates close-to-optimal expected utility for the
seller. We show that if each buyer receives at most one offer, each
buyers dominant strategy is to act truthfully. In more general TLAs,
the buyers optimal strategies are more intricate, and we derive the
perfect Bayesian equilibrium for the game. We develop algorithms for
finding the equilibrium and also for optimizing the offers so as to
maximize the sellers expected utility. In several example settings we
show that the sellers expected utility already is close to optimal
for a small number of offers. As the number of buyers increases, the
sellers expected utility increases, and becomes increasingly (but not
monotonically) more competitive with Myersons expected utility
maximizing auction.