Sequences of take-it-or-leave-it offers: near-optimal auctions without full valuation revelation

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 buyer's 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 seller's expected utility. In several example settings we show that the seller's expected utility already is close to optimal for a small number of offers. As the number of buyers increases, the seller's expected utility increases, and becomes increasingly (but not monotonically) more competitive with Myerson's expected utility maximizing auction.

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