Buyout prices in online auctions

Abstract

Buyout options allow bidders to instantly purchase at a specified price an item listed for sale through an online auction. A temporary buyout option disappears once a regular bid above the reserve price is made, while a permanent option remains available until it is exercised or the auction ends. Buyout options are widely used in online auctions and have significant economic importance: nearly half of the auctions today are listed with a buyout price and the option is exercised in nearly one fourth of them. We formulate a game-theoretic model featuring time-sensitive bidders with independent private valuations and Poisson arrivals but endogenous bidding times in order to answer the following questions: How should buyout prices be set in order to maximize the seller's discounted revenue? What are the relative benefits of using each type of buyout option? While all existing buyout options we are aware of currently rely on a static buyout price (i.e. with a constant value), what is the potential benefit associated with using instead a dynamic buyout price that varies as the auction progresses?

(cont.) For all buyout option types we exhibit a Nash equilibrium in bidder strategies, argue that this equilibrium constitutes a plausible outcome prediction, and study the problem of maximizing the corresponding seller revenue. In particular, the equilibrium strategy in all cases is such that a bidder exercises the buyout option provided it is still available and his valuation is above a time-dependent threshold. Our numerical experiments suggest that a seller may significantly increase his utility by introducing a buyout option when any of the participants are time-sensitive. Furthermore, while permanent buyout options yield higher predicted revenue than temporary options, they also provide additional incentives for late bidding and may therefore not be always more desirable. The numerical results also imply that the increase in seller's utility (over a fixed buyout price auction) enabled by a dynamic buyout price is small and does not seem to justify the corresponding increase in complexity.