Revenue-enhancing effect of a buyout price in multi-unit uniform-price auctions

We frequently observe that many items are sold in multi-unit auctions in the actual world. The examples of multi-unit auctions include Treasury bill auctions, spectrum auctions, and online auctions such as eBay and Yahoo. A demand reduction, in which buyers lower a bid on a lesser-valued unit, is prominent and prevalent in multi-unit auctions. This bidding strategy is optimal in general environments involving many buyers who demand more than two units. A demand reduction yields inefficient allocations and causes low seller revenue. In the extreme, all units are sold for a zero price. This paper is motivated by potential usage of buyout prices to prevent such a demand reduction.

We introduce a two-stage model to study multi-unit uniform-price auctions with a buyout price where two buyers with two-unit demand have a buyout option. In the first stage, buyers simultaneously choose a quantity of items they wish to buy at a buyout price. In the second stage, if any, buyer(s) compete in bid. In our model, a buyout price is exogenous. We focus on a situation in which buyers submit a single-unit bid whenever they have a chance to bid. Such a single-unit bid yields zero revenue to a seller.

We derive a symmetric undominated Bayesian equilibrium and show that a buyout price improves seller revenue. The revenue-enhancing effect of a buyout price arises from a trade-off faced by buyers between the benefit of obtaining two units at a given buyout price and the cost of losing a chance to win one unit at zero price. Multi-unit auctions have grown increasingly important in terms of practical usage, and thus the result obtained in this paper is beneficial to auctioneers and auction designers.