Approximation Schemes for Sequential Posted Pricing in Multi-unit Auctions

We design algorithms for computing approximately revenue-maximizing sequential postedpricing mechanisms (SPM) in K-unit auctions, in a standard Bayesian model. A seller has K copies of an item to sell, and there are n buyers, each interested in only one copy, who have some value for the item. The seller must post a price for each buyer, the buyers arrive in a sequence enforced by the seller, and a buyer buys the item if its value exceeds the price posted to it. The seller does not know the values of the buyers, but have Bayesian information about them. An SPM specifies the ordering of buyers and the posted prices, and may be adaptive or non-adaptive in its behavior. The goal is to design SPM in polynomial time to maximize expected revenue. We compare against the expected revenue of optimal SPM, and provide a polynomial time approximation scheme (PTAS) for both non-adaptive and adaptive SPMs. This is achieved by two algorithms: an efficient algorithm that gives a (1- 1 2K )-approximati...

• Type: Journal
• Year: 2010
• Where: WINE
• Authors: Tanmoy Chakraborty, Eyal Even-Dar, Sudipto Guha, Yishay Mansour, S. Muthukrishnan
• Keywords: Algorithm, Buyers, Economy, Seller, WINE 2010