2012/09/30 by Ning Chen, Xiaotie Deng, Chen, Ning +5
Business, Management and Accounting · Computer Science · Decision Sciences · #91-08 #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #Consumer Market Behavior and Pricing #FOS: Computer and information sciences #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.1210.0203
openalex publication_date 2012/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider markets consisting of a set of indivisible items, and buyers that have \em sharp multi-unit demand. This means that each buyer i wants a specific number di of items; a bundle of size less than di has no value, while a bundle of size greater than di is worth no more than the most valued di items (valuations being additive). We consider the objective of setting prices and allocations in order to maximize the total revenue of the market maker. The pricing problem with sharp multi-unit demand buyers has a number of properties that the unit-demand model does not possess, and is an important question in algorithmic pricing. We consider the problem of computing a revenue maximizing solution for two solution concepts: competitive equilibrium and envy-free pricing. For unrestricted valuations, these problems are NP-complete; we focus on a realistic special case of "correlated values" where each buyer i has a valuation vi\qualj for item j, where vi and \qualj are positive quantities associated with buyer i and item j respectively. We present a polynomial time algorithm to solve the revenue-maximizing competitive equilibrium problem. For envy-free pricing, if the demand of each buyer is bounded by a constant, a revenue maximizing solution can be found efficiently; the general demand case is shown to be NP-hard.