Allocation and Pricing of Substitutable Goods: Theory and Algorithm

forthcoming in Production and Operations Management

66 Pages Posted: 12 Jul 2013 Last revised: 20 Dec 2016

See all articles by Huaxia Rui

Huaxia Rui

University of Rochester - Simon Business School

De Liu

University of Minnesota - Twin Cities - Carlson School of Management

Andrew B. Whinston

University of Texas at Austin - Department of Information, Risk and Operations Management

Date Written: October 16, 2016

Abstract

Abstract Motivated by the thriving market of online display advertising, we study a problem of allocating numerous types of goods among many agents who have concave valuations (capturing risk aversion) and heterogeneous substitution preferences across types of goods. The goal is both to provide a theory for optimal allocation of such goods, and to offer a scalable algorithm to compute the optimal allocation and the associated price vectors. Drawing on the economic concept of Pareto optimality, we develop an equilibrium pricing theory for heterogeneous substitutable goods that parallels the pricing theory for financial assets. We then develop a fast algorithm called SIMS (Standardization-and-Indicator-Matrix-Search). Extensive numerical simulations suggest that the SIMS algorithm is very scalable and is up to three magnitudes faster than well-known alternative algorithms. Our theory and algorithm have important implications for the pricing and scheduling of online display advertisement and beyond.

Keywords: display advertising, substitutable goods, optimal allocation, algorithm

JEL Classification: C6

Suggested Citation

Rui, Huaxia and Liu, De and Whinston, Andrew B., Allocation and Pricing of Substitutable Goods: Theory and Algorithm (October 16, 2016). forthcoming in Production and Operations Management, Available at SSRN: https://ssrn.com/abstract=2292784 or http://dx.doi.org/10.2139/ssrn.2292784

Huaxia Rui (Contact Author)

University of Rochester - Simon Business School ( email )

Rochester, NY 14627
United States

De Liu

University of Minnesota - Twin Cities - Carlson School of Management ( email )

19th Avenue South
Minneapolis, MN 55455
United States

Andrew B. Whinston

University of Texas at Austin - Department of Information, Risk and Operations Management ( email )

CBA 5.202
Austin, TX 78712
United States
512-471-8879 (Phone)

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