Multi-Product Price and Assortment Competition

49 Pages Posted: 13 Dec 2013 Last revised: 16 Nov 2014

See all articles by Awi Federgruen

Awi Federgruen

Columbia University - Columbia Business School, Decision Risk and Operations

Ming Hu

University of Toronto - Rotman School of Management

Date Written: December 11, 2013

Abstract

We address a generic price competition model in an industry with an arbitrary number of competitors, each offering all or a subset of a given line of N products. The products are substitutes in the sense that the demand volume of each product weakly increases whenever the price of another product increases. The cost structure is linear, with arbitrary cost rates.

Our demand model is the unique regular extension of a set of demand functions that are affine in a limited polyhedral subset of the price space. A set of demand functions is regular if it satisfies the following conditions: under any given price vector, when some product is priced out of the market, i.e., has zero demand, any increase of its price has no impact on the demand volumes. Depending on the set of prices selected by the competing firms, a different product assortment is offered on the market.

We characterize the equilibrium prices, product assortment and sales volumes in the price competition model, under this demand model. Under minimal conditions, we show that a pure Nash equilibrium always exists; while multiple price equilibria may arise, they are equivalent in the sense of generating an identical product assortment and sales volumes.

Keywords: Bertrand Competition, Differentiated Products, Linear Complementarity Problem

JEL Classification: C6, C72, D43, D58, L13

Suggested Citation

Federgruen, Awi and Hu, Ming, Multi-Product Price and Assortment Competition (December 11, 2013). Columbia Business School Research Paper No. 14-3, Rotman School of Management Working Paper No. 2366487, Available at SSRN: https://ssrn.com/abstract=2366487 or http://dx.doi.org/10.2139/ssrn.2366487

Awi Federgruen

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

Ming Hu (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada
416-946-5207 (Phone)

HOME PAGE: http://ming.hu

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