Global Robust Stability in a General Price and Assortment Competition Model

33 Pages Posted: 2 Aug 2017 Last revised: 11 Sep 2019

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: June 28, 2018

Abstract

We analyze a general but parsimonious price competition model for an oligopoly in which each firm offers any number of products. The demand volumes are general piecewise affine functions of the full price vector, generated as the "regular" extension of a base set of affine functions. The model specifies a product assortment, along with their prices and demand volumes, in contrast to most commonly used demand models such as the MNL model or any of its variants. We show that a special equilibrium in this model has global robust stability. This means that, from any starting point, the market converges to this equilibrium when firms use a particular response mapping to dynamically adjust their own prices in response to their competitors' prices. The mapping involves each firm optimizing its own prices over a limited subset of possible prices and requires each firm to only know the demand function and cost structure for its own products (but not for other firms' products).

Keywords: equilibrium, price competition, assortment competition, global stability, robust stability, best response, contraction mapping

JEL Classification: D43, D58, L13

Suggested Citation

Federgruen, Awi and Hu, Ming, Global Robust Stability in a General Price and Assortment Competition Model (June 28, 2018). Columbia Business School Research Paper No. 17-78, Available at SSRN: https://ssrn.com/abstract=3010503 or http://dx.doi.org/10.2139/ssrn.3010503

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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