Price Competition Under Mixed Multinomial Logit Demand Functions

Management Science, 2013 59:8, 1817-1835

Columbia Business School Research Paper No. 14-15

20 Pages Posted: 8 Mar 2014

See all articles by Margaret P. Pierson

Margaret P. Pierson

Independent

Gad Allon

University of Pennsylvania - The Wharton School

Awi Federgruen

Columbia Business School - Decision Risk and Operations

Date Written: August 1, 2013

Abstract

In this paper, we postulate a general class of price competition models with mixed multinomial logit demand functions under affine cost functions. In these models, the market is partitioned into a finite set of market segments. We characterize the equilibrium behavior of this class of models in the case where each product in the market is sold by a separate, independent firm. We identify a simple and very broadly satisfied condition under which a pure Nash equilibrium exists and the set of Nash equilibria coincides with the solutions of the system of first-order-condition equations, a property of essential importance to empirical studies. This condition specifies that in every market segment, each firm captures less than 50% of the potential customer population when pricing at a specific level that, under the condition, is an upper bound for a rational price choice for the firm irrespective of the competitors' prices. We show that under a somewhat stronger, but still broadly satisfied, version of the above condition, a unique equilibrium exists. We complete the picture by establishing the existence of a Nash equilibrium, indeed a unique Nash equilibrium, for markets with an arbitrary degree of concentration, under sufficiently tight price bounds. We discuss how our results extend to a continuum of customer types. A discussion of the multiproduct case is included. The paper concludes with a discussion of implications for structural estimation methods.

Keywords: marketing, competitive strategy, pricing

Suggested Citation

Pierson, Margaret P. and Allon, Gad and Federgruen, Awi, Price Competition Under Mixed Multinomial Logit Demand Functions (August 1, 2013). Management Science, 2013 59:8, 1817-1835, Columbia Business School Research Paper No. 14-15, Available at SSRN: https://ssrn.com/abstract=2405684

Gad Allon

University of Pennsylvania - The Wharton School ( email )

3641 Locust Walk
Philadelphia, PA 19104-6365
United States

Awi Federgruen

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

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