Price Competition Under Mixed Multinomial Logit Demand Functions

Margaret Aksoy-Pierson (), Gad Allon () and Awi Federgruen ()
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Margaret Aksoy-Pierson: Tuck School of Business, Dartmouth College, Hanover, New Hampshire 03755
Gad Allon: Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
Awi Federgruen: Graduate School of Business, Columbia University, New York, New York 10027

Management Science, 2013, vol. 59, issue 8, 1817-1835

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. This paper was accepted by J. Miguel Villas-Boas, marketing.

Keywords: marketing; competitive strategy; pricing (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (16)

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