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On Nash equilibrium in prices in an oligopolistic market with demand characterized by a nested multinomial logit model and multiproduct firm as nest

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Abstract

This note provides a proof on existence and uniqueness of Nash equilibrium in prices in a market where the demand side is characterized by a nested multinomial logit model with multiproduct firm as nest and the supply side consists of oligopolistic price-setting multiproduct firms with each producing various differentiated variants.

Suggested Citation

  • Gang Liu, 2006. "On Nash equilibrium in prices in an oligopolistic market with demand characterized by a nested multinomial logit model and multiproduct firm as nest," Discussion Papers 454, Statistics Norway, Research Department.
    • Handle: RePEc:ssb:dispap:454
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    File URL: https://www.ssb.no/a/publikasjoner/pdf/DP/dp454.pdf
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    1. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    2. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    3. ANDERSON, Simon P. & de PALMA, André & THISSE, Jacques-François, 1992. "Interpretations of the logit discrete choice models and the theory of product differentiation," LIDAM Reprints CORE 1017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Goldberg, Pinelopi Koujianou, 1995. "Product Differentiation and Oligopoly in International Markets: The Case of the U.S. Automobile Industry," Econometrica, Econometric Society, vol. 63(4), pages 891-951, July.
    5. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
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    Cited by:

    1. Guillermo Gallego & Ruxian Wang, 2014. "Multiproduct Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities," Operations Research, INFORMS, vol. 62(2), pages 450-461, April.
    2. Yangyang Xie & Lei Xie & Meng Lu & Houmin Yan, 2021. "Performance‐Price‐Ratio Utility: Market Equilibrium Analysis and Empirical Calibration Studies," Production and Operations Management, Production and Operations Management Society, vol. 30(5), pages 1442-1456, May.
    3. Margaret Aksoy-Pierson & Gad Allon & Awi Federgruen, 2013. "Price Competition Under Mixed Multinomial Logit Demand Functions," Management Science, INFORMS, vol. 59(8), pages 1817-1835, August.
    4. Sylvia Bleker & Christiaan Behrens & Paul Koster & Erik T. Verhoef, 2014. "Market Structure and the Pricing of New Products: A Nested Logit Approach with Asymmetric Firms," Tinbergen Institute Discussion Papers 14-142/VIII, Tinbergen Institute.
    5. Hai Jiang & Rui Chen & He Sun, 2017. "Multiproduct price optimization under the multilevel nested logit model," Annals of Operations Research, Springer, vol. 254(1), pages 131-164, July.

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    More about this item

    Keywords

    oligopolistic market; multiproduct firm; nested multinomial logit model; Nash equilibrium;
    All these keywords.

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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