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Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach

Author

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  • Régis Chenavaz

    (LTCI - Laboratoire Traitement et Communication de l'Information - Télécom ParisTech - IMT - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche Scientifique)

  • Corina Paraschiv

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, IUF - Institut Universitaire de France - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche)

  • Gabriel Turinici

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique, IUF - Institut Universitaire de France - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche)

Abstract

Dynamic pricing of new products has been extensively studied in monopolistic and oligopolistic markets. But, the optimal control and differential game tools used to investigate the pricing behavior on markets with a finite number of firms are not well-suited to model competitive markets with an infinity of firms. Using a mean-field games approach, this paper examines dynamic pricing policies in competitive markets, where no firm exerts market power. The theoretical setting is based on a diffusion modeì a la Bass. We prove both the existence and the uniqueness of a mean-field game equilibrium, and we investigate mean tendencies and firms dispersion in the market. Numerical simulations show that the competitive market splits into two separate groups of firms depending on their production experience. The two groups differ in price and profit. Thus, high prices and profits do not have to signal anticompetitive practices, stimulating the debate on market regulation.

Suggested Citation

  • Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2020. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Post-Print hal-01592958, HAL.
    • Handle: RePEc:hal:journl:hal-01592958
    DOI: 10.1007/s13235-020-00369-6
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    1. Salhab, Rabih & Le Ny, Jérôme & Malhamé, Roland P. & Zaccour, Georges, 2022. "Dynamic marketing policies with rating-sensitive consumers: A mean-field games approach," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1079-1093.
    2. Chaab, Jafar & Salhab, Rabih & Zaccour, Georges, 2022. "Dynamic pricing and advertising in the presence of strategic consumers and social contagion: A mean-field game approach," Omega, Elsevier, vol. 109(C).
    3. Ryan Donnelly & Zi Li, 2022. "Dynamic Inventory Management with Mean-Field Competition," Papers 2210.17208, arXiv.org.
    4. Anton, Ramona & Chenavaz, Régis Y. & Paraschiv, Corina, 2023. "Dynamic pricing, reference price, and price-quality relationship," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).

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