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Dynamic equilibrium with randomly entering and exiting firms of different types

Author

Listed:
  • Pierre Bernhard

    (MACBES - Modélisation et commande de systèmes biologiques et écologiques - Centre Inria d'Université Côte d'Azur - Inria - Institut National de Recherche en Informatique et en Automatique - IPMC - Institut de pharmacologie moléculaire et cellulaire - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique - UniCA - Université Côte d'Azur - ISA - Institut Sophia Agrobiotech - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - UniCA - Université Côte d'Azur)

  • Romain Biard

    (LMB - Laboratoire de Mathématiques de Besançon (UMR 6623) - CNRS - Centre National de la Recherche Scientifique - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE], CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Marc Deschamps

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

Abstract

There exist situations where firms (identical or not) are in a state of renewed interaction and where, at each period, in addition to exits, new firms (identical or not) may arrive. In such cases, no one is able to know ex ante exactly how many firms there will be in each period. One of the questions an incumbent firm might therefore ask itself, in this context, is what expected payoff it can expect. Our paper aims to provide an answer to this question, in finite and infinite horizons, using a discrete-time dynamic game with random arrival(s) and exit(s) of different types of firm(s). We first propose a general model, which we then particularize by considering the types as composed of identical players. Within this framework, we address the case of a dynamic Cournot oligopoly with sticky prices, and provide numerical illustrations to underline the interest of this approach and demonstrate its operational character.

Suggested Citation

  • Pierre Bernhard & Romain Biard & Marc Deschamps, 2025. "Dynamic equilibrium with randomly entering and exiting firms of different types," Working Papers hal-05494442, HAL.
    • Handle: RePEc:hal:wpaper:hal-05494442
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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary 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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