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Cournot oligopoly with randomly arriving producers

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  • Pierre Bernhard

    (BIOCORE - Biological control of artificial ecosystems - LOV - Laboratoire d'océanographie de Villefranche - OOVM - Observatoire océanologique de Villefranche-sur-mer - UPMC - Université Pierre et Marie Curie - Paris 6 - INSU - CNRS - Institut national des sciences de l'Univers - CNRS - Centre National de la Recherche Scientifique - UPMC - Université Pierre et Marie Curie - Paris 6 - INSU - CNRS - Institut national des sciences de l'Univers - CNRS - Centre National de la Recherche Scientifique - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - INRA - Institut National de la Recherche Agronomique)

  • Marc Deschamps

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

Abstract

Cournot model of oligopoly appears as a central model of strategic interaction between competing firms both from a theoretical and applied perspective (e.g antitrust). As such it is an essential tool in the economics toolbox and always a stimulus. Although there is a huge and deep literature on it and as far as we know, we think that there is a "mouse hole" wich has not already been studied: Cournot oligopoly with randomly arriving producers. In a companion paper [Bernhard and Deschamps, 2016b] we have proposed a rather general model of a discrete dynamic decision process where producers arrive as a Bernoulli random process and we have given some examples relating to oligopoly theory (Cournot, Stackelberg, cartel). In this paper we study Cournot oligopoly with random entry in discrete (Bernoulli) and continuous (Poisson) time, whether time horizon is finite or infinite. Moreover we consider here constant and variable probability of entry or density of arrivals. In this framework, we are able to provide algorithmes answering four classical questions: 1/ what is the expected profit for a firm inside the Cournot oligopoly at the beginning of the game?, 2/ How do individual quantities evolve?, 3/ How do market quantities evolve?, and 4/ How does market price evolve?

Suggested Citation

  • Pierre Bernhard & Marc Deschamps, 2016. "Cournot oligopoly with randomly arriving producers," Working Papers hal-01413910, HAL.
    • Handle: RePEc:hal:wpaper:hal-01413910
    Note: View the original document on HAL open archive server: https://hal.science/hal-01413910
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    References listed on IDEAS

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    1. Amir, Rabah & De Castro, Luciano & Koutsougeras, Leonidas, 2014. "Free entry versus socially optimal entry," Journal of Economic Theory, Elsevier, vol. 154(C), pages 112-125.
    2. Saloner, Garth, 1987. "Cournot duopoly with two production periods," Journal of Economic Theory, Elsevier, vol. 42(1), pages 183-187, June.
    3. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    4. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
    5. van den Berg, Anita & Bos, Iwan & Herings, P. Jean-Jacques & Peters, Hans, 2012. "Dynamic Cournot duopoly with intertemporal capacity constraints," International Journal of Industrial Organization, Elsevier, vol. 30(2), pages 174-192.
    6. Pierre Bernhard & Marc Deschamps, 2016. "Dynamic equilibrium in games with randomly arriving players," Working Papers 2016-10, CRESE.
    7. Pal, Debashis, 1991. "Cournot duopoly with two production periods and cost differentials," Journal of Economic Theory, Elsevier, vol. 55(2), pages 441-448, December.
    8. Kebriaei, Hamed & Rahimi-Kian, Ashkan, 2011. "Decision making in dynamic stochastic Cournot games," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1202-1217.
    9. N. Gregory Mankiw & Michael D. Whinston, 1986. "Free Entry and Social Inefficiency," RAND Journal of Economics, The RAND Corporation, vol. 17(1), pages 48-58, Spring.
    10. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
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    Cited by:

    1. Pierre Bernhard & Marc Deschamps, 2021. "Dynamic Equilibrium with Randomly Arriving Players," Dynamic Games and Applications, Springer, vol. 11(2), pages 242-269, June.

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    More about this item

    Keywords

    Cournot market structure; Bernoulli process of entry; Poisson density of arrivals; Dynamic Programming;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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