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On the Optimal Number of Firms in the Commons: Cournot vs Bertrand

Author

Listed:
  • Dragone Davide

    (Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna, Italy)

  • Lambertini Luca

    (Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna, Italy and ENCORE, University of Amsterdam, Roeterstraat 11, WB1018 Amsterdam, The Netherlands)

  • Palestini Arsen

    (MEMOTEF, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy)

  • Tampieri Alessandro

    (Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna, Italy)

Abstract

We revisit the debate on the optimal number of firms in the commons in a differential oligopoly game in which firms are either quantity- or price-setting agents. Production exploits a natural resource and involves a negative externality. We calculate the number of firms maximising industry profits, finding that it is larger in the Cournot case. While industry structure is always inefficient under Bertrand behaviour, it may or may not be so under Cournot behaviour, depending on parameter values. The comparison of private industry optima reveals that the Cournot steady state welfare level exceeds the corresponding Bertrand magnitude if the weight of the stock of pollution is large enough.

Suggested Citation

  • Dragone Davide & Lambertini Luca & Palestini Arsen & Tampieri Alessandro, 2013. "On the Optimal Number of Firms in the Commons: Cournot vs Bertrand," Mathematical Economics Letters, De Gruyter, vol. 1(1), pages 25-34, October.
    • Handle: RePEc:bpj:maecol:v:1:y:2013:i:1:p:25-34:n:6
    DOI: 10.1515/mel-2013-0011
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    2. L. Lambertini, 2014. "On the Interplay between Resource Extraction and Polluting Emissions in Oligopoly," Working Papers wp976, Dipartimento Scienze Economiche, Universita' di Bologna.
    3. Luca Grilli & Michele Bisceglia, 2017. "A Duopoly with Common Renewable Resource and Incentives," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-20, December.
    4. Luca Grilli & Michele Bisceglia, 2017. "A differential game in a duopoly with instantaneous incentives," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 317-333, November.

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    Keywords

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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General
    • Q51 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Valuation of Environmental Effects

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