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On agreements in a nonrenewable resource market: A cooperative differential game approach

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  • Berthod, Mathias
  • Benchekroun, Hassan

Abstract

We consider a nonrenewable resource duopoly with economic exhaustion. We characterize the set of Pareto efficient equilibria. We show that when firms are sufficiently patient, there exists no Pareto efficient agreement that yields short-run gains with respect to the noncooperative equilibrium. Given a pair of stocks, there exists a unique interior Pareto efficient agreement. We characterize the set of stocks where a Pareto efficient agreement results in larger discounted sum of profits for both players. We show that social welfare under the interior Pareto efficient agreement is smaller than under non-cooperation, despite the gains from a more cost effective extraction of the resources under an agreement.

Suggested Citation

  • Berthod, Mathias & Benchekroun, Hassan, 2019. "On agreements in a nonrenewable resource market: A cooperative differential game approach," Journal of Economic Dynamics and Control, Elsevier, vol. 98(C), pages 23-39.
    • Handle: RePEc:eee:dyncon:v:98:y:2019:i:c:p:23-39
    DOI: 10.1016/j.jedc.2018.11.001
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    More about this item

    Keywords

    Nonrenewable resources; Oligopolies; Cartel; Cooperative games; Differential games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • 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
    • Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General
    • Q32 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - Exhaustible Resources and Economic Development

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