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A differential game in a duopoly with instantaneous incentives

Author

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  • Luca Grilli

    (Università degli Studi di Foggia)

  • Michele Bisceglia

    (Università degli Studi di Bergamo)

Abstract

In this paper, we study a differential game in which two competing firms exploit a public renewable resource that is relevant from a landscape point of view. We consider a policy maker that provides an instantaneous incentive to the firms in order to prevent the resource exhaustion during the whole extraction period, which coincides with the harvesting license period. We compute an open-loop Nash equilibrium of the differential game, showing that it coincides with a linear feedback Nash equilibrium. Finally, we compute the value of the incentive that leads to the maximization of social welfare considering the incentive both as a pure transfer and as a cost.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0189-5
    DOI: 10.1007/s10203-017-0189-5
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    References listed on IDEAS

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    1. Lambertini, Luca & Mantovani, Andrea, 2014. "Feedback equilibria in a dynamic renewable resource oligopoly: Pre-emption, voracity and exhaustion," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 115-122.
    2. Colombo, Luca & Labrecciosa, Paola, 2015. "On the Markovian efficiency of Bertrand and Cournot equilibria," Journal of Economic Theory, Elsevier, vol. 155(C), pages 332-358.
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    6. Benchekroun, Hassan, 2008. "Comparative dynamics in a productive asset oligopoly," Journal of Economic Theory, Elsevier, vol. 138(1), pages 237-261, January.
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    Cited by:

    1. Luca Grilli & Michele Bisceglia, 2020. "A dynamic private property resource game with asymmetric firms," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 109-127, June.
    2. Michele Bisceglia, 2020. "Optimal taxation in a common resource oligopoly game," Journal of Economics, Springer, vol. 129(1), pages 1-31, January.

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    More about this item

    Keywords

    Open-loop Nash equilibrium; Feedback Nash equilibrium; Resource extraction; Finite time horizon; Incentives;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D23 - Microeconomics - - Production and Organizations - - - Organizational Behavior; Transaction Costs; Property Rights
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D60 - Microeconomics - - Welfare Economics - - - General
    • H23 - Public Economics - - Taxation, Subsidies, and Revenue - - - Externalities; Redistributive Effects; Environmental Taxes and Subsidies
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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