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A differential game in a duopoly with instantaneous incentives

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  • Luca Grilli

    () (Università degli Studi di Foggia)

  • Michele Bisceglia

    (Università degli Studi di Bergamo)

Abstract

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.
    3. Fujiwara, Kenji, 2011. "Losses from competition in a dynamic game model of a renewable resource oligopoly," Resource and Energy Economics, Elsevier, vol. 33(1), pages 1-11, January.
    4. Dragone Davide & Tampieri Alessandro & Lambertini Luca & Palestini Arsen, 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.
    5. Colombo, Luca & Labrecciosa, Paola, 2013. "On the convergence to the Cournot equilibrium in a productive asset oligopoly," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 441-445.
    6. Benchekroun, Hassan, 2008. "Comparative dynamics in a productive asset oligopoly," Journal of Economic Theory, Elsevier, vol. 138(1), pages 237-261, January.
    7. Benchekroun, Hassan & Van Long, Ngo, 2002. "Transboundary Fishery: A Differential Game Model," Economica, London School of Economics and Political Science, vol. 69(274), pages 207-221, May.
    8. Colombo, Luca & Labrecciosa, Paola, 2013. "Oligopoly exploitation of a private property productive asset," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 838-853.
    9. Wu, JunJie & Babcock, Bruce A., 1999. "The Relative Efficiency of Voluntary vs Mandatory Environmental Regulations," Journal of Environmental Economics and Management, Elsevier, vol. 38(2), pages 158-175, September.
    10. Fershtman, Chaim & Kamien, Morton I, 1990. "Turnpike Properties in a Finite-Horizon Differential Game: Dynamic Duopoly with Sticky Prices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 49-60, February.
    11. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    12. Dockner, Engelbert, 1988. "On the relation between dynamic oligopolistic competition and long-run competitive equilibrimn," European Journal of Political Economy, Elsevier, vol. 4(1), pages 47-64.
    13. Hahn, Robert W & Stavins, Robert N, 1992. "Economic Incentives for Environmental Protection: Integrating Theory and Practice," American Economic Review, American Economic Association, vol. 82(2), pages 464-468, May.
    14. Benchekroun, Hassan, 2003. "Unilateral production restrictions in a dynamic duopoly," Journal of Economic Theory, Elsevier, vol. 111(2), pages 214-239, August.
    15. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
    16. Fujiwara, Kenji, 2008. "Duopoly can be more anti-competitive than monopoly," Economics Letters, Elsevier, vol. 101(3), pages 217-219, December.
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    More about this item

    Keywords

    Open-loop Nash equilibrium; Feedback Nash equilibrium; Resource extraction; Finite time horizon; Incentives;

    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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