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Extraction of non-renewable resources: a differential game approach

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  • Halkos, George
  • Papageorgiou, George

Abstract

Exploitation of non–renewable resources is an intensively studied field of environmental economics in the last century. Since the influential Hotelling’s paper a huge progress is made in the depletable resources literature. Although a variety of methodologies is used in that problem’s solutions a basic question of time inconsistency arises in the solution process. We show the sources of dynamical time inconsistency in a leader – follower game for which the buyer leads while the extractor follows and the players employ open loop strategies. Also we make use of Markovian informational structure, in a non – renewable resource Nash game, in order to extract strategies that are time consistent. Finally we enlarge the utility function space from the logarithmic utility to the utility functions that exhibits relative risk aversion with the same, with respect to time consistency, strategies.

Suggested Citation

  • Halkos, George & Papageorgiou, George, 2008. "Extraction of non-renewable resources: a differential game approach," MPRA Paper 37596, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:37596
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    References listed on IDEAS

    as
    1. Lewis, Tracy R & Matthews, Steven A & Burness, H Stuart, 1979. "Monopoly and the Rate of Extraction of Exhaustible Resources: Note," American Economic Review, American Economic Association, vol. 69(1), pages 227-230, March.
    2. Engelbert Dockner & Florian Wagener, 2014. "Markov perfect Nash equilibria in models with a single capital stock," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 585-625, August.
    3. A. M. Ulph & G. M. Folie, 1980. "Exhaustible Resources and Cartels: An Intertemporal Nash-Cournot Model," Canadian Journal of Economics, Canadian Economics Association, vol. 13(4), pages 645-658, November.
    4. Stiglitz, Joseph E, 1976. "Monopoly and the Rate of Extraction of Exhaustible Resources," American Economic Review, American Economic Association, vol. 66(4), pages 655-661, September.
    5. Karp, Larry, 1984. "Optimality and consistency in a differential game with non-renewable resources," Journal of Economic Dynamics and Control, Elsevier, vol. 8(1), pages 73-97, October.
    6. Harold Hotelling, 1931. "The Economics of Exhaustible Resources," Journal of Political Economy, University of Chicago Press, vol. 39(2), pages 137-137.
    7. Partha Dasgupta & Geoffrey Heal, 1974. "The Optimal Depletion of Exhaustible Resources," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 3-28.
    8. Bergstrom, Theodore C. & Cross, John G. & Porter, Richard C., 1981. "Efficiency-inducing taxation for a monopolistically supplied depletable resource," Journal of Public Economics, Elsevier, vol. 15(1), pages 23-32, February.
    9. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
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    Cited by:

    1. Yuanyu Cao & Tao Xu, 2024. "The Impact of Environmental Social Responsibility on Total Factor Productivity: Evidence from Listed Companies in China," Sustainability, MDPI, vol. 16(18), pages 1-26, September.
    2. Halkos, George & Kitsos, Christos, 2018. "Mathematics vs. Statistics in tackling Environmental Economics uncertainty," MPRA Paper 85280, University Library of Munich, Germany.
    3. Halkos, George & Tsilika, Kyriaki, 2012. "Stability analysis in economic dynamics: A computational approach," MPRA Paper 41371, University Library of Munich, Germany.
    4. George Halkos & George Papageorgiou, 2013. "Dynamic modeling of pulse fishing: A game theoretic approach," DEOS Working Papers 1324, Athens University of Economics and Business.
    5. Halkos, George & Kitsos, Christos, 2018. "Uncertainty in environmental economics: The problem of entropy and model choice," Economic Analysis and Policy, Elsevier, vol. 60(C), pages 127-140.

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    More about this item

    Keywords

    Non-renewable resources; time consistency; Markovian strategies; leader-follower;
    All these keywords.

    JEL classification:

    • Q00 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - General
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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