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Extinction in common property resource models: an analytically tractable example

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  • Tapan Mitra
  • Gerhard Sorger

Abstract

We discuss an analytically tractable discrete-time dynamic game in which a finite number of players extract a renewable resource. We characterize a symmetric Markov-perfect Nash equilibrium of this game and derive a necessary and sufficient condition under which the resource does not become extinct in equilibrium. This condition requires that the intrinsic growth rate of the resource exceeds a certain threshold value that depends on the number of players and on their time-preference rates. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Tapan Mitra & Gerhard Sorger, 2014. "Extinction in common property resource models: an analytically tractable example," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(1), pages 41-57, September.
    • Handle: RePEc:spr:joecth:v:57:y:2014:i:1:p:41-57
    DOI: 10.1007/s00199-013-0799-2
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    Cited by:

    1. Geir B. Asheim & Kuntal Banerjee & Tapan Mitra, 2021. "How stationarity contradicts intergenerational equity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 423-444, September.
    2. Colombo, Luca & Labrecciosa, Paola, 2019. "Stackelberg versus Cournot: A differential game approach," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 239-261.
    3. Fabbri, G. & Faggian, S. & Freni, G., 2018. "Spatial resource wars: A two region example," Working Papers 2018-04, Grenoble Applied Economics Laboratory (GAEL).
    4. Partha Dasgupta & Tapan Mitra & Gerhard Sorger, 2019. "Harvesting the Commons," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(3), pages 613-636, March.
    5. Kirill Borissov & Mikhail Pakhnin, 2018. "Economic growth and property rights on natural resources," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 423-482, March.
    6. Koichi Futagami & Yuta Nakabo, 2021. "Capital accumulation game with quasi-geometric discounting and consumption externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 251-281, February.
    7. Tapan Mitra & Gerhard Sorger, 2015. "Noncooperative Resource Exploitation by Patient Players," Dynamic Games and Applications, Springer, vol. 5(3), pages 361-377, September.
    8. Tapan Mitra & Santanu Roy, 2022. "Propensity to consume and the optimality of Ramsey–Euler policies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 55-89, February.
    9. Tapan Mitra & Santanu Roy, 2023. "Stochastic growth, conservation of capital and convergence to a positive steady state," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 311-351, July.
    10. Tapan Mitra & Gerhard Sorger, 2015. "Noncooperative Resource Exploitation by Patient Players," Dynamic Games and Applications, Springer, vol. 5(3), pages 361-377, September.
    11. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 2020. "Policy effectiveness in spatial resource wars: A two-region model," Journal of Economic Dynamics and Control, Elsevier, vol. 111(C).
    12. Liuchun Deng & Minako Fujio & M. Ali Khan, 2023. "On optimal extinction in the matchbox two-sector model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 445-494, August.
    13. Ricardo Josa-Fombellida & Juan Rincón-Zapatero, 2015. "Euler–Lagrange equations of stochastic differential games: application to a game of a productive asset," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 61-108, May.
    14. Mitra, Tapan & Roy, Santanu, 2017. "Optimality of Ramsey–Euler policy in the stochastic growth model," Journal of Economic Theory, Elsevier, vol. 172(C), pages 1-25.

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    More about this item

    Keywords

    Tragedy of the commons; Extinction; Markov-perfect Nash equilibrium; C73; Q20;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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