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Extinction in common property resource models: an analytically tractable example

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  • Tapan Mitra

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  • Gerhard Sorger

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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

Suggested Citation

  • 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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    References listed on IDEAS

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    5. Juan Pablo RincÛn-Zapatero & Carlos RodrÌguez-Palmero, 2003. "Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case," Econometrica, Econometric Society, vol. 71(5), pages 1519-1555, September.
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    Citations

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    Cited by:

    1. Fabbri, G. & Faggian, S. & Freni, G., 2018. "Spatial resource wars: A two region example," Working Papers 2018-04, Grenoble Applied Economics Laboratory (GAEL).
    2. 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.
    3. Tapan Mitra & Gerhard Sorger, 2015. "Noncooperative Resource Exploitation by Patient Players," Dynamic Games and Applications, Springer, vol. 5(3), pages 361-377, September.
    4. repec:eee:jetheo:v:172:y:2017:i:c:p:1-25 is not listed on IDEAS
    5. 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.

    More about this item

    Keywords

    Tragedy of the commons; Extinction; Markov-perfect Nash equilibrium; C73; Q20;

    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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