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Sequential Games of Resource Extraction: Existence of Nash Equilibria

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  • Rabah Amir

    (SUNY at Stony Brook)

Abstract

A general model for noncooperative extraction of common-property resource is considered. The main result is that this sequential game has a Nash equilibrium in stationary strategies. The proof is based on an infinite dimensional fixed-point theorem, and relies crucially on the topology of epi-convergence. A byproduct of the analysis is that Nash equilibrium strategies may be selected such that marginal propensities of consumption are bounded above by one.

Suggested Citation

  • Rabah Amir, 1987. "Sequential Games of Resource Extraction: Existence of Nash Equilibria," Cowles Foundation Discussion Papers 825, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:825
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d08/d0825.pdf
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    References listed on IDEAS

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    1. Hildenbrand, W. & Kirman, A. P., 1976. "Introduction to Equilibrium Analysis," Elsevier Monographs, Elsevier, edition 1, number 9780720436068 edited by Bliss, C. J. & Intriligator, M. D..
    2. David Levhari & Leonard J. Mirman, 1980. "The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 322-334, Spring.
    3. Peter Kall, 1986. "Approximation to Optimization Problems: An Elementary Review," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 9-18, February.
    4. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    5. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    6. Rabah Amir, 1985. "A Characterization of Globally Optimal Paths in the Non-Classical Growth Model," Cowles Foundation Discussion Papers 754, Cowles Foundation for Research in Economics, Yale University.
    7. Martin Shubik & Ward Whitt, 1973. "Fiat Money in an Economy with One Nondurable Good and No Credit (A Noncooperative Sequential Game)," Cowles Foundation Discussion Papers 355, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Eilon Solan, 2003. "Continuity of the Value of Competitive Markov Decision Processes," Journal of Theoretical Probability, Springer, vol. 16(4), pages 831-845, October.

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