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Resource Dynamics under Partial Cooperation in an Oligopoly

Author

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  • M. Kopel

    (Vienna University of Technology)

  • F. Szidarovszky

    (University of Arizona)

Abstract

We study the long-run evolution of a renewable resource which is subject to harvest by partially cooperating players who sell the harvested quantities on distinct markets. We derive explicit expressions for the total harvesting quantity of all players in this general framework and investigate the dependence of the total and relative harvest rates on the level of cooperation, available fish stock, and fishing costs. Combining the biological growth model with oligopoly leads to a nonlinear dynamic law for the evolution of the fish stock in the presence of commercial fishing. We provide also existence results for its equilibrium and examine the asymptotic behavior of the equilibrium.

Suggested Citation

  • M. Kopel & F. Szidarovszky, 2006. "Resource Dynamics under Partial Cooperation in an Oligopoly," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 393-410, February.
    • Handle: RePEc:spr:joptap:v:128:y:2006:i:2:d:10.1007_s10957-006-9018-7
    DOI: 10.1007/s10957-006-9018-7
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    References listed on IDEAS

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    1. Rajesh K. Aggarwal & Andrew A. Samwick, 1999. "Executive Compensation, Strategic Competition, and Relative Performance Evaluation: Theory and Evidence," Journal of Finance, American Finance Association, vol. 54(6), pages 1999-2043, December.
    2. Cyert, Richard M & DeGroot, Morris H, 1973. "An Analysis of Cooperation and Learning in a Duopoly Context," American Economic Review, American Economic Association, vol. 63(1), pages 24-37, March.
    3. Sandal, Leif K. & Steinshamn, Stein I., 2004. "Dynamic Cournot-competitive harvesting of a common pool resource," Journal of Economic Dynamics and Control, Elsevier, vol. 28(9), pages 1781-1799, July.
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    Cited by:

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    2. Marco F. Boretto & Fausto Cavalli & Ahmad Naimzada, 2021. "Oligopoly model with interdependent preferences: existence and uniqueness of Nash equilibrium," Working Papers 462, University of Milano-Bicocca, Department of Economics, revised Mar 2021.
    3. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1469-1478.
    4. Panchuk, A. & Puu, T., 2015. "Oligopoly model with recurrent renewal of capital revisited," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 119-128.
    5. Marco F. Boretto & Fausto Cavalli & Ahmad Naimzada, 2021. "Characterization of Nash equilibria in Cournotian oligopolies with interdependent preferences," Working Papers 463, University of Milano-Bicocca, Department of Economics, revised Mar 2021.

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