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A dynamic common property resource problem with amenity value and extraction costs

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  • Gerhard Sorger

Abstract

An analytically tractable differential game is presented that describes the exploitation of a common‐property resource by finitely many competing players. The resource stock has an amenity value and there are positive extraction costs. We derive both the cooperative solution and Markov‐perfect Nash equilibria of the non‐cooperative game. After a comparative analysis of the equilibrium strategies and payoffs with respect to all model parameters, we study the effect of a unilateral extraction restriction and discuss the design of a revenue‐neutral tax/transfer scheme that supports the cooperative solution.

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  • Gerhard Sorger, 2005. "A dynamic common property resource problem with amenity value and extraction costs," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(1), pages 3-19, March.
    • Handle: RePEc:bla:ijethy:v:1:y:2005:i:1:p:3-19
    DOI: 10.1111/j.1742-7363.2005.00002.x
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    2. Ngo Long & Gerhard Sorger, 2006. "Insecure property rights and growth: the role of appropriation costs, wealth effects, and heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 513-529, August.
    3. Naïla Hayek, 2011. "A Generalization of Mixed Problems with an Application to Multiobjective Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 498-515, September.
    4. Takuma Kunieda & Kazuo Nishimura, 2018. "Finance and Economic Growth in a Dynamic Game," Dynamic Games and Applications, Springer, vol. 8(3), pages 588-600, September.
    5. Zaruhi Hakobyan & Christos Koulovatianos, 2021. "Symmetric Markovian Games of Commons with Potentially Sustainable Endogenous Growth," Dynamic Games and Applications, Springer, vol. 11(1), pages 54-83, March.
    6. 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.
    7. Walker, Adam N. & Weikard, Hans-Peter & Richter, Andries, 2015. "The Rise and Fall of the Great Fish Pact under Endogenous Risk of Stock Collapse," Climate Change and Sustainable Development 206466, Fondazione Eni Enrico Mattei (FEEM).
    8. Fujiwara, Kenji, 2008. "Duopoly can be more anti-competitive than monopoly," Economics Letters, Elsevier, vol. 101(3), pages 217-219, December.
    9. Antoniadou, Elena & Koulovatianos, Christos & Mirman, Leonard J., 2013. "Strategic exploitation of a common-property resource under uncertainty," Journal of Environmental Economics and Management, Elsevier, vol. 65(1), pages 28-39.
    10. Sakamoto, Hiroaki, 2014. "Dynamic resource management under the risk of regime shifts," Journal of Environmental Economics and Management, Elsevier, vol. 68(1), pages 1-19.
    11. Long, Ngo Van & Wang, Shengzu, 2009. "Resource-grabbing by status-conscious agents," Journal of Development Economics, Elsevier, vol. 89(1), pages 39-50, May.
    12. Antoniadou, Elena & Koulovatianos, Christos & Mirman, Leonard J., 2013. "Strategic exploitation of a common-property resource under uncertainty," Journal of Environmental Economics and Management, Elsevier, vol. 65(1), pages 28-39.
    13. Petros G. Sekeris, 2014. "The tragedy of the commons in a violent world," RAND Journal of Economics, RAND Corporation, vol. 45(3), pages 521-532, September.
    14. Nguyen Thi Toan & Le Quang Thuy, 2023. "S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 240-265, January.
    15. Russell Davidson & Adriana Cornea, 2008. "A Refined Bootstrap For Heavy Tailed Distributions," Departmental Working Papers 2008-03, McGill University, Department of Economics.
    16. Colombo, Luca & Labrecciosa, Paola, 2013. "On the convergence to the Cournot equilibrium in a productive asset oligopoly," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 441-445.
    17. Koulovatianos, Christos & Mirman, Leonard J., 2007. "The effects of market structure on industry growth: Rivalrous non-excludable capital," Journal of Economic Theory, Elsevier, vol. 133(1), pages 199-218, March.
    18. Athanassoglou, Stergios, 2010. "Dynamic nonpoint-source pollution control policy: Ambient transfers and uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2494-2509, December.
    19. Nguyen Thi Toan & Le Quang Thuy & Nguyen Tuyen & Yi-Bin Xiao, 2021. "Second-order KKT optimality conditions for multiobjective discrete optimal control problems," Journal of Global Optimization, Springer, vol. 79(1), pages 203-231, January.
    20. Caleb M. Koch & Heinrich H. Nax, 2022. "Groundwater Usage and Strategic Complements: Part I (Instrumental Variables)," Games, MDPI, vol. 13(5), pages 1-19, October.
    21. Ngo Long, 2011. "Dynamic Games in the Economics of Natural Resources: A Survey," Dynamic Games and Applications, Springer, vol. 1(1), pages 115-148, March.
    22. Koulovatianos, Christos & Mirman, Leonard J., 2007. "The effects of market structure on industry growth: Rivalrous non-excludable capital," Journal of Economic Theory, Elsevier, vol. 133(1), pages 199-218, March.

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