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A stochastic differential Fishery game for a two species fish population with ecological interaction

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  • Wang, Wen-Kai
  • Ewald, Christian-Oliver

Abstract

We combine and extend two existing lines of research in game theoretic studies of fisheries, building up on Quirk and Smith (1977), Anderson (1975), Fisher and Mirman (1996), Sumaila (1997) and most recently Datta and Mirman (1999) who developed either static or discrete time models, not including ecological uncertainty and Jorgensen and Yeung (1996) who do include uncertainty but do not capture any features of ecological interaction. In this article we develop a continuous time framework, where ecological interaction is described by a stochastic dynamics, including the cases of predator-prey and competition. We obtain a stochastic differential game and derive Markov feedback Nash-equilibrium strategies in semi-analytic form. Furthermore we compare the results with the case where fisheries regulations restrict each fishery to harvest only one species and study the inefficiencies which arise from this. In addition to that, we also consider the case where fisheries cooperate. Here we observe quite different effects on the ecosystem, depending on whether the system is competitive or predator-prey.

Suggested Citation

  • Wang, Wen-Kai & Ewald, Christian-Oliver, 2010. "A stochastic differential Fishery game for a two species fish population with ecological interaction," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 844-857, May.
    • Handle: RePEc:eee:dyncon:v:34:y:2010:i:5:p:844-857
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    References listed on IDEAS

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    1. Sumaila, U.R., 1997. "Strategic Dynamic Interaction: The Case of Barents Sea Fisheries," Norway; Department of Economics, University of Bergen 172, Department of Economics, University of Bergen.
    2. Datta, Manjira & Mirman, Leonard J., 1999. "Externalities, Market Power, and Resource Extraction," Journal of Environmental Economics and Management, Elsevier, vol. 37(3), pages 233-255, May.
    3. Dockner, Engelbert & Feichtinger, Gustav & Mehlmann, Alexander, 1989. "Noncooperative solutions for a differential game model of fishery," Journal of Economic Dynamics and Control, Elsevier, vol. 13(1), pages 1-20, January.
    4. Fischer, Ronald D. & Mirman, Leonard J., 1996. "The Compleat Fish Wars: Biological and Dynamic Interactions," Journal of Environmental Economics and Management, Elsevier, vol. 30(1), pages 34-42, January.
    5. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
    6. Ewald, Christian-Oliver & Wang, Wen-Kai, 2011. "Analytic solutions for infinite horizon stochastic optimal control problems via finite horizon approximation: A practical guide," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 146-151, May.
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    Cited by:

    1. Colombo, Luca & Labrecciosa, Paola, 2021. "A stochastic differential game of duopolistic competition with sticky prices," Journal of Economic Dynamics and Control, Elsevier, vol. 122(C).
    2. Wen-Kai Wang & Christian-Oliver Ewald, 2010. "Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(2), pages 97-116, November.
    3. Fesselmeyer, Eric & Santugini, Marc, 2013. "Strategic exploitation of a common resource under environmental risk," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 125-136.
    4. Emmi Nieminen & Lone Grønbæk Kronbak & Marko Lindroos, 2016. "International Agreements in the Multispecies Baltic Sea Fisheries," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(1), pages 109-134, September.
    5. Stein Ivar Steinshamn, 2017. "Predators in the market: implications of market interaction on optimal resource management," Journal of Bioeconomics, Springer, vol. 19(3), pages 327-341, October.
    6. Guennady Ougolnitsky & Anatoly Usov, 2019. "Spatially Distributed Differential Game Theoretic Model of Fisheries," Mathematics, MDPI, vol. 7(8), pages 1-13, August.
    7. Colombo, Luca & Labrecciosa, Paola, 2022. "Product quality differentiation in a renewable resource oligopoly," Journal of Environmental Economics and Management, Elsevier, vol. 111(C).
    8. van Dijk, Diana & Hendrix, Eligius M.T. & Haijema, Rene & Groeneveld, Rolf A. & van Ierland, Ekko C., 2014. "On solving a bi-level stochastic dynamic programming model for analyzing fisheries policies: Fishermen behavior and optimal fish quota," Ecological Modelling, Elsevier, vol. 272(C), pages 68-75.
    9. 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.
    10. Engwerda, Jacob, 2017. "Stabilization of an Uncertain Simple Fishery Management Game," Other publications TiSEM 3823c5f7-1ade-4bd2-bcb8-e, Tilburg University, School of Economics and Management.
    11. Ewald, Christian-Oliver & Wang, Wen-Kai, 2011. "Analytic solutions for infinite horizon stochastic optimal control problems via finite horizon approximation: A practical guide," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 146-151, May.

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