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Asymmetric Nash Solutions in the River Sharing Problem

Author

Listed:
  • Harold Houba

    (VU University Amsterdam)

  • Gerard van der Laan

    (VU University Amsterdam)

  • Yuyu Zeng

    (VU University Amsterdam)

Abstract

This discussion paper resulted in a publication in Strategic Behavior and the Environment , 2014, 4, 321-360. We study multiple agents along a general river structure that is expressed by a geography matrix and who have access to limited local resources, quasi-linear preferences over water and money and cost functions dependent upon river inflow and own extraction. Unanimity bargaining determines the water allocation and monetary transfers. We translate International Water Law into either disagreement outcomes or individual aspiration levels. In the former case, we apply the asymmetric Nash bargaining solution, in the latter case the agents have to compromise in order to agree and we apply the asymmetric Nash rationing solution. In both cases the optimization problem is separable into two subproblems: the efficient water allocation that maximizes utilitarian welfare given the geography matrix; and the determination of the monetary transfers associated with the weights. We show that the Nash rationing solution may result in nonparticipation, therefore we generalize to the case with participation constraints.

Suggested Citation

  • Harold Houba & Gerard van der Laan & Yuyu Zeng, 2013. "Asymmetric Nash Solutions in the River Sharing Problem," Tinbergen Institute Discussion Papers 13-051/II, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20130051
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    References listed on IDEAS

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    1. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 189-215, January.
    2. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2012. "Fair agreements for sharing international rivers with multiple springs and externalities," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 388-403.
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    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    6. Harold Houba, 2008. "Computing Alternating Offers And Water Prices In Bilateral River Basin Management," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(03), pages 257-278.
    7. D. Kilgour & Ariel Dinar, 2001. "Flexible Water Sharing within an International River Basin," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 18(1), pages 43-60, January.
    8. Marco Mariotti & Antonio Villar, 2005. "The Nash rationing problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 367-377, September.
    9. Ansink, Erik & Houba, Harold, 2012. "Market power in water markets," Journal of Environmental Economics and Management, Elsevier, vol. 64(2), pages 237-252.
    10. Gerard van der Laan & Nigel Moes, 2012. "Transboundary Externalities and Property Rights: An International River Pollution Model," Tinbergen Institute Discussion Papers 12-006/1, Tinbergen Institute.
    11. Dimitrios Giannias & Joseph Lekakis, 1996. "Fresh surface water resource allocation between Bulgaria and Greece," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 8(4), pages 473-483, December.
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    Citations

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    Cited by:

    1. Lea Melnikovová, 2017. "Can Game Theory Help to Mitigate Water Conflicts in the Syrdarya Basin?," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 65(4), pages 1393-1401.
    2. Rémy Delille & Jean-Christophe Pereau, 2014. "The Seawall Bargaining Game," Games, MDPI, vol. 5(2), pages 1-13, June.
    3. Ansink, Erik & Houba, Harold, 2016. "Sustainable agreements on stochastic river flow," Resource and Energy Economics, Elsevier, vol. 44(C), pages 92-117.
    4. Dagmawi Mulugeta Degefu & Weijun He & Liang Yuan, 2017. "Monotonic Bargaining Solution for Allocating Critically Scarce Transboundary Water," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2627-2644, July.
    5. Harold Houba & Gerard Laan & Yuyu Zeng, 2015. "International Environmental Agreements for River Sharing Problems," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 62(4), pages 855-872, December.
    6. Erik Ansink & Harold Houba, 2014. "The Economics of Transboundary River Management," Tinbergen Institute Discussion Papers 14-132/VIII, Tinbergen Institute.
    7. Shahmir Janjua & Ishtiaq Hassan & Muhammad Umair Ali & Malik Muhammad Ibrahim & Amad Zafar & Sangil Kim, 2021. "Addressing Social Inequality and Improper Water Distribution in Cities: A Case Study of Karachi, Pakistan," Land, MDPI, vol. 10(11), pages 1-15, November.
    8. Gudmundsson, Jens & Hougaard, Jens Leth & Ko, Chiu Yu, 2019. "Decentralized mechanisms for river sharing," Journal of Environmental Economics and Management, Elsevier, vol. 94(C), pages 67-81.
    9. Shivshanker Singh Patel & Parthasarathy Ramachandran, 2022. "A bargaining model for sharing water in a river with negative externality," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 645-666, June.
    10. Radim Valencik & Jan Cervenka, 2016. "Analysis Tools of Connecting Investment Opportunities and Investment Means in the Area of Small and Medium-Sized Enterprises," European Research Studies Journal, European Research Studies Journal, vol. 0(4), pages 130-139.
    11. Abraham, Anand & Ramachandran, Parthasarathy, 2021. "The welfare implications of transboundary storage and dam ownership on river water trade," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 18-27.

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    More about this item

    Keywords

    River Basin Management; International Water Law; Negotiations; Externalities; Political Economy of Property Rights;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D60 - Microeconomics - - Welfare Economics - - - General
    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling

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