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Asymmetric Nash Solutions in the River Sharing Problem

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  • Houba, Harold
  • van der Laan, Gerard
  • Zeng, Yuyu

Abstract

We study unanimity bargaining among agents along a general river structure that is expressed by a geography matrix and who have access to limited local resources, cost functions that depend upon river inflow and own extraction, and quasi-linear preferences over water and money. Bargaining determines the water allocation and monetary transfers. We translate the legal principles of Absolute Territorial Sovereignty (ATS) and Unlimited Territorial Integrity (UTI) from International Water Law into our model. ATS and a strict interpretation of UTI result in disagreement outcomes that are feasible. And a second interpretation of UTI is translated into individual aspiration levels that are infeasible. For disagreement outcomes, we apply the asymmetric Nash bargaining solution. Common intuition that upstream and midstream countries always prefer the ATS principle to the strict UTI principle (while the opposite preference holds for the downstream country) is reversed for such countries with sufficient bargaining power. For individual aspiration levels, the agents have to compromise in order to agree and we apply the asymmetric Nash rationing solution. The participation constraints in the Nash rationing solution matter. In all cases the optimization problem is separable into two subproblems: the efficient water allocation that maximizes utilitarian welfare; and the determination of monetary transfers.

Suggested Citation

  • Houba, Harold & van der Laan, Gerard & Zeng, Yuyu, 2014. "Asymmetric Nash Solutions in the River Sharing Problem," Strategic Behavior and the Environment, now publishers, vol. 4(4), pages 321-360, December.
    • Handle: RePEc:now:jnlsbe:102.00000049
    DOI: 10.1561/102.00000049
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    References listed on IDEAS

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    1. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
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    5. 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.
    6. 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.
    7. 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.
    8. Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
    9. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
    10. 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.
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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

    International rivers; International treaties; River basin management; Pareto efficiency; Disagreement outcome; International water law; Negotiations; Externalities; Political economy of property rights; Pollution;
    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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