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The river sharing problem: A review of the technical literature for policy economists


  • Beard, Rodney


Water is essential for life. However, the basic problem of water resource allocation has been that water tends to be over-allocated. Demand for water exceeds the available supply. Essentially, the water economy is bankrupt. Bankruptcy problems have been almost exhaustively studied in the literature on economic theory-primarily from the perspective of cooperative game theory. The main concern of this literature has been how to fairly divide up the assets of a bankrupt entity. In water resource economics cooperative game theory has often been employed as a means of analyzing water resource allocation. It was only recently that the problem of directional flow was incorporated into such analyses. This has come to be known as the “river sharing problem” in the theoretical literature. Accounting for the direction of flow in water resource allocation problems has profound implications for policies that wish to facilitate both fair and efficient water allocations. This is the case whether proposed policies are interventionist or market based in nature. There is now a considerable literature on the allocation and distribution of water resources characterized by unidirectional flow. In this paper I critically review and appraise this literature with a view to making it more accessible to applied and policy economists. A key feature of the paper is that the connection between the bankruptcy literature, which has recently also realized the importance of flow, and the river sharing literature is discussed. The current state of the art in game theoretic models of water resource allocation with directional flow is discussed and implications and consequences for water resource policy highlighted

Suggested Citation

  • Beard, Rodney, 2011. "The river sharing problem: A review of the technical literature for policy economists," MPRA Paper 34382, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:34382

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    References listed on IDEAS

    1. Ambec, S. & Ehlers, L., 2007. "Cooperation and equity in the river sharing problem," Working Papers 200705, Grenoble Applied Economics Laboratory (GAEL).
    2. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    3. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
    4. d'Albis, Hippolyte & Ambec, Stefan, 2010. "Fair intergenerational sharing of a natural resource," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 170-183, March.
    5. Rodica Branzei & Giulio Ferrari & Vito Fragnelli & Stef Tijs, 2008. "A Flow Approach to Bankruptcy Problems," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(2), pages 146-153, September.
    6. Parrachino, Irene & Dinar, Ariel & Patrone, Fioravante, 2006. "Cooperative game theory and its application to natural, environmental, and water resource issues : 3. application to water resources," Policy Research Working Paper Series 4074, The World Bank.
    7. 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.
    8. Weber, Marian L., 2001. "Markets for Water Rights under Environmental Constraints," Journal of Environmental Economics and Management, Elsevier, vol. 42(1), pages 53-64, July.
    9. Hendrickx, R.L.P., 2004. "Cooperation and allocation," Other publications TiSEM ab33e762-204c-46e2-86b1-0, Tilburg University, School of Economics and Management.
    10. Mitsuo Suzuki & Mikio Nakayama, 1976. "The Cost Assignment of the Cooperative Water Resource Development: A Game Theoretical Approach," Management Science, INFORMS, vol. 22(10), pages 1081-1086, June.
    11. Ni, Debing & Wang, Yuntong, 2007. "Sharing a polluted river," Games and Economic Behavior, Elsevier, vol. 60(1), pages 176-186, July.
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    Cited by:

    1. Nadine Wittmann, 2014. "A Microeconomic Perspective on Water Resources Management: Analyzing the Effects on Optimal Land Rents Along a River Basin," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(5), pages 1309-1325, March.
    2. Alcalde-Unzu, Jorge & Gómez-Rúa, María & Molis, Elena, 2015. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Games and Economic Behavior, Elsevier, vol. 90(C), pages 134-150.
    3. Nadine Wittmann, 2014. "A Note on Distortional Distributional Effects in River Basin Discharge Permit Trade," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(1), pages 279-285, January.
    4. Wittmann Nadine, 2013. "A microeconomic analysis of the socio-economic situation along the Kat River Water Basin: Comment," Agrekon, Taylor & Francis Journals, vol. 52(2), pages 128-135, June.
    5. CN Mbatha & GG Antrobus, 2013. "Institutions and economic research: A case of location externalities on agricultural resource allocation in the Kat River basin, South Africa: A Rejoinder," Agrekon, Taylor & Francis Journals, vol. 52(2), pages 136-145, June.

    More about this item


    River sharing problem; Bankruptcy; Cooperative game theory; Water resouyrce allocation; distributive justice;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • Q25 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Water

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