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The River Sharing Problem: A Survey

Author

Listed:
  • SYLVAIN BEAL

    (CRESE, University of Franche-Comté, 30 Avenue de l'Observatoire, 25009 Besançon, France)

  • AMANDINE GHINTRAN

    (EQUIPPE, University of Lille 3, Domaine universitaire du Pont de Bois, BP 59653 Villeneuve d'Ascq Cedex, France)

  • ERIC REMILA

    (LIP, CNRS-ENS Lyon-University of Lyon 1, University of Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France)

  • PHILIPPE SOLAL

    (GATE-CNRS, University of Saint-Etienne, 06 rue Basse des Rives, 42023 Saint-Etienne, France)

Abstract

The river sharing problem deals with the fair distribution of welfare resulting from the optimal allocation of water among a set of riparian agents. Ambec and Sprumont [Sharing a river, J. Econ. Theor.107, 453–462] address this problem by modeling it as a cooperative TU-game on the set of riparian agents. Solutions to that problem are reviewed in this article. These solutions are obtained via an axiomatic study on the class of river TU-games or via a market mechanism.

Suggested Citation

  • Sylvain Beal & Amandine Ghintran & Eric Remila & Philippe Solal, 2013. "The River Sharing Problem: A Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-19.
    • Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:03:n:s0219198913400161
    DOI: 10.1142/S0219198913400161
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    References listed on IDEAS

    as
    1. Khmelnitskaya, Anna & Talman, Dolf, 2014. "Tree, web and average web values for cycle-free directed graph games," European Journal of Operational Research, Elsevier, vol. 235(1), pages 233-246.
    2. Rene van den Brink & Arantza Estevez-Fernandez & Gerard van der Laan & Nigel Moes, 2011. "Independence Axioms for Water Allocation," Tinbergen Institute Discussion Papers 11-128/1, Tinbergen Institute.
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    Citations

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    Cited by:

    1. Ricardo Martinez & Juan D. Moreno-Ternero, 2024. "Fair allocation of riparian water rights," Papers 2407.14623, arXiv.org.
    2. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
    3. Jens Gudmundsson & Jens Leth Hougaard, 2021. "River pollution abatement: Decentralized solutions and smart contracts," IFRO Working Paper 2021/07, University of Copenhagen, Department of Food and Resource Economics, revised Oct 2021.
    4. Ansink, Erik & Gengenbach, Michael & Weikard, Hans-Peter, 2012. "River Sharing and Water Trade," Climate Change and Sustainable Development 122860, Fondazione Eni Enrico Mattei (FEEM).
    5. Gonzalez, Stéphane & Rostom, Fatma Zahra, 2022. "Sharing the global outcomes of finite natural resource exploitation: A dynamic coalitional stability perspective," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 1-10.
    6. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    7. Wenzhong Li & Genjiu Xu & René van den Brink, 2023. "Two new classes of methods to share the cost of cleaning up a polluted river," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(1), pages 35-59, July.
    8. 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.
    9. Rene van den Brink & Saish Nevrekar, 2020. "Peaceful Agreements to Share a River," Tinbergen Institute Discussion Papers 20-016/II, Tinbergen Institute.
    10. Erik Ansink & Hans-Peter Weikard, 2015. "Composition properties in the river claims problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 807-831, April.
    11. Rémy Delille & Jean-Christophe Pereau, 2014. "The Seawall Bargaining Game," Games, MDPI, vol. 5(2), pages 1-13, June.
    12. Ansink, Erik & Houba, Harold, 2016. "Sustainable agreements on stochastic river flow," Resource and Energy Economics, Elsevier, vol. 44(C), pages 92-117.
    13. Stéphane Gonzalez & Fatma Rostom, 2019. "Sharing the Global Benefits of Finite Natural Resource Exploitation: A Dynamic Coalitional Stability Perspective," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02430751, HAL.
    14. Wenzhong Li & Genjiu Xu & Rene van den Brink, 2021. "Sharing the cost of cleaning up a polluted river," Tinbergen Institute Discussion Papers 21-028/II, Tinbergen Institute.
    15. 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.
    16. Erik Ansink & Harold Houba, 2014. "The Economics of Transboundary River Management," Tinbergen Institute Discussion Papers 14-132/VIII, Tinbergen Institute.
    17. 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.

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    More about this item

    Keywords

    Core; externalities; graph games; marginal vectors; river sharing problem; C71; D62; H23;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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