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Sharing Water from many Rivers

Author

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  • Yann Rébillé

    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - IEMN-IAE Nantes - Institut d'Économie et de Management de Nantes - Institut d'Administration des Entreprises - Nantes - UN - Université de Nantes)

  • Lionel Richefort

    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - IEMN-IAE Nantes - Institut d'Économie et de Management de Nantes - Institut d'Administration des Entreprises - Nantes - UN - Université de Nantes)

Abstract

This paper studies the problem of non-cooperative water allocation between heterogeneous communities embodied in an acyclic network of water sources. The extraction activity of a community has a negative impact on the extraction activity of its direct successors: it reduces the intensity of water flows entering their source, and thus, increase their convex costs of water extraction. We show that the equilibrium profile is unique and may be expressed through complementarity and substitutability effects which sharacterize the incoming centrality of a community in the network of sources. For each community, the efficient activity is a combination of two opposite network effects, the incoming centrality and the outcoming centrality. Then, the optimal tax rate imposed to a community depends on the network structure, and reflects both the marginal damages and the marginal benefits this community delivers to other communities at the efficient extraction activity profile.

Suggested Citation

  • Yann Rébillé & Lionel Richefort, 2012. "Sharing Water from many Rivers," Working Papers hal-00678997, HAL.
    • Handle: RePEc:hal:wpaper:hal-00678997
    Note: View the original document on HAL open archive server: https://hal.science/hal-00678997
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    Cited by:

    1. Rébillé, Yann & Richefort, Lionel, 2014. "Equilibrium existence and uniqueness in network games with additive preferences," European Journal of Operational Research, Elsevier, vol. 232(3), pages 601-606.
    2. Shivshanker Singh Patel & Parthasarathy Ramachandran, 2019. "A Bilateral River Bargaining Problem with Negative Externality," Papers 1912.05844, arXiv.org.
    3. 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.
    4. Yann Rébillé & Lionel Richefort, 2015. "Influence and Social Tragedy in Networks," Revue d'économie politique, Dalloz, vol. 125(6), pages 811-833.
    5. 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.

    More about this item

    Keywords

    flowing water; network of sources; equilibrium effects; efficiency effects; optimal tax;
    All these keywords.

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