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Independence of downstream and upstream benefits in river water allocation problems

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  • René Brink
  • Arantza Estévez-Fernández
  • Gerard Laan
  • Nigel Moes

Abstract

We consider the problem of sharing water among agents located along a river, who have quasi-linear preferences over water and money. The benefit of consuming an amount of water is given by a continuous, concave benefit function. In this setting, a solution efficiently distributes water over the agents and wastes no money. Since we deal with concave benefit functions, it is not always possible to follow the usual approach and define a cooperative river game. Instead, we directly introduce axioms for solutions on the water allocation problem. Besides three basic axioms, we introduce two independence axioms to characterize the downstream incremental solution, introduced by Ambec and Sprumont (J Econ Theory 107:453–462, 2002 ), and a new solution, called the UTI incremental solution. Both solutions can be implemented by allocating the water optimally among the agents and monetary transfers between the agents. We also consider the particular case in which every agent has a satiation point, constant marginal benefit equal to one up to its satiation point and marginal benefit of zero thereafter. This boils down to a water claim problem, where each agent only has a nonnegative claim on water, but no benefit function is specified. In this case, both solutions can be implemented without monetary transfers. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • René Brink & Arantza Estévez-Fernández & Gerard Laan & Nigel Moes, 2014. "Independence of downstream and upstream benefits in river water allocation problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 173-194, June.
  • Handle: RePEc:spr:sochwe:v:43:y:2014:i:1:p:173-194
    DOI: 10.1007/s00355-013-0771-x
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    References listed on IDEAS

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    2. 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.
    3. Anna Khmelnitskaya, 2010. "Values for rooted-tree and sink-tree digraph games and sharing a river," Theory and Decision, Springer, vol. 69(4), pages 657-669, October.
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    Cited by:

    1. Yuzhi Yang & Erik Ansink & Jens Gudmundsson, 2023. "How to Pollute a River If You Must," Tinbergen Institute Discussion Papers 23-036/VIII, Tinbergen Institute.
    2. Yuzhi Yang & Erik Ansink, 2022. "The river pollution claims problem," Tinbergen Institute Discussion Papers 22-058/VIII, Tinbergen Institute.
    3. René van den Brink & Simin He & Jia-Ping Huang, 2015. "Polluted River Problems and Games with a Permission Structure," Tinbergen Institute Discussion Papers 15-108/II, Tinbergen Institute.
    4. 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.
    5. Dongshuang Hou & Aymeric Lardon & Panfei Sun & Genjiu Xu, 2019. "Sharing a Polluted River under Waste Flow Control," GREDEG Working Papers 2019-23, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    6. Ansink, Erik & Houba, Harold, 2016. "Sustainable agreements on stochastic river flow," Resource and Energy Economics, Elsevier, vol. 44(C), pages 92-117.
    7. Erik Ansink & Carmen Marchiori, 2015. "Reallocating Water: An Application of Sequential Sharing Rules to Cyprus," Water Economics and Policy (WEP), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-22, December.
    8. Erik Ansink & Harold Houba, 2014. "The Economics of Transboundary River Management," Tinbergen Institute Discussion Papers 14-132/VIII, Tinbergen Institute.
    9. van den Brink, René & He, Simin & Huang, Jia-Ping, 2018. "Polluted river problems and games with a permission structure," Games and Economic Behavior, Elsevier, vol. 108(C), pages 182-205.
    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. Erik Ansink & Carmen Marchiori, 2015. "Reallocating Water: An Application of Sequential Sharing Rules to Cyprus," Water Economics and Policy (WEP), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-22, December.

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