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Fair Agreements for Sharing International Rivers with Multiple Springs and Externalities

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  • Rene van den Brink

    (VU University Amsterdam)

  • Gerard van der Laan

    (VU University Amsterdam)

  • Nigel Moes

    (VU University Amsterdam)

Abstract

This discussion paper led to a publication in , 'Journal of Environmental Economics and Management' , 63(3), 388-403. In this paper we consider the problem of sharing water from a river among a group of agents (countries, cities, firms) located along the river. The benefit of each agent depends on the amount of water consumed by the agent. An allocation of the water among the agents is efficient when it maximizes the total benefits. To sustain an efficient water allocation, the agents can compensate each other by paying monetary transfers. Every water allocation and transfer schedule yields a welfare distribution, where the utility of an agent is equal to its benefit from the water consumption plus its monetary transfer (which can be negative). The problem of finding a fair welfare distribution can be modelled by a cooperative game. For a river with one spring and increasing benefit functions, Ambec and Sprumont (2002) propose the downstream incremental solution as the unique welfare distribution that is core-stable and satisfies the condition that no agent gets a utility payoff above its aspiration level. Ambec and Ehlers (2008) generalized the Ambec and Sprumont river game to river situations with satiable agents, i.e., the benefit function is decreasing beyond some satiation point. In such situations externalities appear, yielding a cooperative game in partition function form. In this paper we consider river situations with satiable agents and with multiple springs. For this type of river systems we propose the class of so-called weighted hierarchical solutions as the class of solutions satisfying several principles to be taken into account for solving water disputes. When every agent has an increasing benefit function (no externalities) then every weighted hierarchical solution is core-stable. In case of satiation points, it appears that every weighted hierarchical solution is independent of the externalities.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 10-096/1.

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Date of creation: 20 Sep 2010
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Handle: RePEc:dgr:uvatin:20100096

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Web page: http://www.tinbergen.nl

Related research

Keywords: water allocation; river game; externality; core; hierarchical outcome;

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References

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  1. Ambec, Stefan & Sprumont, Yves, 2000. "Sharing a River," Cahiers de recherche, GREEN 0006, GREEN.
  2. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, Econometric Society, vol. 76(6), pages 1413-1436, November.
  3. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, Elsevier, vol. 135(1), pages 339-356, July.
  4. Armando Gomes, 2005. "Multilateral Contracting with Externalities," Econometrica, Econometric Society, Econometric Society, vol. 73(4), pages 1329-1350, 07.
  5. René Brink & Gerard Laan & Valeri Vasil’ev, 2007. "Component efficient solutions in line-graph games with applications," Economic Theory, Springer, Springer, vol. 33(2), pages 349-364, November.
  6. Bhaskar Dutta & Lars Ehlers & Anirban Kar, 2008. "Externalities, Potential, Value And Consistency," Working papers, Centre for Development Economics, Delhi School of Economics 168, Centre for Development Economics, Delhi School of Economics.
  7. D. Kilgour & Ariel Dinar, 2001. "Flexible Water Sharing within an International River Basin," Environmental & Resource Economics, European Association of Environmental and Resource Economists, European Association of Environmental and Resource Economists, vol. 18(1), pages 43-60, January.
  8. Ray, D. & Vohra, R., 1996. "A Theory of Endogenous Coalition Structure," Papers, Boston University - Industry Studies Programme 68, Boston University - Industry Studies Programme.
  9. P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman, 2004. "The Socially Stable Core in Structured Transferable Utility Games," Tinbergen Institute Discussion Papers, Tinbergen Institute 04-043/1, Tinbergen Institute.
  10. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2008. "The average tree solution for cycle-free graph games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-377604, Tilburg University.
  11. Ambec, Stefan & Ehlers, Lars, 2008. "Sharing a river among satiable agents," Games and Economic Behavior, Elsevier, Elsevier, vol. 64(1), pages 35-50, September.
  12. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print, HAL halshs-00581662, HAL.
  13. M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72.
  14. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Rooted-tree solutions for tree games," European Journal of Operational Research, Elsevier, Elsevier, vol. 203(2), pages 404-408, June.
  15. Anna Khmelnitskaya, 2010. "Values for rooted-tree and sink-tree digraph games and sharing a river," Theory and Decision, Springer, Springer, vol. 69(4), pages 657-669, October.
  16. Yukihiko Funaki & Takehiko Yamato, 1999. "The core of an economy with a common pool resource: A partition function form approach," International Journal of Game Theory, Springer, Springer, vol. 28(2), pages 157-171.
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Citations

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Cited by:
  1. Gerard van der Laan & Nigel Moes, 2012. "Transboundary Externalities and Property Rights: An International River Pollution Model," Tinbergen Institute Discussion Papers, Tinbergen Institute 12-006/1, Tinbergen Institute.
  2. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Weighted component fairness for forest games," Mathematical Social Sciences, Elsevier, Elsevier, vol. 64(2), pages 144-151.
  3. Ansink, Erik & Weikard, Hans-Peter, 2013. "Composition properties in the river claims problem," MPRA Paper 51618, University Library of Munich, Germany.
  4. 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., World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1340016-1-1.
  5. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2013. "A strategic implementation of the Average Tree solution for cycle-free graph games," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(6), pages 2737-2748.
  6. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2012. "The Sequential Equal Surplus Division for Sharing International Rivers with Bifurcations," Working Papers, CRESE 2012-02, CRESE.
  7. Weikard, Hans-Peter & Ansink, Erik & Gengenbach, Michael, 2013. "River Sharing and Water Trade," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79931, Verein für Socialpolitik / German Economic Association.
  8. Ambec, Stefan & Dinar, Ariel & McKinney, Daene, 2013. "Water sharing agreements sustainable to reduced flows," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 639-655.
  9. Harold Houba & Erik Ansink, 2013. "Sustainable Agreements on Stochastic River Flow," Tinbergen Institute Discussion Papers, Tinbergen Institute 13-182/II, Tinbergen Institute.
  10. repec:dgr:uvatin:2013051 is not listed on IDEAS
  11. Rene van den Brink & Arantza Estevez-Fernandez & Gerard van der Laan & Nigel Moes, 2011. "Independence Axioms for Water Allocation," Tinbergen Institute Discussion Papers, Tinbergen Institute 11-128/1, Tinbergen Institute.
  12. Harold Houba & Gerard van der Laan, 2013. "International Environmental Agreements for River Sharing Problems," Tinbergen Institute Discussion Papers, Tinbergen Institute 13-157/II, Tinbergen Institute.
  13. repec:dgr:uvatin:2012050 is not listed on IDEAS
  14. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "The sequential equal surplus division for sharing a river," MPRA Paper 37346, University Library of Munich, Germany.
  15. Jorge Alcalde-Unzu & Maria Gomez-Rua & Elena Molis, 2013. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," ThE Papers, Department of Economic Theory and Economic History of the University of Granada. 13/03, Department of Economic Theory and Economic History of the University of Granada..
  16. 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, Springer, vol. 43(1), pages 173-194, June.
  17. repec:dgr:uvatin:2012006 is not listed on IDEAS
  18. repec:dgr:uvatin:2011128 is not listed on IDEAS
  19. repec:dgr:kubcen:2013078 is not listed on IDEAS

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