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Fair agreements for sharing international rivers with multiple springs and externalities

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  • van den Brink, René
  • van der Laan, Gerard
  • Moes, Nigel

Abstract

We consider the problem of sharing water among agents located along a river. Each agent's benefit depends on the amount of water consumed. An allocation of water is efficient when it maximizes total benefits. To sustain an efficient water allocation the agents can compensate each other by monetary transfers. Every water allocation and transfer schedule yield a welfare distribution, where an agent's utility equals its benefit plus (possibly negative) monetary transfer. The problem of finding a fair welfare distribution can be modeled by a cooperative game. We consider river situations with satiable agents and multiple springs. We propose the class of weighted hierarchical solutions, including the downstream incremental solution of Ambec and Sprumont (2002, [3]), as a class of solutions satisfying the ‘Territorial Integration of all Basin States’ principle for sharing water of international rivers. When all agents have increasing benefit functions, every weighted hierarchical solution is core-stable. In case of satiation points, every weighted hierarchical solution is independent of the externalities.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Environmental Economics and Management.

Volume (Year): 63 (2012)
Issue (Month): 3 ()
Pages: 388-403

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Handle: RePEc:eee:jeeman:v:63:y:2012:i:3:p:388-403

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Web page: http://www.elsevier.com/locate/inca/622870

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Keywords: Water allocation; River game; Externality; Core; Hierarchical outcome;

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References

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  1. Armando Gomes, 2005. "Multilateral Contracting with Externalities," Econometrica, Econometric Society, vol. 73(4), pages 1329-1350, 07.
  2. Geoffroy de Clippel & Roberto Serrano, 2005. "Marginal Contributions and Externalities in the Value," Working Papers 2005-11, Brown University, Department of Economics.
  3. Dutta, Bhaskar & Ehlers, Lars & Kar, Anirban, 2010. "Externalities, potential, value and consistency," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2380-2411, November.
  4. 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.
  5. D. Kilgour & Ariel Dinar, 2001. "Flexible Water Sharing within an International River Basin," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 18(1), pages 43-60, January.
  6. Ambec, Stefan & Sprumont, Yves, 2000. "Sharing a River," Cahiers de recherche 0006, GREEN.
  7. Debraj Ray & Rajiv Vohra, 1998. "A Theory of Endogenous Coalition Structures," Working Papers 98-1, Brown University, Department of Economics, revised Jan 1998.
  8. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print halshs-00581662, HAL.
  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 04-043/1, Tinbergen Institute.
  10. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Rooted-tree solutions for tree games," European Journal of Operational Research, Elsevier, vol. 203(2), pages 404-408, June.
  11. 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, vol. 28(2), pages 157-171.
  12. Ambec, Stefan & Ehlers, Lars, 2008. "Sharing a river among satiable agents," Games and Economic Behavior, Elsevier, vol. 64(1), pages 35-50, September.
  13. 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, vol. 135(1), pages 339-356, July.
  14. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
  15. 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., vol. 7(01), pages 63-72.
  16. René Brink & Gerard Laan & Valeri Vasil’ev, 2007. "Component efficient solutions in line-graph games with applications," Economic Theory, Springer, vol. 33(2), pages 349-364, November.
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Citations

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Cited by:
  1. Harold Houba & Erik Ansink, 2013. "Sustainable Agreements on Stochastic River Flow," Tinbergen Institute Discussion Papers 13-182/II, Tinbergen Institute.
  2. Erik Ansink & Michael Gengenbach & Hans-Peter Weikard, 2012. "River Sharing and Water Trade," Working Papers 2012.17, Fondazione Eni Enrico Mattei.
  3. Jorge Alcalde-Unzu & Maria Gomez-Rua & Elena Molis, 2013. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," ThE Papers 13/03, Department of Economic Theory and Economic History of the University of Granada..
  4. repec:dgr:kubcen:2013078 is not listed on IDEAS
  5. Rene van den Brink & Gerard van der Laan & Nigel Moes, 2012. "A Strategic Implementation of the Average Tree Solution for Cycle-Free Graph Games," Tinbergen Institute Discussion Papers 12-050/1, Tinbergen Institute.
  6. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "The sequential equal surplus division for sharing a river," MPRA Paper 37346, University Library of Munich, Germany.
  7. Gerard van der Laan & Nigel Moes, 2012. "Transboundary Externalities and Property Rights: An International River Pollution Model," Tinbergen Institute Discussion Papers 12-006/1, Tinbergen Institute.
  8. Erik Ansink & Hans-Peter Weikard, 2013. "Composition Properties in the River Claims Problem," Tinbergen Institute Discussion Papers 13-199/VIII, Tinbergen Institute.
  9. repec:dgr:uvatin:2012006 is not listed on IDEAS
  10. repec:dgr:uvatin:2012050 is not listed on IDEAS
  11. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2009. "Weighted Component Fairness for Forest Games," MPRA Paper 17455, University Library of Munich, Germany.
  12. 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.
  13. repec:dgr:uvatin:2011128 is not listed on IDEAS
  14. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2012. "The Sequential Equal Surplus Division for Sharing International Rivers with Bifurcations," Working Papers 2012-02, CRESE.
  15. Harold Houba & Gerard van der Laan, 2013. "International Environmental Agreements for River Sharing Problems," Tinbergen Institute Discussion Papers 13-157/II, Tinbergen Institute.
  16. 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 1340016-1-1.
  17. 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, vol. 43(1), pages 173-194, June.
  18. repec:dgr:uvatin:2013051 is not listed on IDEAS
  19. 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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