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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. 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.
  2. AMBEC, Steve & SPRUMONT, Yves, 2000. "Sharing a River," Cahiers de recherche 2000-08, Universite de Montreal, Departement de sciences economiques.
  3. Ray, Debraj & Vohra, Rajiv, 1999. "A Theory of Endogenous Coalition Structures," Games and Economic Behavior, Elsevier, vol. 26(2), pages 286-336, January.
  4. 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.
  5. Ambec, Stefan & Ehlers, Lars, 2008. "Sharing a river among satiable agents," Games and Economic Behavior, Elsevier, vol. 64(1), pages 35-50, September.
  6. Geoffroy de Clippel & Roberto Serrano, 2005. "Marginal Contributions And Externalities In The Value," Economics Working Papers we057339, Universidad Carlos III, Departamento de Economía.
  7. 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.
  8. 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.
  9. Bhaskar Dutta & Lars Ehlers & Anirban Kar, 2008. "Externalities, Potential, Value And Consistency," Working papers 168, Centre for Development Economics, Delhi School of Economics.
  10. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print halshs-00581662, HAL.
  11. HERINGS, P. Jean-Jacques & van der LAAN, Gerard & TALMAN, Dolf, . "The average tree solution for cycle-free graph games," CORE Discussion Papers RP -2155, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Armando Gomes, 2005. "Multilateral Contracting with Externalities," Econometrica, Econometric Society, vol. 73(4), pages 1329-1350, 07.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
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Citations

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Cited by:
  1. 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.
  2. Erik Ansink & Hans-Peter Weikard, 2013. "Composition Properties in the River Claims Problem," Tinbergen Institute Discussion Papers 13-199/VIII, Tinbergen Institute.
  3. 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.
  4. 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.
  5. Harold Houba & Erik Ansink, 2013. "Sustainable Agreements on Stochastic River Flow," Tinbergen Institute Discussion Papers 13-182/II, Tinbergen Institute.
  6. 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.
  7. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "The sequential equal surplus division for sharing a river," MPRA Paper 37346, University Library of Munich, Germany.
  8. repec:dgr:kubcen:2013078 is not listed on IDEAS
  9. Jorge Alcalde-Unzu & María Gómez-Rúa & Elena Molis, 2013. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 1301, Departamento de Economía - Universidad Pública de Navarra.
  10. 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.
  11. repec:dgr:uvatin:2012006 is not listed on IDEAS
  12. 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.
  13. 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.
  14. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2009. "Weighted Component Fairness for Forest Games," MPRA Paper 17455, University Library of Munich, Germany.
  15. repec:dgr:uvatin:2012050 is not listed on IDEAS
  16. repec:dgr:uvatin:2011128 is not listed on IDEAS
  17. Harold Houba & Gerard van der Laan, 2013. "International Environmental Agreements for River Sharing Problems," Tinbergen Institute Discussion Papers 13-157/II, Tinbergen Institute.
  18. 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.
  19. repec:dgr:uvatin:2013051 is not listed on IDEAS

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