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Sequential sharing rules for river sharing problems

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  • Erik Ansink

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  • Hans-Peter Weikard

Abstract

We analyse the redistribution of a resource among agents who have claims to the resource and who are ordered linearly. A well known example of this particular situation is the river sharing problem. We exploit the linear order of agents to transform the river sharing problem to a sequence of two-agent river sharing problems. These reduced problems are mathematically equivalent to bankruptcy problems and can therefore be solved using any bankruptcy rule. Our proposed class of solutions, that we call sequential sharing rules, solves the river sharing problem. Our approach extends the bankruptcy literature to settings with a sequential structure of both the agents and the resource to be shared. In the paper, we first characterise a class of sequential sharing rules. Subsequently, we apply sequential sharing rules based on four classical bankruptcy rules, assess their properties, and compare them to four alternative solutions to the river sharing problem.

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 38 (2012)
Issue (Month): 2 (February)
Pages: 187-210

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Handle: RePEc:spr:sochwe:v:38:y:2012:i:2:p:187-210

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References

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  1. Erik Ansink & Arjan Ruijs, 2008. "Climate Change and the Stability of Water Allocation Agreements," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 41(2), pages 249-266, October.
  2. Gianmarco I.P. Ottaviano & Gregory Corcos & Massimo Del Gatto & Giordano Mion, 2009. "Productivity and Firm Selection: Quantifying the “New” Gains from Trade," Working Papers 2009.115, Fondazione Eni Enrico Mattei.
  3. P. Herings & Gerard Laan & Dolf Talman, 2007. "Socially Structured Games," Theory and Decision, Springer, vol. 62(1), pages 1-29, February.
  4. Rodica Branzei & Giulio Ferrari & Vito Fragnelli & Stef Tijs, 2008. "A Flow Approach to Bankruptcy Problems," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(2), pages 146-153, September.
  5. Ilkilic, Rahmi & Kayi, Cagatay, 2012. "Allocation rules on networks," MPRA Paper 37305, University Library of Munich, Germany.
  6. Marc D. Davidson, 2008. "Wrongful Harm to Future Generations: The Case of Climate Change," Environmental Values, White Horse Press, vol. 17(4), pages 471-488, November.
  7. 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.
  8. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  9. Coram, Alex, 2006. "The optimal allocation of water along a system of rivers: a continuous model with sequential bidding," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 50(3), September.
  10. P. Herings & Arkadi Predtetchinski, 2012. "Sequential share bargaining," International Journal of Game Theory, Springer, vol. 41(2), pages 301-323, May.
  11. Parrachino, Irene & Dinar, Ariel & Patrone, Fioravante, 2006. "Cooperative game theory and its application to natural, environmental, and water resource issues : 3. application to water resources," Policy Research Working Paper Series 4074, The World Bank.
  12. Harold Houba, 2008. "Computing Alternating Offers And Water Prices In Bilateral River Basin Management," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(03), pages 257-278.
  13. Marc Fleurbaey & Walter Bossert, 1996. "Redistribution and compensation (*)," Social Choice and Welfare, Springer, vol. 13(3), pages 343-355.
  14. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
  15. Carraro, Carlo & Marchiori, Carmen & Sgobbi, Alessandra, 2007. "Negotiating on water: insights from non-cooperative bargaining theory," Environment and Development Economics, Cambridge University Press, vol. 12(02), pages 329-349, April.
  16. Bergantinos, Gustavo & Sanchez, Estela, 2002. "The proportional rule for problems with constraints and claims," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 225-249, March.
  17. Ansink, Erik & Weikard, Hans-Peter, 2009. "Contested water rights," European Journal of Political Economy, Elsevier, vol. 25(2), pages 247-260, June.
  18. 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.
  19. Goetz, Renan U. & Martinez, Yolanda & Rodrigo, Jofre, 2008. "Water allocation by social choice rules: The case of sequential rules," Ecological Economics, Elsevier, vol. 65(2), pages 304-314, April.
  20. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  21. Bettina Klaus & Hans Peters & Ton Storcken, 1997. "Reallocation of an infinitely divisible good," Economic Theory, Springer, vol. 10(2), pages 305-333.
  22. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
  23. Kenneth Arrow & Partha Dasgupta & Lawrence Goulder & Gretchen Daily & Paul Ehrlich & Geoffrey Heal & Simon Levin & Karl-Göran Mäler & Stephen Schneider & David Starrett & Brian Walker, 2004. "Are We Consuming Too Much?," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 147-172, Summer.
  24. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
  25. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
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Citations

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Cited by:
  1. Ambec, Stefan & Dinar, Ariel & McKinney, Daene, 2011. "Fixed Water Sharing Agreements Sustainable to Drought," LERNA Working Papers 11.19.353, LERNA, University of Toulouse.
  2. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," MSAP Working Paper Series 05_2010, University of Copenhagen, Department of Food and Resource Economics.
  3. repec:dgr:kubcen:2013078 is not listed on IDEAS
  4. Julien Chevallier & Benoît Sévi, 2009. "On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting," EconomiX Working Papers 2009-24, University of Paris West - Nanterre la Défense, EconomiX.
  5. 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.
  6. Beard, Rodney, 2011. "The river sharing problem: A review of the technical literature for policy economists," MPRA Paper 34382, University Library of Munich, Germany.
  7. 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.
  8. 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.
  9. 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.
  10. Erik Ansink & Hans-Peter Weikard, 2013. "Composition Properties in the River Claims Problem," Tinbergen Institute Discussion Papers 13-199/VIII, Tinbergen Institute.
  11. 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.
  12. Erik Ansink & Carmen Marchiori, 2009. "Reallocating Water: An Application of Sequent," Working Papers 2009.126, Fondazione Eni Enrico Mattei.
  13. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "The sequential equal surplus division for sharing a river," MPRA Paper 37346, University Library of Munich, Germany.
  14. 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.
  15. 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.
  16. Ansink, Erik & Weikard, Hans-Peter, 2013. "Composition properties in the river claims problem," MPRA Paper 51618, University Library of Munich, Germany.

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