Social Choice and Welfare

, Volume 44, Issue 4, pp 807–831 | Cite as

Composition properties in the river claims problem

  • Erik AnsinkEmail author
  • Hans-Peter Weikard


In a river claims problem, agents are ordered linearly, and they have both an initial water endowment as well as a claim to the total water resource. We provide characterizations of two solutions to this problem, using Composition properties which have particularly relevant interpretations for the river claims problem. Specifically, these properties relate to situations where river flow is uncertain or highly variable, possibly due to climate change impacts. The only solution that satisfies all Composition properties is the ‘Harmon rule’ induced by the Harmon Doctrine, which says that agents are free to use any water available on their territory, without concern for downstream impacts. The other solution that we assess is the ‘No-harm rule’, an extreme interpretation of the “no-harm” principle from international water law, which implies that water is allocated with priority to downstream needs. In addition to characterizing both solutions, we show their relation to priority rules and to sequential sharing rules, and we extend our analysis to general river systems.


River claims problem Sharing rule Harmon Doctrine  Composition axioms Water allocation 

JEL Classification

D63 C71 Q25 



We thank seminar participants of the 2013 Tinbergen Workshop on Decision Making in Water Problems at VU University Amsterdam, Stergios Athanassoglou, an associate editor and two reviewers for helpful comments. The first author acknowledges financial support from FP7-IDEAS-ERC Grant No. 269788.


  1. Ambec S, Dinar A, McKinney D (2013) Water sharing agreements sustainable to reduced flows. J Environ Econ Manag 66(3):639–655CrossRefGoogle Scholar
  2. Ambec S, Ehlers L (2008) Sharing a river among satiable agents. Games Econ Behav 64(1):35–50CrossRefGoogle Scholar
  3. Ambec S, Sprumont Y (2002) Sharing a river. J Econ Theory 107(2):453–462CrossRefGoogle Scholar
  4. Ansink E, Gengenbach M, Weikard H-P (2012). River sharing and water trade. FEEM Working Paper 017.2012Google Scholar
  5. Ansink E, Houba H (2013). Sustainable agreements on stochastic river flow. Tinbergen Institute Discussion Paper 2013/182Google Scholar
  6. Ansink E, Ruijs A (2008) Climate change and the stability of water allocation agreements. Environ Resour Econ 41(2):249–266CrossRefGoogle Scholar
  7. Ansink E, Weikard H-P (2009) Contested water rights. Eur J Polit Econ 25(2):247–260CrossRefGoogle Scholar
  8. Ansink E, Weikard H-P (2012) Sequential sharing rules for river sharing problems. Soc Choice Welf 38(2):187–210CrossRefGoogle Scholar
  9. Arrow K, Dasgupta P, Goulder L, Daily G, Ehrlich P, Heal G, Levin S, Mäler K-G, Schneider S, Starrett D, Walker B (2004) Are we consuming too much? J Econ Perspect 18(3):147–172CrossRefGoogle Scholar
  10. Bates B, Kundzewicz Z, Wu S, Palutikof J (2008) Climate change and water. Intergovernmental panel on climate change, Technical Paper VIGoogle Scholar
  11. Beach H, Hammer J, Hewitt J, Kaufman E, Kurki A, Oppenheimer J, Wolf A (2000) Transboundary freshwater dispute resolution: theory, practice, and annotated references. United Nations University Press, TokyoGoogle Scholar
  12. Béal S, Ghintran A, Rémila E, Solal P (2013) The river sharing problem: a survey. Int Game Theory Rev 15(3):1340016CrossRefGoogle Scholar
  13. Béal S, Ghintran A, Rémila E, Solal P (2014) The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations (Forthcoming in Theory and Decision)Google Scholar
  14. Chun Y (1988) The proportional solution for rights problems. Math Soc Sci 15(3):231–246CrossRefGoogle Scholar
  15. Daoudy M (2008) Hydro-hegemony and international water law: laying claims to water rights. Water Policy 10(S2):89–102CrossRefGoogle Scholar
  16. De Stefano L, Duncan J, Dinar S, Stahl K, Strzepek K, Wolf A (2012) Climate change and the institutional resilience of international river basins. J Peace Res 49(1):193–209CrossRefGoogle Scholar
  17. Demange G (2004) On group stability in hierarchies and networks. J Polit Econ 112(4):754–778CrossRefGoogle Scholar
  18. Dettinger M, Diaz H (2000) Global characteristics of stream flow seasonality and variability. J Hydrometeorol 1(4):289–310CrossRefGoogle Scholar
  19. Dinar A, Nigatu G (2013) Distributional considerations of international water resources under externality: the case of Ethiopia, Sudan and Eypt on the Blue Nile. Water Resour Econ 2–3:1–16CrossRefGoogle Scholar
  20. Dinar A, Ratner A, Yaron D (1992) Evaluating cooperative game theory in water resources. Theory Decis 32(1):1–20CrossRefGoogle Scholar
  21. Herrero C, Maschler M, Villar A (1999) Individual rights and collective responsibility: the rights-egalitarian solution. Math Soc Sci 37(1):59–77CrossRefGoogle Scholar
  22. Houba H (2008) Computing alternating offers and water prices in bilateral river basin management. Int Game Theory Rev 10(3):257–278CrossRefGoogle Scholar
  23. İlkılıç R (2011) Networks of common property resources. Econ Theory 47(1):105–134CrossRefGoogle Scholar
  24. İlkılıç R, Kayı C (2014) Allocation rules on networks. Soc Choice Welf 43(4):877–892Google Scholar
  25. Khmelnitskaya A (2010) Values for rooted-tree and sink-tree digraph games and sharing a river. Theory Decis 69(4):657–669CrossRefGoogle Scholar
  26. Kilgour D, Dinar A (2001) Flexible water sharing within an international river basin. Environ Resour Econ 18(1):43–60CrossRefGoogle Scholar
  27. Krzysztofowicz R (2001) The case for probabilistic forecasting in hydrology. J Hydrol 249(1–4):2–9CrossRefGoogle Scholar
  28. McCaffrey S (2007) The law of international water courses. Oxford University Press, OxfordGoogle Scholar
  29. Milly P, Dunne K, Vecchia A (2005) Global pattern of trends in streamflow and water availability in a changing climate. Nature 438(7066):347–350CrossRefGoogle Scholar
  30. Montanari A, Grossi G (2008) Estimating the uncertainty of hydrological forecasts: a statistical approach. Water Resour Res 44(12):W00B08CrossRefGoogle Scholar
  31. Moreno-Ternero J (2011) A coalitional procedure leading to a family of bankruptcy rules. Oper Res Lett 39(1):1–3CrossRefGoogle Scholar
  32. Moulin H (1987) Equal or proportional division of a surplus, and other methods. Int J Game Theory 16(3):161–186CrossRefGoogle Scholar
  33. Moulin H (2000) Priority rules and other asymmetric rationing methods. Econometrica 68(3):643–684CrossRefGoogle Scholar
  34. Olmstead S (2010) The economics of managing scarce water resources. Rev Environ Econ Policy 4(2):179–198CrossRefGoogle Scholar
  35. O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2(4):345–371CrossRefGoogle Scholar
  36. Salman S (2007) The Helsinki Rules, the UN Watercourses Convention and the Berlin Rules: perspectives on international water law. Int J Water Resour Dev 23(4):625–640CrossRefGoogle Scholar
  37. Tanzeema S, Faisal I (2001) Sharing the Ganges: a critical analysis of the water sharing treaties. Water Policy 3(1):13–28CrossRefGoogle Scholar
  38. Thomson W (2001) On the axiomatic method and its recent applications to game theory and resource allocation. Soc Choice Welf 18(2):327–386CrossRefGoogle Scholar
  39. Thomson W (2003) Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45(3):249–297CrossRefGoogle Scholar
  40. Thomson W (2013) A characterization of a family of rules for the adjudication of conflicting claims. Games Econ Behav 82:157–168CrossRefGoogle Scholar
  41. Van den Brink R, Estévez-Fernández A, van der Laan G, Moes N (2011) Independence axioms for water allocation. Tinbergen Institute Discussion Paper 2011/128Google Scholar
  42. Van den Brink R, Estévez-Fernández A, van der Laan G, Moes N (2014) Independence of downstream and upstream benefits in river water allocation problems. Soc Choice Welf 43(1):173–194Google Scholar
  43. Van den Brink R, van der Laan G, Moes N (2012) Fair agreements for sharing international rivers with multiple springs and externalities. J Environ Econ Manag 63(3):388–403CrossRefGoogle Scholar
  44. Van den Brink R, van der Laan G, Vasil’ev V (2007) Component efficient solutions in line-graph games with applications. Econ Theory 33(2):349–364CrossRefGoogle Scholar
  45. Ward P, Beets W, Bouwer L, Aerts J, Renssen H (2010) Sensitivity of river discharge to ENSO. Geophys Res Lett 37(12):L12402CrossRefGoogle Scholar
  46. Wolf A (1999) Criteria for equitable allocations: the heart of international water conflict. Nat Resour Forum 23(1):3–30CrossRefGoogle Scholar
  47. Young P (1988) Distributive justice in taxation. J Econ Theory 43(2):321–335CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Spatial Economics and IVMVU University AmsterdamAmsterdamThe Netherlands
  2. 2.Tinbergen InstituteAmsterdamThe Netherlands
  3. 3.Department of Social SciencesWageningen UniversityWageningenThe Netherlands

Personalised recommendations