# Composition properties in the river claims problem

- 265 Downloads
- 5 Citations

## Abstract

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.

## Keywords

River claims problem Sharing rule Harmon Doctrine Composition axioms Water allocation## JEL Classification

D63 C71 Q25## Notes

### Acknowledgments

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.

## References

- Ambec S, Dinar A, McKinney D (2013) Water sharing agreements sustainable to reduced flows. J Environ Econ Manag 66(3):639–655CrossRefGoogle Scholar
- Ambec S, Ehlers L (2008) Sharing a river among satiable agents. Games Econ Behav 64(1):35–50CrossRefGoogle Scholar
- Ambec S, Sprumont Y (2002) Sharing a river. J Econ Theory 107(2):453–462CrossRefGoogle Scholar
- Ansink E, Gengenbach M, Weikard H-P (2012). River sharing and water trade. FEEM Working Paper 017.2012Google Scholar
- Ansink E, Houba H (2013). Sustainable agreements on stochastic river flow. Tinbergen Institute Discussion Paper 2013/182Google Scholar
- Ansink E, Ruijs A (2008) Climate change and the stability of water allocation agreements. Environ Resour Econ 41(2):249–266CrossRefGoogle Scholar
- Ansink E, Weikard H-P (2009) Contested water rights. Eur J Polit Econ 25(2):247–260CrossRefGoogle Scholar
- Ansink E, Weikard H-P (2012) Sequential sharing rules for river sharing problems. Soc Choice Welf 38(2):187–210CrossRefGoogle Scholar
- 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
- Bates B, Kundzewicz Z, Wu S, Palutikof J (2008) Climate change and water. Intergovernmental panel on climate change, Technical Paper VIGoogle Scholar
- 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
- Béal S, Ghintran A, Rémila E, Solal P (2013) The river sharing problem: a survey. Int Game Theory Rev 15(3):1340016CrossRefGoogle Scholar
- 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
- Chun Y (1988) The proportional solution for rights problems. Math Soc Sci 15(3):231–246CrossRefGoogle Scholar
- Daoudy M (2008) Hydro-hegemony and international water law: laying claims to water rights. Water Policy 10(S2):89–102CrossRefGoogle Scholar
- 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
- Demange G (2004) On group stability in hierarchies and networks. J Polit Econ 112(4):754–778CrossRefGoogle Scholar
- Dettinger M, Diaz H (2000) Global characteristics of stream flow seasonality and variability. J Hydrometeorol 1(4):289–310CrossRefGoogle Scholar
- 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
- Dinar A, Ratner A, Yaron D (1992) Evaluating cooperative game theory in water resources. Theory Decis 32(1):1–20CrossRefGoogle Scholar
- Herrero C, Maschler M, Villar A (1999) Individual rights and collective responsibility: the rights-egalitarian solution. Math Soc Sci 37(1):59–77CrossRefGoogle Scholar
- Houba H (2008) Computing alternating offers and water prices in bilateral river basin management. Int Game Theory Rev 10(3):257–278CrossRefGoogle Scholar
- İlkılıç R (2011) Networks of common property resources. Econ Theory 47(1):105–134CrossRefGoogle Scholar
- İlkılıç R, Kayı C (2014) Allocation rules on networks. Soc Choice Welf 43(4):877–892Google Scholar
- Khmelnitskaya A (2010) Values for rooted-tree and sink-tree digraph games and sharing a river. Theory Decis 69(4):657–669CrossRefGoogle Scholar
- Kilgour D, Dinar A (2001) Flexible water sharing within an international river basin. Environ Resour Econ 18(1):43–60CrossRefGoogle Scholar
- Krzysztofowicz R (2001) The case for probabilistic forecasting in hydrology. J Hydrol 249(1–4):2–9CrossRefGoogle Scholar
- McCaffrey S (2007) The law of international water courses. Oxford University Press, OxfordGoogle Scholar
- 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
- Montanari A, Grossi G (2008) Estimating the uncertainty of hydrological forecasts: a statistical approach. Water Resour Res 44(12):W00B08CrossRefGoogle Scholar
- Moreno-Ternero J (2011) A coalitional procedure leading to a family of bankruptcy rules. Oper Res Lett 39(1):1–3CrossRefGoogle Scholar
- Moulin H (1987) Equal or proportional division of a surplus, and other methods. Int J Game Theory 16(3):161–186CrossRefGoogle Scholar
- Moulin H (2000) Priority rules and other asymmetric rationing methods. Econometrica 68(3):643–684CrossRefGoogle Scholar
- Olmstead S (2010) The economics of managing scarce water resources. Rev Environ Econ Policy 4(2):179–198CrossRefGoogle Scholar
- O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2(4):345–371CrossRefGoogle Scholar
- 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
- Tanzeema S, Faisal I (2001) Sharing the Ganges: a critical analysis of the water sharing treaties. Water Policy 3(1):13–28CrossRefGoogle Scholar
- 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
- Thomson W (2003) Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45(3):249–297CrossRefGoogle Scholar
- Thomson W (2013) A characterization of a family of rules for the adjudication of conflicting claims. Games Econ Behav 82:157–168CrossRefGoogle Scholar
- 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
- 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
- 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
- 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
- Ward P, Beets W, Bouwer L, Aerts J, Renssen H (2010) Sensitivity of river discharge to ENSO. Geophys Res Lett 37(12):L12402CrossRefGoogle Scholar
- Wolf A (1999) Criteria for equitable allocations: the heart of international water conflict. Nat Resour Forum 23(1):3–30CrossRefGoogle Scholar
- Young P (1988) Distributive justice in taxation. J Econ Theory 43(2):321–335CrossRefGoogle Scholar