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Fair Agreements for Sharing International Rivers with Multiple Springs and Externalities

Author

Listed:
  • 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.

Suggested Citation

  • Rene van den Brink & Gerard van der Laan & Nigel Moes, 2010. "Fair Agreements for Sharing International Rivers with Multiple Springs and Externalities," Tinbergen Institute Discussion Papers 10-096/1, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20100096
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Houba, Harold & van der Laan, Gerard & Zeng, Yuyu, 2014. "Asymmetric Nash Solutions in the River Sharing Problem," Strategic Behavior and the Environment, now publishers, vol. 4(4), pages 321-360, December.
    2. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Weighted component fairness for forest games," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 144-151.
    3. René van den Brink & Simin He & Jia-Ping Huang, 2015. "Polluted River Problems and Games with a Permission Structure," Tinbergen Institute Discussion Papers 15-108/II, Tinbergen Institute.
    4. Takayuki Oishi, 2018. "Legal and Political Agreements for Sharing International Rivers with Water Shortage," Working Papers 39, Meisei University, School of Economics.
    5. Erik Ansink & Michael Gengenbach & Hans-Peter Weikard, 2012. "River Sharing and Water Trade," Working Papers 2012.17, Fondazione Eni Enrico Mattei.
    6. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2013. "A strategic implementation of the Average Tree solution for cycle-free graph games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2737-2748.
    7. 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.
    8. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "The sequential equal surplus division for sharing a river," MPRA Paper 37346, University Library of Munich, Germany.
    9. Li, Zhi & Zhang, Xin & Xu, Wenchao, 2018. "Water Transactions along a River: A Multilateral Bargaining Experiment with a Veto Player," 2018 Annual Meeting, August 5-7, Washington, D.C. 274048, Agricultural and Applied Economics Association.
    10. Grundel, S. & Borm, P.E.M. & Hamers, H.J.M., 2013. "Resource Allocation Problems with Concave Reward Functions," Discussion Paper 2013-070, Tilburg University, Center for Economic Research.
    11. 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.
    12. Erik Ansink & Hans-Peter Weikard, 2015. "Composition properties in the river claims problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 807-831, April.
    13. 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;The Society for Social Choice and Welfare, vol. 43(1), pages 173-194, June.
    14. Ansink, Erik & Houba, Harold, 2016. "Sustainable agreements on stochastic river flow," Resource and Energy Economics, Elsevier, vol. 44(C), pages 92-117.
    15. Khmelnitskaya, A. & van der Laan, G. & Talman, Dolf, 2016. "Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games," Discussion Paper 2016-035, Tilburg University, Center for Economic Research.
    16. Encarnacion Algaba & René van den Brink & Chris Dietz, 2015. "Power Measures and Solutions for Games under Precedence Constraints," Tinbergen Institute Discussion Papers 15-007/II, Tinbergen Institute.
    17. René Brink & Gerard Laan & Nigel Moes, 2015. "Values for transferable utility games with coalition and graph structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 77-99, April.
    18. Alcalde-Unzu, Jorge & Gómez-Rúa, María & Molis, Elena, 2015. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Games and Economic Behavior, Elsevier, vol. 90(C), pages 134-150.
    19. 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.
    20. 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.
    21. Sarina Steinmann und Ralph Winkler, 2015. "Sharing a River with Downstream Externalities," Diskussionsschriften dp1508, Universitaet Bern, Departement Volkswirtschaft.
    22. Harold Houba & Gerard Laan & Yuyu Zeng, 2015. "International Environmental Agreements for River Sharing Problems," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 62(4), pages 855-872, December.
    23. Erik Ansink & Harold Houba, 2014. "The Economics of Transboundary River Management," Tinbergen Institute Discussion Papers 14-132/VIII, Tinbergen Institute.
    24. Jorge Alcalde-Unzu & Maria Gomez-Rua & Elena Molis, 2018. "Allocating the costs of cleaning a river; estimating responsibilities versus incentive compatibility," ThE Papers 18/02, Department of Economic Theory and Economic History of the University of Granada..
    25. repec:eee:gamebe:v:108:y:2018:i:c:p:182-205 is not listed on IDEAS

    More about this item

    Keywords

    water allocation; river game; externality; core; hierarchical outcome;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • H23 - Public Economics - - Taxation, Subsidies, and Revenue - - - Externalities; Redistributive Effects; Environmental Taxes and Subsidies

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