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Allocating the costs of cleaning a river: expected responsibility versus median responsibility

Author

Listed:
  • Jorge Alcalde-Unzu

    (Public University of Navarre)

  • María Gómez-Rúa

    (University of Vigo)

  • Elena Molis

    (University of Granada)

Abstract

We consider the problem of cleaning a transboundary river, proposed by Ni and Wang (Games Econ Behav 60:176–186, 2007). A river is modeled as a segment divided into subsegments, each occupied by one region, from upstream to downstream. The waste is transferred from one region to the next at some rate. Since this transfer rate may be unknown, the social planner could have uncertainty over each region’s responsibility. Two natural candidates to distribute the costs in this setting would be the method that assigns to each region its expected responsibility and the one that assigns to each region its median responsibility. We show that the latter is equivalent to the Upstream Responsibility method (Alcalde-Unzu et al. in Games Econ Behav 90:134–150, 2015) and the former is a new method that we call Expected Responsibility. We compare both solutions and analyze them in terms of a new property of monotonicity.

Suggested Citation

  • Jorge Alcalde-Unzu & María Gómez-Rúa & Elena Molis, 2021. "Allocating the costs of cleaning a river: expected responsibility versus median responsibility," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 185-214, March.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:1:d:10.1007_s00182-020-00746-w
    DOI: 10.1007/s00182-020-00746-w
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    References listed on IDEAS

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    4. 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.
    5. 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.
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    8. 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.
    9. Wang, Yuntong, 2011. "Trading water along a river," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 124-130, March.
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    12. Panfei Sun & Dongshuang Hou & Hao Sun, 2019. "Responsibility and sharing the cost of cleaning a polluted river," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 143-156, February.
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    Cited by:

    1. Jens Gudmundsson & Jens Leth Hougaard, 2021. "River pollution abatement: Decentralized solutions and smart contracts," IFRO Working Paper 2021/07, University of Copenhagen, Department of Food and Resource Economics, revised Oct 2021.
    2. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2023. "A linear model for freight transportation," MPRA Paper 119301, University Library of Munich, Germany.
    3. Acosta-Vega, Rick K. & Algaba, Encarnación & Sánchez-Soriano, Joaquín, 2023. "Design of water quality policies based on proportionality in multi-issue problems with crossed claims," European Journal of Operational Research, Elsevier, vol. 311(2), pages 777-788.
    4. Durga Prasad Panday & Rakesh Khosa & Rathinasamy Maheswaran & K. Ravikumar & Ankit Agarwal, 2021. "Game theoretic-based modelling of Krishna waters dispute: equilibrium solutions by hypergame analysis," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(6), pages 1-11, June.
    5. Durga Prasad Panday & Rakesh Khosa & Rathinasamy Maheswaran & K. Ravikumar & Ankit Agarwal, 2021. "Game-theoretic-based modelling of Krishna waters dispute: equilibrium solutions by Metagame Analysis," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(5), pages 1-12, May.

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    More about this item

    Keywords

    Cost allocation; Waste river; Expected responsibility; Median responsibility; Monotonicity;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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