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The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations

Author

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  • Sylvain Béal

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Amandine Ghintran

    (EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie - Université de Lille, Sciences et Technologies - Université de Lille, Sciences Humaines et Sociales - PRES Université Lille Nord de France - Université de Lille, Droit et Santé)

  • Eric Rémila

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Philippe Solal

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We introduce a new allocation rule, called the sequential equal surplus division for rooted forest TU-games. We provide two axiomatic characterizations for this allocation rule. The first one uses the classical property of component efficiency plus an edge deletion property. The second characterization uses standardness, an edge deletion property applied to specific rooted trees, a consistency property, and an amalgamation property. We also provide an extension of the sequential equal surplus division applied to the problem of sharing a river with bifurcations.
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Suggested Citation

  • Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Post-Print halshs-01212167, HAL.
    • Handle: RePEc:hal:journl:halshs-01212167
    DOI: 10.1007/s11238-014-9463-y
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    1. Herings, P. Jean-Jacques & van der Laan, Gerard & Talman, Dolf, 2007. "The socially stable core in structured transferable utility games," Games and Economic Behavior, Elsevier, vol. 59(1), pages 85-104, April.
    2. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    3. M. J. Albizuri, 2001. "An axiomatization of the modified Banzhaf Coleman index," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 167-176.
    4. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    5. Khmelnitskaya, Anna & Talman, Dolf, 2014. "Tree, web and average web values for cycle-free directed graph games," European Journal of Operational Research, Elsevier, vol. 235(1), pages 233-246.
    6. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
    7. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Rooted-tree solutions for tree games," European Journal of Operational Research, Elsevier, vol. 203(2), pages 404-408, June.
    8. van den Brink, René, 2012. "Efficiency and collusion neutrality in cooperative games and networks," Games and Economic Behavior, Elsevier, vol. 76(1), pages 344-348.
    9. 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 1-19.
    10. René Brink & Gerard Laan & Valeri Vasil’ev, 2007. "Component efficient solutions in line-graph games with applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 349-364, November.
    11. René Brink, 2008. "Vertical wage differences in hierarchically structured firms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 225-243, February.
    12. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    13. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
    14. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Weighted component fairness for forest games," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 144-151.
    15. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Other publications TiSEM cd695be5-0f54-4548-a952-2, Tilburg University, School of Economics and Management.
    16. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    17. P. Herings & Gerard Laan & Dolf Talman, 2007. "Socially Structured Games," Theory and Decision, Springer, vol. 62(1), pages 1-29, February.
    18. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Fairness and fairness for neighbors: The difference between the Myerson value and component-wise egalitarian solutions," Economics Letters, Elsevier, vol. 117(1), pages 263-267.
    19. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    20. Anna Khmelnitskaya, 2010. "Values for rooted-tree and sink-tree digraph games and sharing a river," Theory and Decision, Springer, vol. 69(4), pages 657-669, October.
    21. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    22. M. Albizuri & Jesus Aurrekoetxea, 2006. "Coalition Configurations and the Banzhaf Index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 571-596, June.
    23. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
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    Cited by:

    1. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "Axiomatization of an allocation rule for ordered tree TU-games," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 132-140.
    2. Sylvain Béal & Eric Rémila & Philippe Solal, 2017. "A strategic implementation of the sequential equal surplus division rule for digraph cooperative games," Annals of Operations Research, Springer, vol. 253(1), pages 43-59, June.
    3. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, March.
    4. Dongshuang Hou & Aymeric Lardon & Panfei Sun & Genjiu Xu, 2019. "Sharing a Polluted River under Waste Flow Control," GREDEG Working Papers 2019-23, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    5. 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.
    6. Philippe Solal & Sylvain Béal & Sylvain Ferrières & Eric Rémila, 2017. "Axiomatic and bargaining foundation of an allocation rule for ordered tree TU-games," Post-Print halshs-01644811, HAL.
    7. Gudmundsson, Jens & Hougaard, Jens Leth & Ko, Chiu Yu, 2019. "Decentralized mechanisms for river sharing," Journal of Environmental Economics and Management, Elsevier, vol. 94(C), pages 67-81.

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    More about this item

    Keywords

    River TU-game; Sequential Equal Surplus Division; Water allocation; Standard solution; Consistency; Fairness; Amalgamation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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