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Constrained core solutions for totally positive games with ordered players

Author

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  • René Brink
  • Gerard Laan
  • Valeri Vasil’ev

Abstract

In many applications of cooperative game theory to economic allocation problems, such as river-, polluted river- and sequencing games, the game is totally positive (i.e., all dividends are nonnegative), and there is some ordering on the set of the players. A totally positive game has a nonempty core. In this paper we introduce constrained core solutions for totally positive games with ordered players which assign to every such a game a subset of the core. These solutions are based on the distribution of dividends taking into account the hierarchical ordering of the players. The Harsanyi constrained core of a totally positive game with ordered players is a subset of the core of the game and contains the Shapley value. For special orderings it coincides with the core or the Shapley value. The selectope constrained core is defined for acyclic orderings and yields a subset of the Harsanyi constrained core. We provide a characterization for both solutions. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • René Brink & Gerard Laan & Valeri Vasil’ev, 2014. "Constrained core solutions for totally positive games with ordered players," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 351-368, May.
    • Handle: RePEc:spr:jogath:v:43:y:2014:i:2:p:351-368
    DOI: 10.1007/s00182-013-0382-x
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    Cited by:

    1. M. Álvarez-Mozos & R. Brink & G. Laan & O. Tejada, 2017. "From hierarchies to levels: new solutions for games with hierarchical structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1089-1113, November.
    2. Yokote, Koji & Funaki, Yukihiko & Kamijo, Yoshio, 2016. "A new basis and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 21-24.
    3. Demuynck, Thomas & Rock, Bram De & Ginsburgh, Victor, 2016. "The transfer paradox in welfare space," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 1-4.
    4. Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2022. "The priority value for cooperative games with a priority structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 431-450, June.
    5. Manfred Besner, 2020. "Parallel axiomatizations of weighted and multiweighted Shapley values, random order values, and the Harsanyi set," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 193-212, June.
    6. Gustavo Berganti~nos & Juan D. Moreno-Ternero, 2023. "Revenue sharing at music streaming platforms," Papers 2310.11861, arXiv.org.
    7. Manfred Besner, 2020. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 851-873, September.
    8. Besner, Manfred, 2019. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi payoff," MPRA Paper 92247, University Library of Munich, Germany.
    9. Mikel Álvarez-Mozos & René van den Brink & Gerard van der Laan & Oriol Tejada, 2015. "From Hierarchies to Levels: New Solutions for Games," Tinbergen Institute Discussion Papers 15-072/II, Tinbergen Institute.
    10. Sylvain Béal & Sylvain Ferrières & Adriana Navarro‐Ramos & Philippe Solal, 2023. "Axiomatic characterizations of the family of Weighted priority values," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(4), pages 787-816, December.
    11. Pierre Dehez, 2017. "On Harsanyi Dividends and Asymmetric Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-36, September.
    12. 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.
    13. van den Brink, René & He, Simin & Huang, Jia-Ping, 2018. "Polluted river problems and games with a permission structure," Games and Economic Behavior, Elsevier, vol. 108(C), pages 182-205.

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    More about this item

    Keywords

    Totally positive TU-game; Digraph; Harsanyi dividends; Core; Shapley value; Harsanyi set; Selectope; Polluted river games; C71 (Cooperative games);
    All these keywords.

    JEL classification:

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

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