IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-00633612.html
   My bibliography  Save this paper

A note on the monotonicity and superadditivity of TU cooperative games

Author

Listed:
  • Jean-François Caulier

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this note we make a comparison between the class of monotonic TU cooperative games and the class of superadditive TU cooperative games. We first provide the equivalence between a weakening of the class of su- peradditive TU games and zero-monotonic TU games. Then, we show that zero-monotonic TU games and monotonic TU games are different classes. Finally, we show under which restrictions the classes of superadditive and monotonic TU games can be related.

Suggested Citation

  • Jean-François Caulier, 2009. "A note on the monotonicity and superadditivity of TU cooperative games," Working Papers hal-00633612, HAL.
    • Handle: RePEc:hal:wpaper:hal-00633612
    Note: View the original document on HAL open archive server: https://hal.science/hal-00633612
    as

    Download full text from publisher

    File URL: https://hal.science/hal-00633612/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jean-Yves Jaffray & Philippe Mongin, 2003. "Constrained egalitarianism in a simple redistributive model," Theory and Decision, Springer, vol. 54(1), pages 33-56, February.
    2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    3. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, December.
    4. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, October.
    5. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.
    6. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    7. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean-François Caulier, 2009. "A note on the monotonicity and superadditivity of TU cooperative games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633612, HAL.
    2. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    3. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    4. Tianhang Lu & Han Xian & Qizhi Fang, 2023. "Approximate Core Allocations for Edge Cover Games," Papers 2308.11222, arXiv.org.
    5. Daphne Cornelisse & Thomas Rood & Mateusz Malinowski & Yoram Bachrach & Tal Kachman, 2022. "Neural Payoff Machines: Predicting Fair and Stable Payoff Allocations Among Team Members," Papers 2208.08798, arXiv.org.
    6. Michel Le Breton & Karine Van der Straeten, 2013. "Alliances électorales entre deux tours de scrutin. Le point de vue de la théorie des jeux coopératifs et une application aux élections régionales de mars 2010," Revue économique, Presses de Sciences-Po, vol. 64(2), pages 173-240.
    7. Westerink-Duijzer, L.E. & Schlicher, L.P.J. & Musegaas, M., 2019. "Fair allocations for cooperation problems in vaccination," Econometric Institute Research Papers EI2019-06, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. Routledge R. R., 2012. "On Communication and the Weak Sequential Core," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-22, September.
    9. M. Fiestras-Janeiro & Ignacio García-Jurado & Manuel Mosquera, 2011. "Cooperative games and cost allocation problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-22, July.
    10. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    11. Qizhi Fang & Bo Li & Xiaohan Shan & Xiaoming Sun, 2018. "Path cooperative games," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 211-229, July.
    12. Lotty E. Westerink‐Duijzer & Loe P. J. Schlicher & Marieke Musegaas, 2020. "Core Allocations for Cooperation Problems in Vaccination," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1720-1737, July.
    13. Hougaard, Jens Leth & Østerdal, Lars Peter, 2010. "Monotonicity of social welfare optima," Games and Economic Behavior, Elsevier, vol. 70(2), pages 392-402, November.
    14. Reiner Wolff & Yavuz Karagök, 2012. "Consistent allocation of cabinet seats: the Swiss Magic Formula," Public Choice, Springer, vol. 150(3), pages 547-559, March.
    15. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Duality and P-core," Working Papers CIE 136, Paderborn University, CIE Center for International Economics.
    16. Shoshana Anily, 2018. "Full characterization of the nonnegative core of some cooperative games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 303-316, June.
    17. Svetlana Tarashnina, 2011. "The simplified modified nucleolus of a cooperative TU-game," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 150-166, July.
    18. Shoshana Anily & Moshe Haviv, 2014. "Subadditive and Homogeneous of Degree One Games Are Totally Balanced," Operations Research, INFORMS, vol. 62(4), pages 788-793, August.
    19. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Efficiency and Duality," Working Papers CIE 138, Paderborn University, CIE Center for International Economics.
    20. Stefan Ambec & Yann Kervinio, 2016. "Cooperative decision-making for the provision of a locally undesirable facility," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 119-155, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00633612. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.