IDEAS home Printed from https://ideas.repec.org/a/spr/etbull/v8y2020i1d10.1007_s40505-019-00171-7.html
   My bibliography  Save this article

A generalization of Peleg’s representation theorem on constant-sum weighted majority games

Author

Listed:
  • Takayuki Oishi

    (Meisei University)

Abstract

We propose a variant of the nucleolus associated with distorted satisfaction of each coalition in TU games. This solution is referred to as the $$\alpha $$α-nucleolus in which $$\alpha $$α is a profile of distortion rates of satisfaction of all the coalitions. We apply the $$\alpha $$α-nucleolus to constant-sum weighted majority games. We show that under assumptions of distortions of satisfaction of winning coalitions the $$\alpha $$α-nucleolus is the unique normalized homogeneous representation of constant-sum weighted majority games which assigns a zero to each null player. As corollary of this result, we derive the well-known Peleg’s representation theorem.

Suggested Citation

  • Takayuki Oishi, 2020. "A generalization of Peleg’s representation theorem on constant-sum weighted majority games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 113-123, April.
    • Handle: RePEc:spr:etbull:v:8:y:2020:i:1:d:10.1007_s40505-019-00171-7
    DOI: 10.1007/s40505-019-00171-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40505-019-00171-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40505-019-00171-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    4. Dongshuang Hou & Panfei Sun & Genjiu Xu & Theo Driessen, 2018. "Compromise for the complaint: an optimization approach to the ENSC value and the CIS value," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(4), pages 571-579, April.
    5. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667, Elsevier.
    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. Montero, M.P., 2002. "Two-Stage Bargaining with Reversible Coalitions : The Case of Apex Games," Other publications TiSEM 7dba0283-bc13-4f2c-8f5e-5, Tilburg University, School of Economics and Management.
    2. J. Arin & V. Feltkamp & M. Montero, 2015. "A bargaining procedure leading to the serial rule in games with veto players," Annals of Operations Research, Springer, vol. 229(1), pages 41-66, June.
    3. Montero, Maria, 2002. "Non-cooperative bargaining in apex games and the kernel," Games and Economic Behavior, Elsevier, vol. 41(2), pages 309-321, November.
    4. Slikker, Marco & Norde, Henk, 2011. "The monoclus of a coalitional game," Games and Economic Behavior, Elsevier, vol. 71(2), pages 420-435, March.
    5. 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.
    6. Kidd, Martin P. & Borm, Peter, 2021. "On Determining Leading Coalitions in Supply Chains: Methodology and Application," Discussion Paper 2021-009, Tilburg University, Center for Economic Research.
    7. Hou, Dongshuang & Lardon, Aymeric, 2020. "An Optimization Characterization of the upper optimal complaint value," Economics Letters, Elsevier, vol. 186(C).
    8. Yair Tauman & Andriy Zapechelnyuk, 2010. "On (non-) monotonicity of cooperative solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 171-175, March.
    9. Slikker, M. & Norde, H.W., 2008. "The Monoclus of a Coalitional Game," Other publications TiSEM 8b2bae34-674a-4632-a64e-9, Tilburg University, School of Economics and Management.
    10. Reiner Wolff & Yavuz Karagök, 2012. "Consistent allocation of cabinet seats: the Swiss Magic Formula," Public Choice, Springer, vol. 150(3), pages 547-559, March.
    11. Wenzhong Li & Genjiu Xu & Hao Sun, 2020. "Maximizing the Minimal Satisfaction—Characterizations of Two Proportional Values," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    12. Theo Driessen & Cheng-Cheng Hu, 2013. "An axiomatization of the kernel for TU games through reduced game monotonicity and reduced dominance," Theory and Decision, Springer, vol. 74(1), pages 1-12, January.
    13. Emilio Calvo, 2021. "Redistribution of tax resources: a cooperative game theory approach," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(4), pages 633-686, December.
    14. Armando Gomes, "undated". "A Theory of Negotiations and Formation of Coalitions," Rodney L. White Center for Financial Research Working Papers 21-99, Wharton School Rodney L. White Center for Financial Research.
    15. Aleksei Y. Kondratev & Vladimir V. Mazalov, 2020. "Tournament solutions based on cooperative game theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 119-145, March.
    16. Panfei Sun & Dongshuang Hou & Hao Sun, 2022. "Optimization implementation of solution concepts for cooperative games with stochastic payoffs," Theory and Decision, Springer, vol. 93(4), pages 691-724, November.
    17. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    18. repec:has:discpr:1321 is not listed on IDEAS
    19. Mario Guajardo & Kurt Jörnsten & Mikael Rönnqvist, 2016. "Constructive and blocking power in collaborative transportation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 25-50, January.
    20. H. Andrew Michener & Daniel J. Myers, 1998. "Probabilistic Coalition Structure Theories," Journal of Conflict Resolution, Peace Science Society (International), vol. 42(6), pages 830-860, December.
    21. Maria Montero & Alex Possajennikov, 2021. "An Adaptive Model of Demand Adjustment in Weighted Majority Games," Games, MDPI, vol. 13(1), pages 1-17, December.

    More about this item

    Keywords

    Constant-sum weighted majority games; Homogeneous representation; $$alpha $$ α -Nucleolus; Distorted satisfaction; Peleg’s representation theorem;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    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:spr:etbull:v:8:y:2020:i:1:d:10.1007_s40505-019-00171-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.