IDEAS home Printed from https://ideas.repec.org/p/hig/wpaper/127-ec-2016.html
   My bibliography  Save this paper

An Extension of a Class of Cost Sharing Methods to the Solutions of the Class of Two-Person Cooperative Games

Author

Listed:
  • Elena Yanovskaya

    (National Research University Higher School of Economics)

Abstract

Two-person games and cost/surplus sharing problems are worth for studying because they are the base for their extending to the classes of such problems with variable population with the help of very powerful consistency properties. In the paper a family of cost-sharing methods for cost sharing problems with two agents [Moulin 2000] is extended to a class of solutions for two-person cooperative games that are larger than both cost-sharing and surplus-sharing problems, since cooperative games have no no restrictions on positivity of costs and surpluses. The tool of the extension is a new invariance axiom -- self covariance -- that can be applied both to cost-sharing methods and to cooperative game solutions. In particular, this axiom replaces the Lower composition axiom not applicable to methods for profit sharing problems

Suggested Citation

  • Elena Yanovskaya, 2016. "An Extension of a Class of Cost Sharing Methods to the Solutions of the Class of Two-Person Cooperative Games," HSE Working papers WP BRP 127/EC/2016, National Research University Higher School of Economics.
    • Handle: RePEc:hig:wpaper:127/ec/2016
    as

    Download full text from publisher

    File URL: https://www.hse.ru/data/2016/03/21/1128192791/127EC2016.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Elena B.Yanovskaya, 2014. "Self-Covariant Solutions To Cooperative Games With Transferable Utilities," HSE Working papers WP BRP 85/EC/2014, National Research University Higher School of Economics.
    2. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    3. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    4. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 153-169.
    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. Emin Karagözoğlu, 2014. "A noncooperative approach to bankruptcy problems with an endogenous estate," Annals of Operations Research, Springer, vol. 217(1), pages 299-318, June.
    2. Peter Knudsen & Lars Østerdal, 2012. "Merging and splitting in cooperative games: some (im)possibility results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 763-774, November.
    3. Cano Berlanga, Sebastian & Giménez Gómez, José M. (José Manuel) & Vilella Bach, Misericòrdia, 2015. "Enjoying cooperative games: The R package GameTheory," Working Papers 2072/247653, Universitat Rovira i Virgili, Department of Economics.
    4. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    5. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
    6. Juan D Moreno-Ternero & John E Roemer, 2006. "Impartiality, Priority, and Solidarity in the Theory of Justice," Econometrica, Econometric Society, vol. 74(5), pages 1419-1427, September.
    7. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," Discussion Papers 10-16, University of Copenhagen. Department of Economics.
    8. Sanchez-Soriano, Joaquin, 2021. "Families of sequential priority rules and random arrival rules with withdrawal limits," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 136-148.
    9. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 107-114.
    10. Alfredo Valencia-Toledo & Juan Vidal-Puga, 2020. "Reassignment-proof rules for land rental problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 173-193, March.
    11. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    12. Boonen, Tim J., 2019. "Equilibrium recoveries in insurance markets with limited liability," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 38-45.
    13. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 791-807, November.
    14. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    15. Biung-Ghi Ju & Juan Moreno-Ternero, 2011. "Progressive and merging-proof taxation," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 43-62, February.
    16. Jaume García-Segarra & Miguel Ginés-Vilar, 2023. "Additive adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 93-116, March.
    17. Hervé Moulin & Jay Sethuraman, 2013. "The Bipartite Rationing Problem," Operations Research, INFORMS, vol. 61(5), pages 1087-1100, October.
    18. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
    19. Thierry Marchant, 2008. "Scale invariance and similar invariance conditions for bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 693-707, December.
    20. Carmen Herrero & Juan Moreno-Ternero & Giovanni Ponti, 2010. "On the adjudication of conflicting claims: an experimental study," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(1), pages 145-179, January.

    More about this item

    Keywords

    cooperative game with transferable utilities; cost/surplus sharing method; self-covariance; solution;
    All these keywords.

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hig:wpaper:127/ec/2016. 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: Shamil Abdulaev or Shamil Abdulaev (email available below). General contact details of provider: https://edirc.repec.org/data/hsecoru.html .

    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.