IDEAS home Printed from https://ideas.repec.org/p/fem/femwpa/2011.88.html
   My bibliography  Save this paper

Finding Maxmin Allocations in Cooperative and Competitive Fair Division

Author

Listed:
  • Marco Dall'Aglio

    (LUISS University Rome, Italy)

  • Camilla Di Luca

    ("G. D'Annunzio" University Pescara, Italy)

Abstract

We consider upper and lower bounds for maxmin allocations of a completely divisible good in both competitive and cooperative strategic contexts. We then derive a subgradient algorithm to compute the exact value up to any fixed degree of precision.

Suggested Citation

  • Marco Dall'Aglio & Camilla Di Luca, 2011. "Finding Maxmin Allocations in Cooperative and Competitive Fair Division," Working Papers 2011.88, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2011.88
    as

    Download full text from publisher

    File URL: https://feem-media.s3.eu-central-1.amazonaws.com/wp-content/uploads/NDL2011-088.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    2. Barbanel, Julius, 1999. "Partition ratios, Pareto optimal cake division, and related notions," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 401-428, December.
    3. Legut, Jerzy, 1990. "On totally balanced games arising from cooperation in fair division," Games and Economic Behavior, Elsevier, vol. 2(1), pages 47-60, March.
    4. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446, October.
    5. Legut, J. & Potters, J.A.M. & Tijs, S.H., 1994. "Economies with land : A game theoretical approach," Other publications TiSEM 37ff121d-d79c-4e41-a06a-9, Tilburg University, School of Economics and Management.
    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. Marco Dall’Aglio & Camilla Luca, 2014. "Finding maxmin allocations in cooperative and competitive fair division," Annals of Operations Research, Springer, vol. 223(1), pages 121-136, December.
    2. Dall'Aglio, M. & Brânzei, R. & Tijs, S.H., 2008. "Cooperation in Dividing the Cake," Discussion Paper 2008-101, Tilburg University, Center for Economic Research.
    3. Marco Mariotii, 1996. "Fair bargains: distributive justice and Nash Bargaining Theory," Game Theory and Information 9611003, University Library of Munich, Germany, revised 06 Dec 1996.
    4. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," 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 2, chapter 21, pages 393-506, Elsevier.
    5. Chambers, Christopher P., 2005. "Allocation rules for land division," Journal of Economic Theory, Elsevier, vol. 121(2), pages 236-258, April.
    6. Dall'Aglio, M. & Brânzei, R. & Tijs, S.H., 2008. "Cooperation in Dividing the Cake," Other publications TiSEM cc8598f8-1be5-46d7-b91d-1, Tilburg University, School of Economics and Management.
    7. Berentsen, Aleksander & Huber, Samuel & Marchesiani, Alessandro, 2016. "The societal benefit of a financial transaction tax," European Economic Review, Elsevier, vol. 89(C), pages 303-323.
    8. Z. Landau & O. Reid & I. Yershov, 2009. "A fair division solution to the problem of redistricting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 479-492, March.
    9. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2022. "Monotonicity in sharing the revenues from broadcasting sports leagues," European Journal of Operational Research, Elsevier, vol. 297(1), pages 338-346.
    10. Yoshihara, Naoki, 2003. "Characterizations of bargaining solutions in production economies with unequal skills," Journal of Economic Theory, Elsevier, vol. 108(2), pages 256-285, February.
    11. 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.
    12. Radzvilas, Mantas, 2016. "Hypothetical Bargaining and the Equilibrium Selection Problem in Non-Cooperative Games," MPRA Paper 70248, University Library of Munich, Germany.
    13. Wulf Gaertner & Richard Bradley & Yongsheng Xu & Lars Schwettmann, 2019. "Against the proportionality principle: Experimental findings on bargaining over losses," PLOS ONE, Public Library of Science, vol. 14(7), pages 1-18, July.
    14. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    15. Lea Melnikovová, 2017. "Can Game Theory Help to Mitigate Water Conflicts in the Syrdarya Basin?," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 65(4), pages 1393-1401.
    16. Berentsen, Aleksander & McBride, Michael & Rocheteau, Guillaume, 2017. "Limelight on dark markets: Theory and experimental evidence on liquidity and information," Journal of Economic Dynamics and Control, Elsevier, vol. 75(C), pages 70-90.
    17. Csóka Péter & Pintér Miklós, 2016. "On the Impossibility of Fair Risk Allocation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(1), pages 143-158, January.
    18. Daniele Cassese & Paolo Pin, 2018. "Decentralized Pure Exchange Processes on Networks," Papers 1803.08836, arXiv.org, revised Mar 2022.
    19. Lorenzo Bastianello & Marco LiCalzi, 2015. "Target-based solutions for Nash bargaining," Working Papers 5, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    20. Jens Leth Hougaard & Mich Tvede, 2010. "n-Person Nonconvex Bargaining: Efficient Proportional Solutions," MSAP Working Paper Series 02_2010, University of Copenhagen, Department of Food and Resource Economics.

    More about this item

    Keywords

    Fair Division; Maxmin Allocation; Kalai Bargaining Solution; Cooperative Game Theory;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:fem:femwpa:2011.88. 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: Alberto Prina Cerai (email available below). General contact details of provider: https://edirc.repec.org/data/feemmit.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.