IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v64y2008i1p268-289.html
   My bibliography  Save this article

Strategic divide and choose

Author

Listed:
  • Nicolò, Antonio
  • Yu, Yan

Abstract

We consider the classic cake-division problem when the cake is a heterogeneous good represented by an interval in the real line. We provide a mechanism to implement, in an anonymous way, an envy-free and efficient allocation when agents have private information on their preferences. The mechanism is a multi-step sequential game form in which each agent at each step receives a morsel of the cake that is the intersection of what she asks for herself and what the other agent concedes to her.

Suggested Citation

  • Nicolò, Antonio & Yu, Yan, 2008. "Strategic divide and choose," Games and Economic Behavior, Elsevier, vol. 64(1), pages 268-289, September.
    • Handle: RePEc:eee:gamebe:v:64:y:2008:i:1:p:268-289
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(08)00027-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Barbanel, J. B. & Brams, S. J., 2001. "Cake Division with Minimal Cuts: Envy-Free Procedures for 3 Person, 4 Persons, and Beyond," Working Papers 01-07, C.V. Starr Center for Applied Economics, New York University.
    2. Edelman, Paul & Fishburn, Peter, 2001. "Fair division of indivisible items among people with similar preferences," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 327-347, May.
    3. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
    4. Weingast, Barry R. & Wittman, Donald, 2008. "The Oxford Handbook of Political Economy," OUP Catalogue, Oxford University Press, number 9780199548477, Decembrie.
    5. Steven J. Brams & Paul H. Edelman & Peter C. Fishburn, 2003. "Fair Division Of Indivisible Items," Theory and Decision, Springer, vol. 55(2), pages 147-180, September.
    6. William Thomson, 1996. "Concepts Of Implementation," The Japanese Economic Review, Japanese Economic Association, vol. 47(2), pages 133-143, June.
    7. Steven J. Brams & Peter C. Fishburn, 2000. "Fair division of indivisible items between two people with identical preferences: Envy-freeness, Pareto-optimality, and equity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 247-267.
    8. Maniquet, Francois & Sprumont, Yves, 2000. "On resource monotonicity in the fair division problem," Economics Letters, Elsevier, vol. 68(3), pages 299-302, September.
    9. Demko, Stephen & Hill, Theodore P., 1988. "Equitable distribution of indivisible objects," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 145-158, October.
    10. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    11. Vincent P. Crawford, 1977. "A Game of Fair Division," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 235-247.
    12. Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216.
    13. Crawford, V. P. & Heller, W. P., 1979. "Fair division with indivisible commodities," Journal of Economic Theory, Elsevier, vol. 21(1), pages 10-27, August.
    14. Thomson, W., 1991. "Resource-Monotonic Solutions to the Problem of Fair Divosion when Preferences are Single-Peaked ," RCER Working Papers 301, University of Rochester - Center for Economic Research (RCER).
    15. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
    16. Thomson, William, 2005. "Divide-and-permute," Games and Economic Behavior, Elsevier, vol. 52(1), pages 186-200, July.
    17. Barbanel, Julius B. & Brams, Steven J., 2004. "Cake division with minimal cuts: envy-free procedures for three persons, four persons, and beyond," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 251-269, November.
    18. Olivier Compte & Philippe Jehiel, 2004. "Gradualism in Bargaining and Contribution Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(4), pages 975-1000.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Josué Ortega & Erel Segal-Halevi, 2022. "Obvious manipulations in cake-cutting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 969-988, November.
    2. Bhardwaj, Bhavook & Kumar, Rajnish & Ortega, Josué, 2020. "Fairness and efficiency in cake-cutting with single-peaked preferences," Economics Letters, Elsevier, vol. 190(C).
    3. Segal-Halevi, Erel & Nitzan, Shmuel & Hassidim, Avinatan & Aumann, Yonatan, 2017. "Fair and square: Cake-cutting in two dimensions," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 1-28.
    4. Erel Segal-Halevi & Shmuel Nitzan & Avinatan Hassidim & Yonatan Aumann, 2020. "Envy-Free Division of Land," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 896-922, August.
    5. Kyropoulou, Maria & Ortega, Josué & Segal-Halevi, Erel, 2022. "Fair cake-cutting in practice," Games and Economic Behavior, Elsevier, vol. 133(C), pages 28-49.
    6. Eleonora Cresto & Diego Tajer, 2022. "Fair cake-cutting for imitative agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(4), pages 801-833, May.
    7. Simina Br^anzei & MohammadTaghi Hajiaghayi & Reed Phillips & Suho Shin & Kun Wang, 2024. "Dueling Over Dessert, Mastering the Art of Repeated Cake Cutting," Papers 2402.08547, arXiv.org, revised Feb 2024.
    8. Nicolò, Antonio & Velez, Rodrigo A., 2017. "Divide and compromise," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 100-110.
    9. Erel Segal-Halevi & Shmuel Nitzan, 2014. "Cake Cutting – Fair and Square," Working Papers 2014-01, Bar-Ilan University, Department of Economics.
    10. Jamie Tucker-Foltz & Richard Zeckhauser, 2022. "Playing Divide-and-Choose Given Uncertain Preferences," Papers 2207.03076, arXiv.org.

    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. 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.
    2. Steven Brams & D. Kilgour & Christian Klamler, 2012. "The undercut procedure: an algorithm for the envy-free division of indivisible items," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 615-631, July.
    3. RAMAEKERS, Eve, 2010. "Fair allocation of indivisible goods among two agents," LIDAM Discussion Papers CORE 2010087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Eve Ramaekers, 2013. "Fair allocation of indivisible goods: the two-agent case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 359-380, July.
    5. Edelman, Paul & Fishburn, Peter, 2001. "Fair division of indivisible items among people with similar preferences," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 327-347, May.
    6. Brown, Alexander L. & Velez, Rodrigo A., 2016. "The costs and benefits of symmetry in common-ownership allocation problems," Games and Economic Behavior, Elsevier, vol. 96(C), pages 115-131.
    7. Marcus Berliant & Karl Dunz & William Thomson, 2000. "On the Fairness Literature: Comment," Southern Economic Journal, John Wiley & Sons, vol. 67(2), pages 479-484, October.
    8. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with voluntary participation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 371-406, March.
    9. Dall'Aglio, Marco & Mosca, Raffaele, 2007. "How to allocate hard candies fairly," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 218-237, December.
    10. R?bert F. Veszteg, 2004. "Fairness under Uncertainty with Indivisibilities," UFAE and IAE Working Papers 613.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    11. Brams, Steven J. & Kaplan, Todd R., 2017. "Dividing the indivisible: procedures for allocation cabinet ministries to political parties in a parlamentary system," Center for Mathematical Economics Working Papers 340, Center for Mathematical Economics, Bielefeld University.
    12. Haris Aziz, 2016. "A generalization of the AL method for fair allocation of indivisible objects," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 307-324, October.
    13. Matt Van Essen, 2013. "An Equilibrium Analysis of Knaster’s Fair Division Procedure," Games, MDPI, vol. 4(1), pages 1-17, January.
    14. Kranich, Laurence, 1995. "Equity and economic theory: reflections on methodology and scope," UC3M Working papers. Economics 3919, Universidad Carlos III de Madrid. Departamento de Economía.
    15. Marco LiCalzi & Antonio Nicolò, 2009. "Efficient egalitarian equivalent allocations over a single good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 27-45, July.
    16. Thomson, William, 2005. "Divide-and-permute," Games and Economic Behavior, Elsevier, vol. 52(1), pages 186-200, July.
    17. Pablo Amorós, 2002. "Single-peaked preferences with several commodities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(1), pages 57-67.
    18. Johannes Hörner & Andrzej Skrzypacz, 2016. "Selling Information," Journal of Political Economy, University of Chicago Press, vol. 124(6), pages 1515-1562.
    19. Dino Gerardi & Lucas Maestri, 2013. "Bargaining over a Divisible Good in the Market for Lemons," Carlo Alberto Notebooks 312, Collegio Carlo Alberto.
    20. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.

    More about this item

    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:eee:gamebe:v:64:y:2008:i:1:p:268-289. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.