IDEAS home Printed from https://ideas.repec.org/a/ucp/jpolec/v109y2001i2p418-443.html
   My bibliography  Save this article

Competitive Fair Division

Author

Listed:
  • Steven J. Brams
  • D. Marc Kilgour

Abstract

Several indivisible goods are to be divided among two or more players, whose bids for the goods determine their prices. An equitable assignment of the goods at competitive prices is given by a fair-division procedure, called the Gap Procedure, that ensures (1) nonnegative prices that never exceed the bid of the player receiving the good; (2) Pareto optimality, though coupled with possible envy; (3) monotonicity, such that higher bids never hurt in obtaining a good; (4) sincere bids that preclude negative utility; and (5) prices that are partially independent of the amounts bid (as in a Vickrey auction). A variety of applications are discussed.

Suggested Citation

  • Steven J. Brams & D. Marc Kilgour, 2001. "Competitive Fair Division," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 418-443, April.
    • Handle: RePEc:ucp:jpolec:v:109:y:2001:i:2:p:418-443
    DOI: 10.1086/319550
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1086/319550
    File Function: main text
    Download Restriction: Access to the online full text or PDF requires a subscription.
    File URL: https://libkey.io/10.1086/319550?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. Steven J. Brams & D. Marc Kilgour, 2001. "Competitive Fair Division," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 418-443, April.
    2. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    3. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
    4. Flip Klijn, 2000. "An algorithm for envy-free allocations in an economy with indivisible objects and money," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 201-215.
    5. Anna, Petrenko, 2016. "Мaркування готової продукції як складова частина інформаційного забезпечення маркетингової діяльності підприємств овочепродуктового підкомплексу," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 2(1), March.
    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. Azacis, Helmuts, 2008. "Double implementation in a market for indivisible goods with a price constraint," Games and Economic Behavior, Elsevier, vol. 62(1), pages 140-154, January.
    2. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
    3. Steven J. Brams & Todd R. Kaplan, 2004. "Dividing the Indivisible," Journal of Theoretical Politics, , vol. 16(2), pages 143-173, April.
    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. Simmons, Forest W. & Su, Francis Edward, 2003. "Consensus-halving via theorems of Borsuk-Ulam and Tucker," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 15-25, February.
    6. Steven J. Brams & Todd R. Kaplan & D. Marc Kilgour, 2015. "A Simple Bargaining Mechanism that Elicits Truthful Reservation Prices," Group Decision and Negotiation, Springer, vol. 24(3), pages 401-413, May.
    7. Haake, Claus-Jochen, 2016. "Dividing by Demanding: Object Division through Market Procedures," Center for Mathematical Economics Working Papers 359, Center for Mathematical Economics, Bielefeld University.
    8. Carraro, Carlo & Marchiori, Carmen & Sgobbi, Alessandra, 2005. "Advances in negotiation theory : bargaining, coalitions, and fairness," Policy Research Working Paper Series 3642, The World Bank.
    9. Andreas Wagener, 2006. "Geometric division with a fixed point: Not half the cake, but at least 4/9," Group Decision and Negotiation, Springer, vol. 15(1), pages 43-53, January.
    10. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    11. Nolan Miller & Alexander Wagner & Richard Zeckhauser, 2013. "Solomonic separation: Risk decisions as productivity indicators," Journal of Risk and Uncertainty, Springer, vol. 46(3), pages 265-297, June.
    12. Francisco Sánchez Sánchez, 2022. "Envy-Free Solutions to the Problem of Room Assignment and Rent Division," Group Decision and Negotiation, Springer, vol. 31(3), pages 703-721, June.
    13. Chakravarty, Surajeet & Kaplan, Todd R., 2013. "Optimal allocation without transfer payments," Games and Economic Behavior, Elsevier, vol. 77(1), pages 1-20.
    14. Tayfun Sönmez & M. Utku Ünver, 2010. "Course Bidding At Business Schools," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 99-123, February.
    15. Atila Abdulkadiroğlu & Tayfun Sönmez & M. Utku Ünver, 2004. "Room assignment-rent division: A market approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 515-538, June.
    16. Haake, Claus-Jochen & Raith, Matthias G. & Su, Francis Edward, 2017. "Bidding for envy freeness," Center for Mathematical Economics Working Papers 311, Center for Mathematical Economics, Bielefeld University.
    17. 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.
    18. Nicolò, Antonio & Velez, Rodrigo A., 2017. "Divide and compromise," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 100-110.
    19. 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.
    20. Andersson, T. & Svensson, L.-G. & Yang, Z., 2010. "Constrainedly fair job assignments under minimum wages," Games and Economic Behavior, Elsevier, vol. 68(2), pages 428-442, March.
    21. 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.
    22. Richard F. Potthoff, 2002. "Use of Linear Programming to Find an Envy-Free Solution Closest to the Brams–Kilgour Gap Solution for the Housemates Problem," Group Decision and Negotiation, Springer, vol. 11(5), pages 405-414, September.
    23. Erel Segal-Halevi, 2019. "Generalized Rental Harmony," Papers 1912.13249, arXiv.org, revised Feb 2020.
    24. Barbanel, Julius B. & Brams, Steven J., 2010. "Two-person pie-cutting: The fairest cuts," MPRA Paper 22703, University Library of Munich, Germany.

    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. Robert Scherf & Matthew Weinzierl, 2020. "Understanding Different Approaches to Benefit‐Based Taxation," Fiscal Studies, John Wiley & Sons, vol. 41(2), pages 385-410, June.
    2. Condorelli, Daniele, 2013. "Market and non-market mechanisms for the optimal allocation of scarce resources," Games and Economic Behavior, Elsevier, vol. 82(C), pages 582-591.
    3. Andrea Canidio, 2023. "Auctions with Tokens: Monetary Policy as a Mechanism Design Choice," Papers 2301.13794, arXiv.org, revised Aug 2023.
    4. Alva, Samson & Manjunath, Vikram, 2019. "Strategy-proof Pareto-improvement," Journal of Economic Theory, Elsevier, vol. 181(C), pages 121-142.
    5. Ezzat Elokda & Saverio Bolognani & Andrea Censi & Florian Dorfler & Emilio Frazzoli, 2022. "A self-contained karma economy for the dynamic allocation of common resources," Papers 2207.00495, arXiv.org, revised May 2023.
    6. Azar, Pablo D. & Kleinberg, Robert & Weinberg, S. Matthew, 2019. "Prior independent mechanisms via prophet inequalities with limited information," Games and Economic Behavior, Elsevier, vol. 118(C), pages 511-532.
    7. Onur Kesten & Ayşe Yazıcı, 2012. "The Pareto-dominant strategy-proof and fair rule for problems with indivisible goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 463-488, June.
    8. Vitalik Buterin & Zoë Hitzig & E. Glen Weyl, 2019. "A Flexible Design for Funding Public Goods," Management Science, INFORMS, vol. 65(11), pages 5171-5187, November.
    9. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    10. Miyagawa, Eiichi, 2001. "House Allocation with Transfers," Journal of Economic Theory, Elsevier, vol. 100(2), pages 329-355, October.
    11. Vitalik Buterin & Zoe Hitzig & E. Glen Weyl, 2018. "A Flexible Design for Funding Public Goods," Papers 1809.06421, arXiv.org, revised Aug 2020.
    12. Mohammad Rasouli & Michael I. Jordan, 2021. "Data Sharing Markets," Papers 2107.08630, arXiv.org, revised Jul 2021.
    13. Lars-Gunnar Svensson, 2009. "Coalitional strategy-proofness and fairness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 227-245, August.
    14. Miralles, Antonio, 2012. "Cardinal Bayesian allocation mechanisms without transfers," Journal of Economic Theory, Elsevier, vol. 147(1), pages 179-206.
    15. Vivian Welch & Christine M. Mathew & Panteha Babelmorad & Yanfei Li & Elizabeth T. Ghogomu & Johan Borg & Monserrat Conde & Elizabeth Kristjansson & Anne Lyddiatt & Sue Marcus & Jason W. Nickerson & K, 2021. "Health, social care and technological interventions to improve functional ability of older adults living at home: An evidence and gap map," Campbell Systematic Reviews, John Wiley & Sons, vol. 17(3), September.
    16. Hongpeng Guo & Zhihao Lv & Junyi Hua & Hongxu Yuan & Qingyu Yu, 2021. "Design of Combined Auction Model for Emission Rights of International Forestry Carbon Sequestration and Other Pollutants Based on SMRA," Sustainability, MDPI, vol. 13(20), pages 1-18, October.
    17. Paul Pezanis-Christou & Abdolkarim Sadrieh, 2003. "Elicited bid functions in (a)symmetric first-price auctions," Working Papers 85, Barcelona School of Economics.
    18. Ewerhart, Christian & Cassola, Nuno & Valla, Natacha, 2012. "Overbidding in fixed rate tenders: The role of exposure risk," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 539-549.
    19. Erkmen Giray Aslim, 2019. "The Relationship Between Health Insurance and Early Retirement: Evidence from the Affordable Care Act," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 45(1), pages 112-140, January.
    20. Tafreshian, Amirmahdi & Masoud, Neda, 2022. "A truthful subsidy scheme for a peer-to-peer ridesharing market with incomplete information," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 130-161.

    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:ucp:jpolec:v:109:y:2001:i:2:p:418-443. 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: Journals Division (email available below). General contact details of provider: https://www.journals.uchicago.edu/JPE .

    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.