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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
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    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. 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.
    3. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    4. 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.
    5. 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.
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    Citations

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    Cited by:

    1. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
    2. 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.
    3. 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.
    4. 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.
    5. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    6. 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.
    7. 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.
    8. Carlo Carraro & Carmen Marchiori & Alessandra Sgobbi, 2005. "Advances in Negotiation Theory: Bargaining, Coalitions and Fairness," Working Papers 2005.66, Fondazione Eni Enrico Mattei.
    9. 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.
    10. 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.
    11. Nicolò, Antonio & Velez, Rodrigo A., 2017. "Divide and compromise," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 100-110.
    12. 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.
    13. Chakravarty, Surajeet & Kaplan, Todd R., 2013. "Optimal allocation without transfer payments," Games and Economic Behavior, Elsevier, vol. 77(1), pages 1-20.
    14. 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.
    15. 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.
    16. Steven J. Brams & Todd R. Kaplan, 2004. "Dividing the Indivisible," Journal of Theoretical Politics, , vol. 16(2), pages 143-173, April.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    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.

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