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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
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    File URL: http://dx.doi.org/10.1086/319550
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. 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.
    2. 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.
    3. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
    4. Claus-Jochen Haake & Matthias G. Raith & Francis Edward Su, 2002. "Bidding for envy-freeness: A procedural approach to n-player fair-division problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 723-749.
    5. 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.
    6. 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.
    7. 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.
    8. Chakravarty, Surajeet & Kaplan, Todd R., 2013. "Optimal allocation without transfer payments," Games and Economic Behavior, Elsevier, vol. 77(1), pages 1-20.
    9. 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.
    10. 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.
    11. repec:eee:matsoc:v:90:y:2017:i:c:p:100-110 is not listed on IDEAS
    12. 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.
    13. 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.
    14. Carlo Carraro & Carmen Marchiori & Alessandra Sgobbi, 2005. "Advances in Negotiation Theory: Bargaining, Coalitions and Fairness," Working Papers 2005.66, Fondazione Eni Enrico Mattei.
    15. Haake,C., 2004. "Dividing by demanding : object division through market procedures," Center for Mathematical Economics Working Papers 359, Center for Mathematical Economics, Bielefeld University.
    16. repec:spr:grdene:v:11:y:2002:i:5:d:10.1023_a:1020485018300 is not listed on IDEAS
    17. repec:spr:grdene:v:15:y:2006:i:1:d:10.1007_s10726-005-9000-z is not listed on IDEAS
    18. 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.
    19. Barbanel, Julius B. & Brams, Steven J., 2010. "Two-person pie-cutting: The fairest cuts," MPRA Paper 22703, University Library of Munich, Germany.
    20. 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.
    21. 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.
    22. Rodrigo A. Velez & Antonio Nicolo, 2016. "Divide and compromise," Working Papers 20160710-001, Texas A&M University, Department of Economics.

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