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The Price of Fairness

Author

Listed:
  • Dimitris Bertsimas

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Vivek F. Farias

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Nikolaos Trichakis

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

In this paper we study resource allocation problems that involve multiple self-interested parties or players and a central decision maker. We introduce and study the price of fairness, which is the relative system efficiency loss under a “fair” allocation assuming that a fully efficient allocation is one that maximizes the sum of player utilities. We focus on two well-accepted, axiomatically justified notions of fairness, viz., proportional fairness and max-min fairness. For these notions we provide a tight characterization of the price of fairness for a broad family of problems.

Suggested Citation

  • Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2011. "The Price of Fairness," Operations Research, INFORMS, vol. 59(1), pages 17-31, February.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:1:p:17-31
    DOI: 10.1287/opre.1100.0865
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    References listed on IDEAS

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    1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    2. M Butler & H P Williams, 2002. "Fairness versus efficiency in charging for the use of common facilities," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(12), pages 1324-1329, December.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Butler, Martin & Williams, H. Paul, 2002. "Fairness versus efficiency in charging for the use of common facilities," LSE Research Online Documents on Economics 18399, London School of Economics and Political Science, LSE Library.
    5. Dimitris Bertsimas & Sarah Stock Patterson, 1998. "The Air Traffic Flow Management Problem with Enroute Capacities," Operations Research, INFORMS, vol. 46(3), pages 406-422, June.
    6. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    7. Guglielmo Lulli & Amedeo Odoni, 2007. "The European Air Traffic Flow Management Problem," Transportation Science, INFORMS, vol. 41(4), pages 431-443, November.
    8. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    9. Ramesh Johari & John N. Tsitsiklis, 2004. "Efficiency Loss in a Network Resource Allocation Game," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 407-435, August.
    10. Dimitris Bertsimas & Sarah Stock Patterson, 2000. "The Traffic Flow Management Rerouting Problem in Air Traffic Control: A Dynamic Network Flow Approach," Transportation Science, INFORMS, vol. 34(3), pages 239-255, August.
    Full references (including those not matched with items on IDEAS)

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