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The price of fairness with the extended Perles–Maschler solution

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  • Feimin Zhong
  • Jinxing Xie
  • Xiaobo Zhao

Abstract

In Nash bargaining problem, due to fairness concerns of players, instead of maximizing the sum of utilities of all players, an implementable solution should satisfy some axioms or characterizations. Such a solution can result in the so-called price of fairness, because of the reduction in the sum of utilities of all players. An important issue is to quantify the system efficiency loss under axiomatic solutions through the price of fairness. Based on Perles–Maschler solution of two-player Nash bargaining problem, this paper deals with the extended Perles–Maschler solution of multi-player Nash bargaining problem. We give lower bounds of three measures of the system efficiency for this solution, and show that the lower bounds are asymptotically tight. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Feimin Zhong & Jinxing Xie & Xiaobo Zhao, 2014. "The price of fairness with the extended Perles–Maschler solution," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(2), pages 193-212, October.
    • Handle: RePEc:spr:mathme:v:80:y:2014:i:2:p:193-212
    DOI: 10.1007/s00186-014-0475-8
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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    3. Imai, Haruo, 1983. "Individual Monotonicity and Lexicographic Maxmin Solution," Econometrica, Econometric Society, vol. 51(2), pages 389-401, March.
    4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    5. Calvo, Emilio & Gutierrez, Esther, 1994. "Extension of the Perles-Maschler Solution to N-Person Bargaining Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(4), pages 325-346.
    6. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284, Elsevier.
    7. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2011. "The Price of Fairness," Operations Research, INFORMS, vol. 59(1), pages 17-31, February.
    8. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2012. "On the Efficiency-Fairness Trade-off," Management Science, INFORMS, vol. 58(12), pages 2234-2250, December.
    9. Diethard Pallaschke & Joachim Rosenmüller, 2007. "A superadditive solution for cephoidal bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 569-590, April.
    10. M. Hinojosa & A. Mármol & L. Monroy, 2005. "Generalized Maximin Solutions in Multicriteria Bargaining," Annals of Operations Research, Springer, vol. 137(1), pages 243-255, July.
    11. Chih Chang & Yan-An Hwang, 1999. "A characterization of the leximin solution of the bargaining problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(3), pages 395-400, July.
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