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Price of Fairness for allocating a bounded resource

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  • Nicosia, Gaia
  • Pacifici, Andrea
  • Pferschy, Ulrich

Abstract

We study the problem faced by a decision maker who wants to allocate a scarce resource among several agents in order to maximize the total utility. An optimal solution may present a very unbalanced allocation of the resource to the agents and hence be perceived as unfair. On the other hand balanced allocations may be far from the optimum. In this paper we are interested in assessing the quality of fair solutions, i.e., in measuring the system efficiency loss under a fair allocation compared to the one that maximizes the total utility. This indicator is called the Price of Fairness and we study it under three different definitions of fairness, namely maximin, Kalai–Smorodinski and proportional fairness.

Suggested Citation

  • Nicosia, Gaia & Pacifici, Andrea & Pferschy, Ulrich, 2017. "Price of Fairness for allocating a bounded resource," European Journal of Operational Research, Elsevier, vol. 257(3), pages 933-943.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:3:p:933-943
    DOI: 10.1016/j.ejor.2016.08.013
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    7. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2012. "On the Efficiency-Fairness Trade-off," Management Science, INFORMS, vol. 58(12), pages 2234-2250, December.
    8. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
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    3. Akoluk, Damla & Karsu, Özlem, 2022. "Ensuring multidimensional equality in public service," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    4. Agnetis, Alessandro & Chen, Bo & Nicosia, Gaia & Pacifici, Andrea, 2019. "Price of fairness in two-agent single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 276(1), pages 79-87.
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    7. Sun, Lishan & Lu, Huabo & Xu, Yan & Kong, Dewen & Shao, Juan, 2022. "Fairness-oriented train service design for urban rail transit cross-line operation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    8. Pferschy, Ulrich & Nicosia, Gaia & Pacifici, Andrea & Schauer, Joachim, 2021. "On the Stackelberg knapsack game," European Journal of Operational Research, Elsevier, vol. 291(1), pages 18-31.
    9. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.
    10. Roberto Aringhieri & Sara Bigharaz & Davide Duma & Alberto Guastalla, 2022. "Fairness in ambulance routing for post disaster management," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(1), pages 189-211, March.
    11. Yubai Zhang & Zhao Zhang & Zhaohui Liu, 0. "The price of fairness for a two-agent scheduling game minimizing total completion time," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-19.
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    14. Yubai Zhang & Zhao Zhang & Zhaohui Liu, 2022. "The price of fairness for a two-agent scheduling game minimizing total completion time," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 2104-2122, October.

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