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Size versus fairness in the assignment problem

Author

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  • Bogomolnaia, Anna
  • Moulin, Herve

Abstract

When not all objects are acceptable to all agents, maximizing the number of objects actually assigned is an important design concern. We compute the guaranteed size ratio of the Probabilistic Serial mechanism, i.e., the worst ratio of the actual expected size to the maximal feasible size. It converges decreasingly to 1−1e≃63.2% as the maximal size increases. It is the best ratio of any Envy-Free assignment mechanism.

Suggested Citation

  • Bogomolnaia, Anna & Moulin, Herve, 2015. "Size versus fairness in the assignment problem," Games and Economic Behavior, Elsevier, vol. 90(C), pages 119-127.
  • Handle: RePEc:eee:gamebe:v:90:y:2015:i:c:p:119-127
    DOI: 10.1016/j.geb.2014.11.006
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    References listed on IDEAS

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    5. Erdil, Aytek, 2014. "Strategy-proof stochastic assignment," Journal of Economic Theory, Elsevier, vol. 151(C), pages 146-162.
    6. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    7. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    8. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Ünver, M. Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
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    1. repec:eee:matsoc:v:90:y:2017:i:c:p:80-92 is not listed on IDEAS
    2. repec:eee:gamebe:v:105:y:2017:i:c:p:1-8 is not listed on IDEAS

    More about this item

    Keywords

    Envy-freeness; Random assignment; Probabilistic serial;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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