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A characterization of the extended serial correspondence

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  • Heo, Eun Jeong
  • Yılmaz, Özgür

Abstract

We study the problem of assigning objects to a group of agents. We focus on probabilistic methods that take agents’ ordinal preferences over the objects. Importantly, we allow for indifferences among objects. Katta and Sethuraman (2006) propose the extended serial correspondence to solve this problem. Our main result is a characterization of the extended serial correspondence in welfare terms by means of stochastic dominance efficiency, stochastic dominance no-envy and “limited invariance,” a requirement we adapt from Heo (2014a). We also prove that an assignment matrix is selected by the extended serial correspondence if and only if it satisfies “non-wastefulness” and “ordinal fairness,” which we adapt from Kesten et al. (2011).

Suggested Citation

  • Heo, Eun Jeong & Yılmaz, Özgür, 2015. "A characterization of the extended serial correspondence," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 102-110.
    • Handle: RePEc:eee:mateco:v:59:y:2015:i:c:p:102-110
    DOI: 10.1016/j.jmateco.2015.05.003
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    References listed on IDEAS

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    1. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    2. 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.
    3. Bogomolnaia, Anna & Heo, Eun Jeong, 2012. "Probabilistic assignment of objects: Characterizing the serial rule," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2072-2082.
    4. 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.
    5. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Unver, Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    6. Onur Kesten & Morimitsu Kurino & M. Utku Ünver, 2010. "Fair and Efficient Assignment via the Probabilistic Serial Mechanism," Boston College Working Papers in Economics 742, Boston College Department of Economics, revised 30 May 2011.
    7. Eun Heo, 2014. "The extended serial correspondence on a rich preference domain," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 439-454, May.
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    Cited by:

    1. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    2. Han, Xiang, 2024. "A theory of fair random allocation under priorities," Theoretical Economics, Econometric Society, vol. 19(3), July.
    3. Mustafa Oǧuz Afacan, 2016. "Characterizations of the cumulative offer process," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 531-542, October.
    4. Youngsub Chun & Kiyong Yun, 2020. "Upper-contour strategy-proofness in the probabilistic assignment problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 667-687, April.
    5. Mustafa Oğuz Afacan, 2023. "Axiomatic characterizations of the constrained probabilistic serial mechanism," Theory and Decision, Springer, vol. 95(3), pages 465-484, October.
    6. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).
    7. Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.
    8. Tayfun Sönmez & M. Utku Ünver, 2024. "Matching under Non-transferable Utility: Theory," Boston College Working Papers in Economics 1068, Boston College Department of Economics.
    9. Ping Zhan, 2023. "A Simple Characterization of Assignment Mechanisms on Set Constraints," SN Operations Research Forum, Springer, vol. 4(2), pages 1-15, June.

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