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Fractional Top Trading Cycle on the Full Preference Domain

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  • Jingsheng Yu
  • Jun Zhang

Abstract

Efficiency and fairness are two desiderata in market design. Fairness requires randomization in many environments. Observing the inadequacy of Top Trading Cycle (TTC) to incorporate randomization, Yu and Zhang (2020) propose the class of Fractional TTC mechanisms to solve random allocation problems efficiently and fairly. The assumption of strict preferences in the paper restricts the application scope. This paper extends Fractional TTC to the full preference domain in which agents can be indifferent between objects. Efficiency and fairness of Fractional TTC are preserved. As a corollary, we obtain an extension of the probabilistic serial mechanism in the house allocation model to the full preference domain. Our extension does not require any knowledge beyond elementary computation.

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  • Jingsheng Yu & Jun Zhang, 2020. "Fractional Top Trading Cycle on the Full Preference Domain," Papers 2005.09340, arXiv.org.
    • Handle: RePEc:arx:papers:2005.09340
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    References listed on IDEAS

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    1. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    2. Jaramillo, Paula & Manjunath, Vikram, 2012. "The difference indifference makes in strategy-proof allocation of objects," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1913-1946.
    3. Bogomolnaia, Anna & Deb, Rajat & Ehlers, Lars, 2005. "Strategy-proof assignment on the full preference domain," Journal of Economic Theory, Elsevier, vol. 123(2), pages 161-186, August.
    4. Alcalde-Unzu, Jorge & Molis, Elena, 2011. "Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms," Games and Economic Behavior, Elsevier, vol. 73(1), pages 1-16, September.
    5. 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.
    6. 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.
    7. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
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