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Extended Random Assignment Mechanisms on a Family of Good Sets

Author

Listed:
  • Yoshio Sano

    (University of Tsukuba)

  • Ping Zhan

    (Edogawa University)

Abstract

For the problem of allocating indivisible goods to agents, we recently generalized the probabilistic serial (PS) mechanism proposed by Bogomolnaia and Moulin (J Econ Theory 100(2):295–328, 2001). We generalized the constraints with the fixed quota on each good to a set of inequality constraints induced by a polytope called polymatroid (Fujishige et al. in ACM Trans Econ Comput 6(1):1–28, 2018. https://doi.org/10.1145/3175496 ; Math Program 178(1–2):485–501, 2019). The main contribution of this paper was to extend the previous mechanism to allow indifference among goods. We show that the extended PS mechanism is ordinally efficient and envy-free. We also characterize the mechanism by lexicographic optimization. Finally, a lottery, an integral decomposition mechanism is outlined.

Suggested Citation

  • Yoshio Sano & Ping Zhan, 2021. "Extended Random Assignment Mechanisms on a Family of Good Sets," SN Operations Research Forum, Springer, vol. 2(4), pages 1-30, December.
    • Handle: RePEc:spr:snopef:v:2:y:2021:i:4:d:10.1007_s43069-021-00095-8
    DOI: 10.1007/s43069-021-00095-8
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    References listed on IDEAS

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    Cited by:

    1. Ping Zhan, 2023. "A Simple Characterization of Assignment Mechanisms on Set Constraints," SN Operations Research Forum, Springer, vol. 4(2), pages 1-15, June.
    2. Ping Zhan, 2023. "Simultaneous eating algorithm and greedy algorithm in assignment problems," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-24, July.

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