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Simultaneous eating algorithm and greedy algorithm in assignment problems

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  • Ping Zhan

    (Edogawa University)

Abstract

The simultaneous eating algorithm (SEA) and probabilistic serial (PS) mechanism are well known for allocating a set of divisible or indivisible goods to agents with ordinal preferences. The PS mechanism is SEA at the same eating speed. The prominent property of SEA is ordinal efficiency. Recently, we extended the PS mechanism (EPS) from a fixed quota of each good to a variable varying in a polytope constrained by submodular functions. In this article, we further generalized some results on SEA. After formalizing the extended ESA (ESEA), we show that it can be characterized by ordinal efficiency. We established a stronger summation optimization than the Pareto type of ordinal efficiency by an introduced weight vector. The weights in the summation optimization coincide with agents’ preferences at the acyclic positive values of an allocation. Hence, the order of goods selected to eat in ESEA is exactly the one chosen in the execution of the well-known greedy algorithm.

Suggested Citation

  • Ping Zhan, 2023. "Simultaneous eating algorithm and greedy algorithm in assignment problems," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-24, July.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:5:d:10.1007_s10878-023-01063-0
    DOI: 10.1007/s10878-023-01063-0
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    References listed on IDEAS

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    1. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
    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. Aziz, Haris & Brandl, Florian, 2022. "The vigilant eating rule: A general approach for probabilistic economic design with constraints," Games and Economic Behavior, Elsevier, vol. 135(C), pages 168-187.
    4. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    5. Eric Budish & Yeon-Koo Che & Fuhito Kojima & Paul Milgrom, 2013. "Designing Random Allocation Mechanisms: Theory and Applications," American Economic Review, American Economic Association, vol. 103(2), pages 585-623, April.
    6. Ping Zhan, 2023. "A Simple Characterization of Assignment Mechanisms on Set Constraints," SN Operations Research Forum, Springer, vol. 4(2), pages 1-15, June.
    7. Manea, Mihai, 2008. "A constructive proof of the ordinal efficiency welfare theorem," Journal of Economic Theory, Elsevier, vol. 141(1), pages 276-281, July.
    8. 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.
    9. 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.
    10. McLennan, Andrew, 2002. "Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem," Journal of Economic Theory, Elsevier, vol. 105(2), pages 435-449, August.
    11. 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.
    12. Harless, Patrick, 2019. "Efficient rules for probabilistic assignment," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 107-116.
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