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A Graph Theoretic Approach to the Slot Allocation Problem

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  • Youngsub Chun

  • Boram Park

Abstract

We consider a problem of assigning slots to a group of agents. Each slot can serve only one agent at a time and it is located along a line. Each agent has a most preferred slot and incurs disutility when she is assigned away from the most preferred slot. Furthermore, we assume that each agent¡¯s utility is equal to the amount of monetary transfer minus the distance from the peak to her assigned slot. In this paper, we investigate how to assign slots to agents in an efficient and fair way. First, by using a bipartite graph of the slot allocation problem, we present a simple way of identifying all efficient assignments. Next, we introduce two allocation rules for the problem, the leximin and the leximax rules, and discuss their properties.

Suggested Citation

  • Youngsub Chun & Boram Park, 2014. "A Graph Theoretic Approach to the Slot Allocation Problem," Working Paper Series no92, Institute of Economic Research, Seoul National University.
    • Handle: RePEc:snu:ioerwp:no92
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    Cited by:

    1. Aziz, Haris & Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2017. "Computational aspects of assigning agents to a line," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 93-99.
    2. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2019. "Recent developments in the queueing problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 1-23, April.
    3. Yu Zhou & Youngsub Chun & Shigehiro Serizawa, 2022. "A characterization of the Vickrey rule in slot allocation problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 38-49, March.

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