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Computational Aspects of Assigning Agents to a Line

Author

Listed:
  • AZIZ, Haris

    (University of New South Wales)

  • HOUGAARD, Jens Leth

    (University of Copenhagen)

  • MORENO-TERNERO, Juan D.

    (Université catholique de Louvain, CORE, Belgium)

  • OSTERDAL, Lars Peter

    (Copenhagen Business School)

Abstract

We consider the problem of assigning agents to slots on a line, where only one agent can be served at a slot and each agent prefers to be served as close as possible to his target. We introduce a general approach to compute aggregate gap-minimizing assignments, as well as gap-egalitarian assignments. The approach relies on an algorithm which is shown to be faster than general purpose algorithms for the assignment problem. We also extend the approach to probabilistic assignments and explore the computational features of existing, as well as new, methods for this setting.

Suggested Citation

  • AZIZ, Haris & HOUGAARD, Jens Leth & MORENO-TERNERO, Juan D. & OSTERDAL, Lars Peter, 2016. "Computational Aspects of Assigning Agents to a Line," LIDAM Discussion Papers CORE 2016054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2016054
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    References listed on IDEAS

    as
    1. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2014. "Assigning agents to a line," Games and Economic Behavior, Elsevier, vol. 87(C), pages 539-553.
    2. 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.
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    4. Youngsub Chun & Boram Park, 2017. "A graph theoretic approach to the slot allocation problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 133-152, January.
    5. Aziz, Haris & Brandt, Felix & Harrenstein, Paul, 2013. "Pareto optimality in coalition formation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 562-581.
    6. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
    7. Demko, Stephen & Hill, Theodore P., 1988. "Equitable distribution of indivisible objects," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 145-158, October.
    8. 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.
    9. Yoichi Kasajima, 2013. "Probabilistic assignment of indivisible goods with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 203-215, June.
    10. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Random assignment; congested facility; aggregate gap minimization; gap-egalitarian assignments; computational speed;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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