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Complexity of finding Pareto-efficient allocations of highest welfare

Author

Listed:
  • Peter Biro

    (Centre for Economic and Regional Studies and Department of Operations Research and Actuarial Sciences, Corvinus University ofBudapest, Hungary)

  • Jens Gudmundsson

    (Department of Food and Resource Economics, University of Copenhagen, Denmark,)

Abstract

We allocate objects to agents as exemplified primarily by school choice. Welfare judgments of the object-allocating agency are encoded as edge weights in the acceptability graph. The welfare of an allocation is the sum of its edge weights. We introduce the constrained welfare-maximizing solution, which is the allocation of highest welfare among the Pareto-efficient allocations. We identify conditions under which this solution is easily determined from a computational point of view. For the unrestricted case, we formulate an integer program and find this to be viable in practice as it quickly solves a real-world instance of kindergarten allocation and large-scale simulated instances. Incentives to report preferences truthfully are discussed briefly.

Suggested Citation

  • Peter Biro & Jens Gudmundsson, 2020. "Complexity of finding Pareto-efficient allocations of highest welfare," CERS-IE WORKING PAPERS 2016, Institute of Economics, Centre for Economic and Regional Studies.
  • Handle: RePEc:has:discpr:2016
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    References listed on IDEAS

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    Cited by:

    1. Kondratev, Aleksei Y. & Nesterov, Alexander S., 2022. "Minimal envy and popular matchings," European Journal of Operational Research, Elsevier, vol. 296(3), pages 776-787.

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    More about this item

    Keywords

    Assignment; Pareto-efficiency; Welfare-maximization; Complexity; Integerprogrammin;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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