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Two-Sided Matchings: An Algorithm for Ensuring They Are Minimax and Pareto-Optimal

Author

Listed:
  • Steven, Brams
  • Marc, Kilgour

Abstract

Gale and Shapley (1962) proposed the deferred-acceptance algorithm for matching (i) college applicants and colleges and (ii) men and women. In the case of the latter, it produces either one or two stable matches whereby no man and woman would prefer to be matched with each other rather than with their present partners. But stable matches can give one or both players in a pair their worst match, whereas the minimax algorithm that we propose, which finds all assignments that minimize the maximum rank of players in matches, avoids such assignments. Although minimax matches may not be stable, at least one is always Pareto-optimal: No other matching is at least as good for all the players and better for one or more. If there are multiple minimax matches, we propose criteria for choosing the most desirable among them and also discuss the settings in which minimax matches seem more compelling than deferred-acceptance matches when they differ. Finally, we calculate the probability that minimax matches differ from deferred-acceptance matches in a simple case.

Suggested Citation

  • Steven, Brams & Marc, Kilgour, 2013. "Two-Sided Matchings: An Algorithm for Ensuring They Are Minimax and Pareto-Optimal," MPRA Paper 48113, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:48113
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    File URL: https://mpra.ub.uni-muenchen.de/48113/1/MPRA_paper_48113.pdf
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    References listed on IDEAS

    as
    1. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    2. Gura,Ein-Ya & Maschler,Michael, 2008. "Insights into Game Theory," Cambridge Books, Cambridge University Press, number 9780521696920, September.
    3. Tayfun Sönmez & M. Utku Ünver, 2009. "Matching, Allocation, and Exchange of Discrete Resources," Boston College Working Papers in Economics 717, Boston College Department of Economics.
    4. Gura,Ein-Ya & Maschler,Michael, 2008. "Insights into Game Theory," Cambridge Books, Cambridge University Press, number 9780521874229, September.
    5. James Boudreau & Vicki Knoblauch, 2013. "Preferences and the price of stability in matching markets," Theory and Decision, Springer, vol. 74(4), pages 565-589, April.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Deferred-acceptance algorithm; minimax algorithm; matchings; stability;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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