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Probabilistic stable rules and Nash equilibrium in two-sided matching problems

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  • Ayşe Yazıcı

    (Durham University Business School)

Abstract

We study many-to-many matching with substitutable and cardinally monotonic preferences. We analyze stochastic dominance (sd) Nash equilibria of the game induced by any probabilistic stable matching rule. We show that a unique match is obtained as the outcome of each sd-Nash equilibrium. Furthermore, individual-rationality with respect to the true preferences is a necessary and sufficient condition for an equilibrium outcome. In the many-to-one framework, the outcome of each equilibrium in which firms behave truthfully is stable for the true preferences. In the many-to-many framework, we identify an equilibrium in which firms behave truthfully and yet the equilibrium outcome is not stable for the true preferences. However, each stable match for the true preferences can be achieved as the outcome of such equilibrium.

Suggested Citation

  • Ayşe Yazıcı, 2017. "Probabilistic stable rules and Nash equilibrium in two-sided matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 103-124, March.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-015-0525-3
    DOI: 10.1007/s00182-015-0525-3
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    References listed on IDEAS

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    More about this item

    Keywords

    Probabilistic rules; Stability; Nash equilibrium; Substitutability; Cardinal monotonicity;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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