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Valuation monotonicity, fairness and stability in assignment problems

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  • van den Brink, René
  • Núñez, Marina
  • Robles, Francisco

Abstract

In two-sided assignment markets with transferable utility, we first introduce two weak monotonicity properties that are compatible with stability. We show that for a fixed population, the sellers-optimal (respectively the buyers-optimal) stable rules are the only stable rules that satisfy object-valuation antimonotonicity (respectively buyer-valuation monotonicity). Essential in these properties is that, after a change in valuations, monotonicity is required only for buyers that stay matched with the same seller. Using Owen's derived consistency, the two optimal rules are characterized among all allocation rules for two-sided assignment markets with a variable population, without explicitly requiring stability.

Suggested Citation

  • van den Brink, René & Núñez, Marina & Robles, Francisco, 2021. "Valuation monotonicity, fairness and stability in assignment problems," Journal of Economic Theory, Elsevier, vol. 195(C).
  • Handle: RePEc:eee:jetheo:v:195:y:2021:i:c:s0022053121000946
    DOI: 10.1016/j.jet.2021.105277
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    Citations

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    Cited by:

    1. Solymosi, Tamás, 2023. "Sensitivity of fair prices in assignment markets," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 1-12.
    2. Gerard Domènech Gironell & Marina Núñez Oliva, 2022. "Axioms for the optimal stable rules and fair-division rules in a multiple-partners job market," UB School of Economics Working Papers 2022/419, University of Barcelona School of Economics.
    3. Domènech, Gerard & Núñez, Marina, 2022. "Axioms for the optimal stable rules and fair-division rules in a multiple-partners job market," Games and Economic Behavior, Elsevier, vol. 136(C), pages 469-484.

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    More about this item

    Keywords

    Assignment problems; Stability; Valuation monotonicity; Grand valuation fairness; Optimal stable rules; Fair division rules;
    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
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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