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Characterizing priorities for deferred acceptance with or without outside options

Author

Listed:
  • Xiang Han

    (School of Economics, Shanghai University of Finance and Economics)

  • Junxiao Zhang

    (School of Economics, Shanghai University of Finance and Economics)

Abstract

In a model of priority-based allocation of indivisible objects where there may not be outside options, we characterize the priority structures under which the deferred acceptance algorithm (DA) satisfies various desiderata. We first identify an acyclicity condition that is necessary and sufficient for DA to be group strategy-proof, robustly stable, weakly group robustly stable, or to implement the stable allocation correspondence in Nash equilibria. When there is no outside option and there are more agents than total resources, the condition becomes considerably weaker, and no longer requires the priorities between any pair of objects to be similar. We further find a condition on priorities that is necessary and sufficient for the efficiency or consistency of DA, which is in general stronger than the above incentive properties for this mechanism.

Suggested Citation

  • Xiang Han & Junxiao Zhang, 2025. "Characterizing priorities for deferred acceptance with or without outside options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(2), pages 497-517, March.
    • Handle: RePEc:spr:joecth:v:79:y:2025:i:2:d:10.1007_s00199-024-01586-5
    DOI: 10.1007/s00199-024-01586-5
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    More about this item

    Keywords

    Priority-based allocation; Outside option; Deferred acceptance algorithm; Group strategy-proofness; Efficiency; Acyclicity;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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