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The Large and Likely Inefficiency of Stable Matching Mechanisms

Author

Listed:
  • Josué Ortega
  • Gabriel Ziegler
  • R. Pablo Arribillaga
  • Geng Zhao

Abstract

We prove that any stable matching mechanism suffers from systematic inefficiency of striking magnitude: in large random markets, any stable allocation is Pareto-inefficient with high probability, and almost all students can simultaneously improve their placements without harming anyone else. We establish this result by showing that the envy digraph generated by the student-proposing Deferred Acceptance mechanism contains a unique giant strongly connected component, implying that nearly all students are improvable via trading cycles. Finally, we show that every maximal cycle packing covers almost all students, revealing a surprising asymptotic equivalence among all efficient mechanisms that Paretodominate DA.

Suggested Citation

  • Josué Ortega & Gabriel Ziegler & R. Pablo Arribillaga & Geng Zhao, 2026. "The Large and Likely Inefficiency of Stable Matching Mechanisms," Berlin School of Economics Discussion Papers 0107, Berlin School of Economics.
    • Handle: RePEc:bdp:dpaper:0107
    DOI: 10.48462/opus4-6310
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    Keywords

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    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

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