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Efficiency, sorting, and selection

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  • Peralta, Esteban

Abstract

In labor markets in which workers’ types are private information, Liu, Mailath, Postlewaite, and Samuelson (2014) show that stable matchings are positive assortative and efficient within monotonic and supermodular domains. I show that efficiency and sorting are obtained because within their domains most failures of positive assortativeness and efficiency lead workers to select themselves favorably with respect to the firms, but prove a more general result, because monotonicity can be weakened, that holds true regardless of how firms’ values depend on workers’ types. The generalization hinges more heavily on firms’ higher-order inferences and requires firms’ values to be nonmonotonic in workers’ types.

Suggested Citation

  • Peralta, Esteban, 2025. "Efficiency, sorting, and selection," Journal of Mathematical Economics, Elsevier, vol. 121(C).
    • Handle: RePEc:eee:mateco:v:121:y:2025:i:c:s0304406825001041
    DOI: 10.1016/j.jmateco.2025.103187
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    References listed on IDEAS

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    1. Peralta, Esteban, 2024. "Not all is lost: Sorting and self-stabilizing sets," Games and Economic Behavior, Elsevier, vol. 146(C), pages 51-58.
    2. Qingmin Liu, 2020. "Stability and Bayesian Consistency in Two-Sided Markets," American Economic Review, American Economic Association, vol. 110(8), pages 2625-2666, August.
    3. Boyan Jovanovic, 1982. "Favorable Selection with Asymmetric Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(3), pages 535-539.
    4. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    5. Roth, Alvin E., 1989. "Two-sided matching with incomplete information about others' preferences," Games and Economic Behavior, Elsevier, vol. 1(2), pages 191-209, June.
    6. Chakraborty, Archishman & Citanna, Alessandro & Ostrovsky, Michael, 2010. "Two-sided matching with interdependent values," Journal of Economic Theory, Elsevier, vol. 145(1), pages 85-105, January.
    7. Chen, Yi-Chun & Hu, Gaoji, 2020. "Learning by matching," Theoretical Economics, Econometric Society, vol. 15(1), January.
    8. Qingmin Liu & George J. Mailath & Andrew Postlewaite & Larry Samuelson, 2014. "Stable Matching With Incomplete Information," Econometrica, Econometric Society, vol. 82(2), pages 541-587, March.
    9. Alston, Max, 2020. "On the non-existence of stable matches with incomplete information," Games and Economic Behavior, Elsevier, vol. 120(C), pages 336-344.
    10. Ehlers, Lars & Masso, Jordi, 2007. "Incomplete information and singleton cores in matching markets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 587-600, September.
    11. Yi-Chun Chen & Gaoji Hu, 2023. "A Theory of Stability in Matching with Incomplete Information," American Economic Journal: Microeconomics, American Economic Association, vol. 15(1), pages 288-322, February.
    12. Pomatto, Luciano, 2022. "Stable matching under forward-induction reasoning," Theoretical Economics, Econometric Society, vol. 17(4), November.
    13. S. Nageeb Ali & Maximilian Mihm & Lucas Siga & Chloe Tergiman, 2021. "Adverse and Advantageous Selection in the Laboratory," American Economic Review, American Economic Association, vol. 111(7), pages 2152-2178, July.
    14. Bikhchandani, Sushil, 2017. "Stability with one-sided incomplete information," Journal of Economic Theory, Elsevier, vol. 168(C), pages 372-399.
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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
    • D6 - Microeconomics - - Welfare Economics
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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