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Existence of a Non-Stationary Equilibrium in Search-And-Matching Models: TU and NTU

Author

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  • Christopher Sandmann
  • Nicolas Bonneton

Abstract

This paper proves the existence of a non-stationary equilibrium in the canonical search- and-matching model with heterogeneous agents. Non-stationarity entails that the number and characteristics of unmatched agents evolve endogenously over time. An equilibrium exists under minimal regularity conditions and for both paradigms considered in the literature: transferable and non-transferable utility. To address potential discontinuities in match opportunities across types, our analysis introduces a generalized Schauder fixed- point theorem suitable for models with discontinuous value functions.

Suggested Citation

  • Christopher Sandmann & Nicolas Bonneton, 2023. "Existence of a Non-Stationary Equilibrium in Search-And-Matching Models: TU and NTU," CRC TR 224 Discussion Paper Series crctr224_2023_427v2, University of Bonn and University of Mannheim, Germany, revised Feb 2025.
    • Handle: RePEc:bon:boncrc:crctr224_2023_427v2
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    File URL: https://www.crctr224.de/research/discussion-papers/archive/dp427
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    More about this item

    Keywords

    equilibrium existence; search and matching; non-stationary; mean-field game;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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