Existence of a non-stationary equilibrium in search-and-matching models: tu and ntu

Christopher Sandmann () and Nicolas Bonneton ()
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Christopher Sandmann: Department of Economics, London School of Economics
Nicolas Bonneton: Department of Economics, Vanderbilt University

Theoretical Economics, Forthcoming

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.

Keywords: Equilibrium existence; search-and-matching; non-stationary search; mean field games; fixed point theorem (search for similar items in EconPapers)
JEL-codes: C62 C78 D83 (search for similar items in EconPapers)
Date: 2025-05-12
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