Existence of a non-stationary equilibrium in search-and-matching models:TU and NTU

This paper proves the existence of a non-stationary equilibrium in the canonical search-and-matching model with heterogeneous agents. Nonstationarity 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.