Lucie Kratochvílová

Lucie Kratochvílová completed her doctorate at the Faculty of Science of Masaryk University in Brno, where her dissertation addressed existence and uniqueness of Nash equilibria in infinite-dimensional strategy spaces, with applications to competitive equilibrium models under non-convex preferences. The work developed a unified fixed-point framework — combining Schauder and Kakutani approaches — applicable to a class of production economies where standard finite-dimensional arguments fail, and established conditions under which the set of equilibria is connected even when uniqueness cannot be guaranteed. She subsequently held a postdoctoral position in the Department of Decision Sciences at Bocconi University in Milan, where she worked on monotone operator methods for general equilibrium systems with externalities and on the stability of equilibria under perturbations to preference structures and endowment distributions.

Her subsequent research extended these foundations to competitive equilibrium existence under weakened convexity assumptions — incorporating quasi-convex preferences and non-convex production sets — and to the convergence properties of tâtonnement-style iterative procedures in infinite-dimensional settings. A parallel line of work examined the conditions under which Walrasian equilibria survive the introduction of aggregate uncertainty and incomplete markets, using monotone operator and lattice-theoretic techniques to characterise the equilibrium correspondence under perturbations. This body of work established rigorous mathematical foundations for equilibrium existence results that appear in applied macroeconomic and general equilibrium modelling without formal justification.

At IADU, Kratochvílová contributes mathematical foundations for the equilibrium analysis underlying the Institute's programme in heterogeneous-agent economies and mean field models. Her work connects classical fixed-point and monotone operator theory to the existence and characterisation of mean field equilibria in the Aiyagari-Huggett class of models, where the coupling between the Hamilton-Jacobi-Bellman equation and the Kolmogorov-Fokker-Planck equation requires rigorous treatment as a fixed-point problem in an infinite-dimensional space of measures. She supports the development of existence and approximation results that underpin the numerical methods deployed across IADU's quantitative macroeconomic research.