My research lies at the intersection of optimal control, optimal transport, calculus of variations, and partial differential equations, with a particular focus on mean-field games and mean-field type control as a framework for modeling strategic decision-making in large populations.
Mean-field games provide tractable approximations of Nash equilibria in large-scale differential games by exploiting mean-field limits.
Mean-field type control provides tractable approximations of socially optimal strategies in large-scale differential games by directly controlling the population distribution through mean-field limits.
My earlier work focused on price-formation models in mean-field games, involving coupled dynamics for the value function, population density, and an endogenous price variable. I studied these models using a combination of analytical techniques and numerical methods.
More recently, I have extended this line of research to Stackelberg mean-field games, motivated by incentive mechanism design and hierarchical decision-making. These extensions introduce new mathematical challenges and are particularly relevant for regulated transportation systems, energy systems, and other large-scale population systems.
Across these settings, I am motivated by the interplay between theory and applications, and by the development of computational methods that combine traditional techniques with machine-learning-based approaches to gain insight into complex systems governed by strategic interaction and uncertainty.
Julian Gutierrez P., M. Umar B. Niazi. Stackelberg Mean-Field Games for Incentive-Driven Eco-Driving Policies, 2026.
Julian Barreiro, Julian Gutierrez P., and Hamidou Tembine. A Comparative Introduction to Mean-Field Games and Mean-Field Type Control, 2026.
Roxana Dumitrescu, Julian Gutierrez P., and Peter Tankov. Multiscale mean-field games with common noise, 2025.
Julian Gutierrez P. and Redouane Silvente. Parametric and Generative Forecasts of Day-Ahead Market Curves for Storage Optimization, 2025. (Submitted to Energy Economics).
We introduce the so-called potential approach for the deterministic price-formation mean-field game model. Using Poincaré Lemma, we obtain a variational problem for a single function (instead of the original three). Our approach relies on the calculus of variations theory.
We extend the machine learning-based approach introduced in our previous work to include the price formation problem with common noise, using a posteriori estimates to guarantee convergence.
We use machine learning to solve the deterministic price-formation mean-field games model numerically. We develop a posteriori estimates to guarantee the training's convergence. Our approach relies on the calculus of variations theory and recurrent neural networks.
We consider the finite players' game with common noise and its mean-field limit. The price arises as a Lagrange multiplier of a market-clearing condition. Our approach relies on the calculus of variations theory.
We merge the potential approach and machine learning methods to solve the deterministic and stochastic mean-field game price formation models. Our approach relies on the (stochastic) calculus of variations theory and recurrent neural networks.
We study the deterministic price formation problem using the Aubry-Mather theory. We obtain a variational problem on a space of measures. Our approach relies on the optimal transport (duality) theory.
We propose the stochastic version (common noise) of the price-formation mean-field game model introduced by Gomes & Saúde in the deterministic setting. Our approach relies on the optimal control theory.