My research focuses on the existence of long-term equilibrium in dynamic games, that is, the existence of equilibrium payoffs and equilibrium strategies for very patient players. In particular, I have studied the case of stochastic games with imperfect observation. I am also interested in the link between discrete-time dynamic models, continuous-time dynamic models and Hamilton-Jacobi equations (differential games, stochastic homogenization, Mean Field Games). Recently, I started working on Prophet and Secretary problems.
Stochastic games:
1. Mertens conjectures in absorbing games with incomplete information.
Annals of Applied Probability, 2024, 34(2), 1948-1986.
2. Time-Dependent Blackwell Approachability and Application to Absorbing Games (joint work with J. Kwon and Y. Wan), 2024. Preprint Arxiv
3. Constant payoff in zero-sum stochastic games (joint work with M. Oliu-Barton and O. Catoni).
Annales de l'IHP: Probabilités et Statistiques, 2021, 57(4), 1888-1900.
4. Limit equilibrium payoffs in Stochastic Games (joint work with J. Renault).
Mathematics of Operations Research, 2020, 45(3), 797-1192.
5. Hidden stochastic games and limit equilibrium payoffs (joint work with J. Renault).
Games and Economic Behavior, 2020, 124, 122-139.
6. Tauberian theorems for general iterations of operators: applications to zero-sum stochastic games.
Games and Economic Behavior, 2018, 108, 486-503.
Annals of Probability, 2016, 44(2), 1107-1133.
8. General limit value in stochastic games.
International J. Game Theory, 2016, 45(1), 353-374.
9. A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games.
Mathematics of Operations Research, 2016, 41(4), 1522-1534.
10. Stochastic games with signals (survey, joint work with E. Solan).
Advances in Dynamic and Evolutionary Games, 2016, 14, 77-94, Springer.
Continuous-time Games and Hamilton-Jacobi equations:
Stochastic homogenization of HJ equations: a differential game approach (joint work with A. Davini and R. Saona), 2024. Preprint arXiv.
Bayesian Learning in Mean Field Games (joint work with E. Shmaya), 2024. To appear in Siam Journal on Control and Optimization.
Percolation Games (joint work with G. Garnier). Mathematics of Operations Research, 2023, 48(4), 2156-2166.
4. An example of failure of stochastic homogenization for viscous Hamilton-Jacobi equations without convexity (joint work with W. Feldman and J-B. Fermanian). Journal of Differential Equations, 2021, 280, 464-476.
5. Convergence of the solutions of the discounted Hamilton-Jacobi equation: a counterexample.
Journal de Mathématiques Pures et Appliquées, 2019, 128, 330-338.
6. Stochastic homogenization of nonconvex Hamilton-Jacobi equations: a counterexample.
Communications on Pure and Applied Mathematics, 2017, 70(9), 1798-1809.
Percolation Games:
The Game Behind Oriented Percolation (joint work with A. Sepulveda), 2024. Preprint arXiv.
Zero-sum Random Games on Directed Graphs (joint work with L. Attia, L. Lichev, D. Mitsche and R. Saona), published online in Dynamic Games and Applications, 2025.
Percolation Games (joint work with G. Garnier). Mathematics of Operations Research, 2023, 48(4), 2156-2166.
Prophet inequalities:
1. Prophet Inequalities Require Only a Constant Number of Samples (joint work with A. Cristi).
Proceedings of the 56th Annual ACM Symposium on Theory of Computing, 2024, 491-502.
2. Prophet secretary through blind strategies (joint work with J. Correa and R. Saona).
Mathematical Programming, 2021, 190, 483-521.
A conference version of this paper has been published in
Proc. of the Thirtieth Annual ACM-SIAM Symp. on Disc. Alg., 2019, 1946-503.
3. Streaming Algorithms for Online Selection Problems (joint work with J. Correa, P. Dütting, F. Fischer and K. Schewior), ITCS 2021.
Partially Observable Markov Decision Processes:
1. Decidability of Ergodic Unobservable Markov Decision Processes (joint work with K. Chatterjee, D. Lurie and R. Saona). Preprint arXiv.
2. Finite-memory strategies in POMDPs with long-run average objectives (joint work with K. Chatterjee and R. Saona).
Mathematics of Operations Research, 2022, 47(1), 100-119.
3. History-dependent evaluations in POMDPs (joint work with X. Venel).
Siam Journal on Control and Optimization, 2021, 59(2), 1730-1755.
4. Pathwise uniform value in gambling houses and Partially Observable Markov Decision Processes (joint work with X. Venel).
SIAM Journal on Control and Optimization, 2016, 54(4), 1859-2233.
Global Games:
Observing and Shaping the Market: The Dilemma of Central Banks (joint work with R. Baeriswyl and C. Cornand).
Journal of Money, Credit and Banking, 2020, 52(8), 1973-2005.