A uniqueness result for finite-state mean field games with non-separable Hamiltonian

Alekos Cecchin; Luca Di Persio; Nicola Fraccarolo

A uniqueness result for finite-state mean field games with non-separable Hamiltonian

Optimization and Control 2026-04-20 v1 Probability

Authors: Alekos Cecchin , Luca Di Persio , Nicola Fraccarolo

Abstract

We study a class of continuous-time mean field games on a finite state space with transition rates depending on the population distribution, leading to a non-separable Hamiltonian. In this setting, classical Lasry--Lions monotonicity arguments do not apply directly. We establish a new uniqueness result on arbitrary time horizons under a combination of strong monotonicity assumptions on the costs and quantitative bounds on the interaction term in the dynamics.

Keywords

mean field games finite state space non-separable hamiltonian uniqueness lasry-lions monotonicity

Cite

@article{arxiv.2607.22537,
  title  = {A uniqueness result for finite-state mean field games with non-separable Hamiltonian},
  author = {Alekos Cecchin and Luca Di Persio and Nicola Fraccarolo},
  journal= {arXiv preprint arXiv:2607.22537},
  year   = {2026}
}