{"ID":2837446,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.18923","arxiv_id":"2511.18923","title":"The local Turnpike Property in Mean Field Control and Games with quadratic Hamiltonian","abstract":"We study the local stability properties of solutions to ergodic and discounted mean field games systems, as the time horizon $T \\to +\\infty$, around stationary equilibria, when the Hamiltonian is quadratic. We replace the usual monotonicity of the coupling term with a weaker, local assumption on the stationary equilibrium (that need not be unique), stemming from a second-order strict positivity condition. This new stability assumption, together with a symmetry property of the system, allows us to derive an exponential turnpike property for those solutions that are close to the stationary one, whenever the spatial domain $Ω$ is either the flat torus $\\mathbb{T}^n$ or $\\mathbb{R}^n$. Finally, through a fixed-point argument, we establish the actual existence of stable solutions, both on the finite horizon $[0,T]$ and on the infinite horizon, in the periodic setting $Ω=\\mathbb{T}^n$, provided that the initial (and terminal) data are close enough to the stationary equilibrium.","short_abstract":"We study the local stability properties of solutions to ergodic and discounted mean field games systems, as the time horizon $T \\to +\\infty$, around stationary equilibria, when the Hamiltonian is quadratic. We replace the usual monotonicity of the coupling term with a weaker, local assumption on the stationary equilibr...","url_abs":"https://arxiv.org/abs/2511.18923","url_pdf":"https://arxiv.org/pdf/2511.18923v2","authors":"[\"Marco Cirant\",\"Nicolò De Bernardi\"]","published":"2025-11-24T09:31:27Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}