{"ID":6138862,"CreatedAt":"2026-07-09T01:07:32.349475501Z","UpdatedAt":"2026-07-10T19:02:20.347454606Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.06742","arxiv_id":"2607.06742","title":"Linear-Quadratic Mean Field Games with Hybrid Local-Global Interactions on Manifolds","abstract":"This paper studies linear-quadratic mean field games on compact Riemannian manifolds with a hybrid interaction topology. The network structure is a superposition of a deterministic graph for local geometric connectivity and a stochastic directed graph for non-local interactions. The global graph is constructed via random sampling based on a continuous kernel $K$. The out-degree of each node scales as $Θ(\\log N)$ or as $Θ(N)$ to represent a sparse or dense network, respectively. In the infinite-population limit, the continuum system is governed by a coupled system of forward-backward partial differential equations, where the dynamics of the expected state incorporate the integral operator corresponding to the non-local sampling. The existence of a Nash equilibrium is established for this limit system. Furthermore, the approximation error is analyzed using operator concentration inequalities and analytic semigroup theory. Non-asymptotic high-probability error bounds between the finite-population empirical state and the continuum limit are derived. The convergence rates differ depending on the two topological regimes. Under the dense regime, the tracking error exhibits a polynomial decay rate dependent on the manifold dimension and Sobolev regularity, while under the sparse regime, the error decays at a rate of $\\mathcal{O}((\\log N)^{-1/2})$.","short_abstract":"This paper studies linear-quadratic mean field games on compact Riemannian manifolds with a hybrid interaction topology. The network structure is a superposition of a deterministic graph for local geometric connectivity and a stochastic directed graph for non-local interactions. The global graph is constructed via rand...","url_abs":"https://arxiv.org/abs/2607.06742","url_pdf":"https://arxiv.org/pdf/2607.06742v1","authors":"[\"Tao Zhang\"]","published":"2026-07-07T19:12:21Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}