{"paper":{"title":"Linear-Quadratic Mean Field Games with Hybrid Local-Global Interactions on Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Tao Zhang","submitted_at":"2026-07-07T19:12:21Z","abstract_excerpt":"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 $\\Theta(\\log N)$ or as $\\Theta(N)$ 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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06742","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06742/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}