{"paper":{"title":"\\epsilon-Nash Mean Field Game Theory for Nonlinear Stochastic Dynamical Systems with Major and Minor Agents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mojtaba Nourian, Peter E. Caines","submitted_at":"2012-09-25T17:04:22Z","abstract_excerpt":"This paper studies a large population dynamic game involving nonlinear stochastic dynamical systems with agents of the following mixed types: (i) a major agent, and (ii) a population of $N$ minor agents where $N$ is very large. The major and minor (MM) agents are coupled via both: (i) their individual nonlinear stochastic dynamics, and (ii) their individual finite time horizon nonlinear cost functions. This problem is approached by the so-called $\\epsilon$-Nash Mean Field Game ($\\epsilon$-NMFG) theory. A distinct feature of the mixed agent MFG problem is that even asymptotically (as the popula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5684","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}