{
  "abstract": "In this work we address a class of Mean-Field Game (MFG) systems on the flat torus $\\mathbb{T}^{d}$ in which individual agent incentives arise from macroscopic, distribution-dependent objectives governed by the Wasserstein-2 ($W_{2}$) distance. Taking the first variation (Lions derivative) of the Wasserstein-based macroscopic functional yields a coupled forward-backward system of Hamilton--Jacobi--Bellman (HJB) and Fokker--Planck (FP) equations featuring a nonlocal coupling driven by the Kantorovich optimal transport potential. As a primary case study, we formulate a large-scale attacker-defender attrition model aimed at protecting High-Value Units (HVUs). By defining population-wise attrition rates via the $W_{2}$ metric and casting the defense strategy as a Pareto-optimal McKean--Vlasov control problem, we derive a concrete HJB--FP system with a Kantorovich potential coupling. We prove the local-in-time existence of classical solutions for this system using Schauder's fixed-point theorem. Finally, we compute the MFG dynamics by combining the Sinkhorn algorithm with ResNet-based Physics-Informed Neural Networks (PINNs), and simulate two-dimensional attacker-defender engagements across diverse attrition parameters, control costs, and multi-HVU configurations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01616",
  "author_total": 5,
  "authors": [
    {
      "name": "Avetik Arakelyan"
    },
    {
      "name": "Davit Alaverdyan"
    },
    {
      "name": "Naira Hovakimyan"
    },
    {
      "name": "Isaac Kaminer"
    },
    {
      "name": "Tigran Bakaryan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3q9g7qdng0y5y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01616",
  "fulltext_url": null,
  "id": "3q9g7qdng0y5y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01616",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3q9g7qdng0y5y.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01616"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Mean Field Game Problem with Kantorovich Potential Coupling: An Attrition model",
  "title_text": "Mean Field Game Problem with Kantorovich Potential Coupling: An Attrition model",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/3q9g7qdng0y5y",
  "venue": "arXiv",
  "versions": []
}