{
  "abstract": "We study the problem of computing the tightest \\(α\\)-potential approximation of a general-sum game over continuous action spaces, within a prescribed class of potential functions and when each player has access only to its own utility function. The difficulty is twofold: the approximation error involves a worst-case search over an infinite set of unilateral deviations, and the required utility information is distributed across players. For a linear-in-parameters potential class, we use an exact finite-tuple reformulation that separates the problem into a global outer search over deviation tuples and distributed convex inner problems. We develop a primal--dual inner oracle tailored to this structure and establish a uniform one-sided accuracy guarantee. This oracle can be combined with global outer search to obtain an end-to-end guarantee on the outer optimization error. We also develop a projected zeroth-order outer method as a computationally lighter alternative for higher-dimensional problems. Numerical experiments illustrate the accuracy--computation tradeoff between the two outer-search methods and show that the proposed optimization framework can improve upon analytical \\(α\\)-potential constructions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05516",
  "author_total": 2,
  "authors": [
    {
      "name": "Yifei Chen"
    },
    {
      "name": "Chinmay Maheshwari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dth5k55d9m912.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05516",
  "fulltext_url": null,
  "id": "dth5k55d9m912",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05516",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.GT"
    ],
    [
      "arxiv",
      "cs.MA"
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      "arxiv",
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      "arxiv",
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      "openalex",
      "1803|Game Theory and Applications"
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  "openalex": "W7220689965",
  "pdf_url": "https://arxiv.org/pdf/2610.05516",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dth5k55d9m912.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05516",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05516"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Distributed Algorithms for $α$-Potential Functions in General-Sum Games",
  "title_text": "Distributed Algorithms for α-Potential Functions in General-Sum Games",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dth5k55d9m912",
  "venue": "arXiv",
  "versions": []
}