{
  "abstract": "We study evolutionary Nash equilibrium learning in large populations whose payoffs are generated by dynamic mechanisms. Counterclockwise dissipativity (CCW) provides a passivity-like framework for establishing learning/convergence under a broad convex cone of so-called well-behaved learning rules satisfying a natural payoff-alignment condition according to which, away from equilibria, the population's state (strategic profile) moves in a direction positively correlated with the payoffs. The cone is closed under conic combinations and encompasses a broad range of noise-free rules, including discontinuous rules such as best response, imitative rules such as the replicator rule that is not $δ$-passive, and all noise-free $δ$-passive rules. Existing CCW results require no knowledge of the particular rule, but establish convergence without providing a Lyapunov function or Lyapunov stability. We develop a methodology that closes this gap by constructing rule-independent Lyapunov functions from CCW storage functions of the payoff mechanism. For a nonlinear class of anticipatory mechanisms, in which agents compare current payoffs with those associated with a smoothed population state, we show that a storage can be derived as a Bregman divergence. The resulting Lyapunov function combines a potential gap with this divergence and establishes global asymptotic stability. A congestion game with a nonlinear congestion-growth toll illustrates the results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04086",
  "author_total": 2,
  "authors": [
    {
      "name": "Tzuyu Jeng"
    },
    {
      "name": "Nuno C. Martins"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4a3meabe4qbyk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04086",
  "fulltext_url": null,
  "id": "4a3meabe4qbyk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04086",
  "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.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Game Theory and Applications"
    ]
  ],
  "openalex": "W7220651164",
  "pdf_url": "https://arxiv.org/pdf/2610.04086",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4a3meabe4qbyk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04086",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04086"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Learning in Large Populations With Anticipatory Payoffs: Bregman Meets Willems and Lyapunov",
  "title_text": "Learning in Large Populations With Anticipatory Payoffs: Bregman Meets Willems and Lyapunov",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4a3meabe4qbyk",
  "venue": "arXiv",
  "versions": []
}