{
  "abstract": "We study two-player zero-sum stochastic games in which a stream of stage payoffs is evaluated by a translation-invariant charge on the set of stages. Every patient valuation, that is, every diffuse charge that obeys the time value of money principle, is translation-invariant, and by Mertens and Neyman each player has, for every $\\varepsilon>0$, a strategy that is $\\varepsilon$-optimal for all patient valuations simultaneously. We show that this robustness breaks down for translation-invariant charges. In the Big Match with $0$--$1$ payoffs, whose uniform value is $1/2$, every strategy of Player 1 is worthless: for every strategy of Player 1 and every $δ>0$, Player 2 has a pure reply, and there is a translation-invariant charge under which Player 1's payoff is less than $δ$. Consequently, the Big Match has no value with respect to all translation-invariant charges. This contrasts with finite Markov decision processes, where every stationary Blackwell optimal strategy is optimal for every translation-invariant charge. We pose questions on robust guarantees in general stochastic games and on optimality with respect to a fixed translation-invariant charge.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19646",
  "author_total": 1,
  "authors": [
    {
      "name": "Abraham Neyman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f63e2zb08es6t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19646",
  "fulltext_url": null,
  "id": "f63e2zb08es6t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19646",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Game Theory and Applications"
    ]
  ],
  "openalex": "W7222339936",
  "pdf_url": "https://arxiv.org/pdf/2610.19646",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f63e2zb08es6t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19646",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19646"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The Big Match under translation-invariant charges",
  "title_text": "The Big Match under translation-invariant charges",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/f63e2zb08es6t",
  "venue": "arXiv",
  "versions": []
}