{
  "abstract": "Introduction: Coordinating extreme-heat adaptation at mega-sporting events is a time-dependent public health challenge because public authorities, event organizers, and participating teams control different protective measures while heat risk evolves over a finite competition horizon. Existing sport-heat research describes exposure and prevention yet provides limited guidance on how adaptation should be timed, coordinated, and financed across responsible institutions.\n\nMethods: We develop a three-actor linear-quadratic differential game with gross event heat-risk pressure and accumulated adaptive capacity as state variables. Open-loop Nash, government-led Stackelberg, and cooperative solutions are evaluated under four normalized heat-shock structures. Early-warning lead time enters through a piecewise information structure, and a budget-balanced cost-sharing rule supports decentralized implementation of the cooperative path.\n\nResults: In the baseline late-peak scenario with a lead time of three normalized units, cooperation reduces modeled social loss by 21.9% relative to Nash and 23.1% relative to government-led Stackelberg; peak residual heat-risk pressure falls by 28.0% and 28.7%, respectively. Under the baseline parameterization, social loss in the government-led regime exceeds the Nash value by 1.6%. Earlier warning lowers loss, residual pressure, and peak effort, although its marginal value declines once a usable preparation window is available. Across the tested combinations of warning lead time and organizer mitigation efficiency, cooperative social gains range from 16.7 to 24.4%. Within the model, the effective preparation-window threshold—defined as the first normalized lead time capturing 80% of the cooperative warning benefit available between L = 0 and L = 6—ranges from 2.2 to 2.6 and responds mainly to heat-shock duration. Cooperation also shifts effort toward organizer-controlled measures, while cost sharing compensates the organizer for carrying greater responsibility despite receiving the smallest uncompensated private gain.\n\nDiscussion: The Nash—Stackelberg ordering is conditional on the government-first sequence, actor-specific objectives, and parameter values used in the analysis. Within the normalized model, these findings indicate that coordinated extreme-heat adaptation can benefit from aligning actor objectives and linking warning information to actionable time, institutional capability, and financing. Event-specific application requires empirical calibration.",
  "abstract_shown": true,
  "affiliations": [
    "College of Physical Education, Hunan Normal University , ,",
    "Department of Physical Education, Zhejiang Chinese Medical University , ,"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jiaxin Zhang"
    },
    {
      "affs": [
        1
      ],
      "name": "Siqing Zhang"
    },
    {
      "affs": [
        0
      ],
      "name": "Junrong Lei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8jg815ns17b8t.bib",
  "cited_by": 0,
  "doi": "10.3389/fpubh.2026.1986768",
  "fulltext_url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13662186/?tool=EBI",
  "id": "8jg815ns17b8t",
  "issns": [
    "2296-2565"
  ],
  "landing_url": "https://europepmc.org/article/PMC/PMC13662186",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2737|Thermoregulation and physiological responses"
    ]
  ],
  "openalex": "W7214930017",
  "pdf_url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13662186/pdf/?tool=EBI",
  "pmcid": "PMC13662186",
  "pmid": null,
  "published": "2026-09-30",
  "publisher": "Frontiers Media SA",
  "ris": "https://research.draconitic.com/paper/8jg815ns17b8t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:21Z",
      "native_id": "PMC:PMC13662186",
      "source": "europepmc",
      "url": "https://europepmc.org/article/PMC/PMC13662186"
    },
    {
      "first_seen": "2026-10-30T12:20:22Z",
      "native_id": "10.3389/fpubh.2026.1986768",
      "source": "crossref",
      "url": "https://www.frontiersin.org/articles/10.3389/fpubh.2026.1986768/full"
    }
  ],
  "subjects": [
    {
      "field": "medicine",
      "origin": "openalex:2737|Thermoregulation and physiological responses",
      "subfield": "physiology"
    }
  ],
  "title": "Coordinating extreme-heat adaptation at mega-sporting events: early warning and cost sharing in a multi-actor differential game",
  "title_text": "Coordinating extreme-heat adaptation at mega-sporting events: early warning and cost sharing in a multi-actor differential game",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:20:22Z",
  "url": "https://research.draconitic.com/paper/8jg815ns17b8t",
  "venue": "Frontiers in public health",
  "versions": []
}