{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T06:56:24Z","timestamp":1790751384461,"version":"4.1.0"},"reference-count":46,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012325","name":"National Office for Philosophy and Social Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012325","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Public Health"],"abstract":"<jats:sec>\n                    <jats:title>Introduction<\/jats:title>\n                    <jats:p>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.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>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.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>\n                      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\u2014defined as the first normalized lead time capturing 80% of the cooperative warning benefit available between\n                      <jats:italic>L<\/jats:italic>\n                      = 0 and\n                      <jats:italic>L<\/jats:italic>\n                      = 6\u2014ranges 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                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Discussion<\/jats:title>\n                    <jats:p>The Nash\u2014Stackelberg 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.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.3389\/fpubh.2026.1986768","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T06:05:32Z","timestamp":1790748332000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Coordinating extreme-heat adaptation at mega-sporting events: early warning and cost sharing in a multi-actor differential game"],"prefix":"10.3389","volume":"14","author":[{"given":"Jiaxin","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Physical Education, Hunan Normal University","place":["Changsha, China"]},{"name":"College of Physical Education, University of South China","place":["Hengyang, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Siqing","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Physical Education, Zhejiang Chinese Medical University","place":["Hangzhou, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junrong","family":"Lei","sequence":"additional","affiliation":[{"name":"College of Physical Education, Hunan Normal University","place":["Changsha, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,9,30]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1016\/S0140-6736(21)01208-3","article-title":"Hot weather and heat extremes: health risks","volume":"398","author":"Ebi","year":"2021","journal-title":"Lancet."},{"key":"B2","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1016\/j.jsams.2024.04.015","article-title":"The impact of extreme heat on mass-gathering sporting events: implications for Australia and other countries","volume":"27","author":"Mason","year":"2024","journal-title":"J Sci Med Sport."},{"key":"B3","doi-asserted-by":"publisher","first-page":"1044","DOI":"10.1136\/bjsports-2024-108131","article-title":"Efficacy of the FIFA cooling break heat policy during an intermittent treadmill football simulation in hot conditions in trained males","volume":"58","author":"Brown","year":"2024","journal-title":"Br J Sports Med."},{"key":"B4","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1007\/s40279-025-02325-z","article-title":"Effects of pre-cooling and cooling breaks on thermoregulatory, physiological and match running responses during football in moderate and hot temperatures","volume":"56","author":"Schwarz","year":"2026","journal-title":"Sports Med."},{"key":"B5","unstructured":"Players to Benefit from Hydration Breaks at FIFA World Cup 2026\n          \n          2025"},{"key":"B6","unstructured":"Advancing heat-health preparedness during mass gatherings: Practical tools\n          \n          2026"},{"key":"B7","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1007\/s00484-025-02852-4","article-title":"Extreme heat risk and the potential implications for the scheduling of football matches at the 2026 FIFA world cup","volume":"69","author":"Mullan","year":"2025","journal-title":"Int J Biometeorol."},{"key":"B8","doi-asserted-by":"publisher","first-page":"26976","DOI":"10.1038\/s41598-024-77540-1","article-title":"Prospective heat stress risk assessment for professional soccer players in the context of the 2026 FIFA world cup","volume":"14","author":"Lindner-Cendrowska","year":"2024","journal-title":"Sci Rep."},{"key":"B9","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1136\/bjsports-2022-105942","article-title":"IOC consensus statement on recommendations and regulations for sport events in the heat","volume":"57","author":"Racinais","year":"2023","journal-title":"Br J Sports Med."},{"key":"B10","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/s40279-017-0808-x","article-title":"Heat acclimation decay and re-induction: a systematic review and meta-analysis","volume":"48","author":"Daanen","year":"2018","journal-title":"Sports Med."},{"key":"B11","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1007\/s00038-013-0465-2","article-title":"Evaluating the effectiveness of heat warning systems: systematic review of epidemiological evidence","volume":"58","author":"Toloo","year":"2013","journal-title":"Int J Public Health."},{"key":"B12","doi-asserted-by":"publisher","first-page":"e20432","DOI":"10.1016\/j.heliyon.2023.e20432","article-title":"Disaster response strategies of governments and social organizations: from the perspective of infrastructure damage and asymmetric resource dependence","volume":"9","author":"Yang","year":"2023","journal-title":"Heliyon."},{"key":"B13","doi-asserted-by":"publisher","first-page":"1620099","DOI":"10.3389\/fpubh.2025.1620099","article-title":"Does government purchase commitment promote regular production to emergency co-production? 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