Coordinating extreme-heat adaptation at mega-sporting events: early warning and cost sharing in a multi-actor differential game
- 1College of Physical Education, Hunan Normal University , ,
- 2Department of Physical Education, Zhejiang Chinese Medical University , ,
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.
Methods: 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.
Results: 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.
Discussion: 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.
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BibTeX
@article{zhang2026coordinating,
title = {{Coordinating extreme-heat adaptation at mega-sporting events: early warning and cost sharing in a multi-actor differential game}},
author = {Jiaxin Zhang and Siqing Zhang and Junrong Lei},
journal = {Frontiers in public health},
year = {2026},
month = sep,
doi = {10.3389/fpubh.2026.1986768},
url = {https://europepmc.org/article/PMC/PMC13662186},
note = {CC BY},
}
RIS
TY - JOUR
TI - Coordinating extreme-heat adaptation at mega-sporting events: early warning and cost sharing in a multi-actor differential game
AU - Jiaxin Zhang
AU - Siqing Zhang
AU - Junrong Lei
PY - 2026
DA - 2026/09/30
JO - Frontiers in public health
DO - 10.3389/fpubh.2026.1986768
UR - https://europepmc.org/article/PMC/PMC13662186
AB - 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. Methods: 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. Results: 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. Discussion: 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.
SN - 2296-2565
ER -