An optimal level of Stubbornness to win a soccer match
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866909470016143360 |
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| author | Pramanik, Paramahansa |
| author_facet | Pramanik, Paramahansa |
| contents | This study conceptualizes stubbornness as an optimal feedback Nash equilibrium within a dynamic setting. To assess a soccer player's performance, we analyze a payoff function that incorporates key factors such as injury risk, assist rate, passing accuracy, and dribbling ability. The evolution of goal-related dynamics is represented through a backward parabolic partial stochastic differential equation (BPPSDE), chosen for its theoretical connection to the Feynman-Kac formula, which links stochastic differential equations (SDEs) to partial differential equations (PDEs). This relationship allows stochastic problems to be reformulated as PDEs, facilitating both analytical and numerical solutions for complex systems. We construct a stochastic Lagrangian and utilize a path integral control framework to derive an optimal measure of stubbornness. Furthermore, we introduce a modified Ornstein-Uhlenbeck BPPSDE to obtain an explicit solution for a player's optimal level of stubbornness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An optimal level of Stubbornness to win a soccer match Pramanik, Paramahansa Optimization and Control Probability 93E03, 93E20 This study conceptualizes stubbornness as an optimal feedback Nash equilibrium within a dynamic setting. To assess a soccer player's performance, we analyze a payoff function that incorporates key factors such as injury risk, assist rate, passing accuracy, and dribbling ability. The evolution of goal-related dynamics is represented through a backward parabolic partial stochastic differential equation (BPPSDE), chosen for its theoretical connection to the Feynman-Kac formula, which links stochastic differential equations (SDEs) to partial differential equations (PDEs). This relationship allows stochastic problems to be reformulated as PDEs, facilitating both analytical and numerical solutions for complex systems. We construct a stochastic Lagrangian and utilize a path integral control framework to derive an optimal measure of stubbornness. Furthermore, we introduce a modified Ornstein-Uhlenbeck BPPSDE to obtain an explicit solution for a player's optimal level of stubbornness. |
| title | An optimal level of Stubbornness to win a soccer match |
| topic | Optimization and Control Probability 93E03, 93E20 |
| url | https://arxiv.org/abs/2501.18050 |