Stubbornness as Control in Professional Soccer Games: A BPPSDE Approach
Abstract
:1. Introduction
2. Background Framework
2.1. General Notation
2.2. Probabilistic Construction
2.3. Existence and Uniqueness of a Solution of the BPPSDE
- (i)
- is -measurable and strongly continuous with respect to s for any and for almost surely , and the terminal condition .
- (ii)
- for every and ,Define with corresponding norm .
- (i)
- , the Sobolev space of functions that are square-integrable, have square-integrable weak derivatives, and vanish on the boundary of .
- (ii)
- , the space of square-integrable functions.
- (iii)
- , the dual space of , consisting of continuous linear functionals on .
2.4. Payoff Function
3. Computation of the Optimal Stubbornness
4. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
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Pramanik, P. Stubbornness as Control in Professional Soccer Games: A BPPSDE Approach. Mathematics 2025, 13, 475. https://doi.org/10.3390/math13030475
Pramanik P. Stubbornness as Control in Professional Soccer Games: A BPPSDE Approach. Mathematics. 2025; 13(3):475. https://doi.org/10.3390/math13030475
Chicago/Turabian StylePramanik, Paramahansa. 2025. "Stubbornness as Control in Professional Soccer Games: A BPPSDE Approach" Mathematics 13, no. 3: 475. https://doi.org/10.3390/math13030475
APA StylePramanik, P. (2025). Stubbornness as Control in Professional Soccer Games: A BPPSDE Approach. Mathematics, 13(3), 475. https://doi.org/10.3390/math13030475