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Scoring a Goal Optimally in a Soccer Game Under Liouville-Like Quantum Gravity Action

Author

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  • Paramahansa Pramanik

    (University of South Alabama)

  • Alan M. Polansky

    (Northern Illinois University)

Abstract

In this paper, we present a new stochastic differential game-theoretic model of optimizing strategic behavior associated with a soccer player under the presence of stochastic goal dynamics by using a Feynman-type path integral approach, where the action of a player is on a $$\sqrt{8/3}$$ 8 / 3 -Liouville quantum gravity surface. Strategies to attack the oppositions have been used as control variables with extremes like excessive defensive and offensive strategies. Before determining the optimal strategy, we first establish an infinitary logic to deal with infinite variables on the strategy space, and then, a quantum formula of this logic is developed. As in a competitive tournament, all possible standard strategies to score goals are known to the opposition team, a player’s action is stochastic, and they would have some comparative advantages to score goals. Furthermore, conditions like uncertainties due to rain, dribbling and passing skills of a player, time of the game, home crowd advantages, and asymmetric information of action profiles are considered to determine the optimal strategy.

Suggested Citation

  • Paramahansa Pramanik & Alan M. Polansky, 2023. "Scoring a Goal Optimally in a Soccer Game Under Liouville-Like Quantum Gravity Action," SN Operations Research Forum, Springer, vol. 4(3), pages 1-39, September.
    • Handle: RePEc:spr:snopef:v:4:y:2023:i:3:d:10.1007_s43069-023-00247-y
    DOI: 10.1007/s43069-023-00247-y
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    References listed on IDEAS

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    1. Mira Frick & Ryota Iijima & Tomasz Strzalecki, 2019. "Dynamic Random Utility," Econometrica, Econometric Society, vol. 87(6), pages 1941-2002, November.
    2. Ricardo Manuel Santos, 2014. "Optimal Soccer Strategies," Economic Inquiry, Western Economic Association International, vol. 52(1), pages 183-200, January.
    3. Giancarlo Moschini, 2010. "Incentives And Outcomes In A Strategic Setting: The 3‐Points‐For‐A‐Win System In Soccer," Economic Inquiry, Western Economic Association International, vol. 48(1), pages 65-79, January.
    4. Hua, Lei & Polansky, Alan & Pramanik, Paramahansa, 2019. "Assessing bivariate tail non-exchangeable dependence," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    5. Dobson, Stephen & Goddard, John, 2010. "Optimizing strategic behaviour in a dynamic setting in professional team sports," European Journal of Operational Research, Elsevier, vol. 205(3), pages 661-669, September.
    6. Paramahansa Pramanik, 2020. "Optimization of Market Stochastic Dynamics," SN Operations Research Forum, Springer, vol. 1(4), pages 1-17, December.
    7. Ziv Hellman & Yehuda John Levy, 2019. "Measurable Selection for Purely Atomic Games," Econometrica, Econometric Society, vol. 87(2), pages 593-629, March.
    8. Alexander Dilger & Hannah Geyer, 2009. "Are Three Points for a Win Really Better Than Two?," Journal of Sports Economics, , vol. 10(3), pages 305-318, June.
    9. Polansky, Alan M. & Pramanik, Paramahansa, 2021. "A motif building process for simulating random networks," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
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