IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v4y2023i3d10.1007_s43069-023-00247-y.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-023-00247-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s43069-023-00247-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Masud Alam, 2021. "Heterogeneous Responses to the U.S. Narrative Tax Changes: Evidence from the U.S. States," Papers 2107.13678, arXiv.org.
    2. Peter-J. Jost, 2021. "“The ball is round, the game lasts 90 minutes, everything else is pure theoryâ€," Journal of Sports Economics, , vol. 22(1), pages 27-74, January.
    3. Masud Alam, 2021. "Time Varying Risk in U.S. Housing Sector and Real Estate Investment Trusts Equity Return," Papers 2107.10455, arXiv.org.
    4. Paramahansa Pramanik & Alan M. Polansky, 2024. "Optimization of a dynamic profit function using Euclidean path integral," SN Business & Economics, Springer, vol. 4(1), pages 1-20, January.
    5. Vincenzo Alfano & Lorenzo Cicatiello & Giuseppe Lucio Gaeta & Michele Gallo & Francesca Rotondo, 2021. "Three is a Magic Number: Evidence on the Effects of the Application of the Three-Point Rule in Italy’s Serie A," Journal of Sports Economics, , vol. 22(3), pages 329-356, April.
    6. Ralf Dewenter & Julian Emami Namini, 2013. "How to Make Soccer More Attractive? Rewards for a Victory, the Teams' Offensiveness, and the Home Bias," Journal of Sports Economics, , vol. 14(1), pages 65-86, February.
    7. Dilger, Alexander & Froböse, Gerrit, 2018. "Effects of the three-point rule in German amateur football," Discussion Papers of the Institute for Organisational Economics 3/2018, University of Münster, Institute for Organisational Economics.
    8. Lee Yoong Hon & Rasyad A. Parinduri, 2016. "Does the Three-Point Rule Make Soccer More Exciting? Evidence From a Regression Discontinuity Design," Journal of Sports Economics, , vol. 17(4), pages 377-395, May.
    9. Richard Duhautois & Romain Eyssautier, 2016. "La victoire à trois points dans le football a-t-elle rendu les équipes plus offensives ?," Revue économique, Presses de Sciences-Po, vol. 67(6), pages 1245-1254.
    10. Liam J.A. Lenten & Jan Libich & Petr Stehlík, 2013. "Policy Timing and Footballers' Incentives," Journal of Sports Economics, , vol. 14(6), pages 629-655, December.
    11. Franck Egon & Theiler Philipp, 2012. "One for Sure or Maybe Three: Empirical Evidence for Overtime Play from a Comparison of Swiss Ice Hockey and the NHL," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 232(3), pages 210-223, June.
    12. Rasyad A Parinduri & Yoong Hon Lee & Kung Ming Tiong, 2019. "The effects of bigger rewards in individual tournaments on efforts and risk taking: evidence from chess," Oxford Economic Papers, Oxford University Press, vol. 71(4), pages 979-995.
    13. Gebrenegus Ghilagaber & Parfait Munezero, 2020. "Bayesian change-point modelling of the effects of 3-points-for-a-win rule in football," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(2), pages 248-264, January.
    14. Turansick, Christopher, 2022. "Identification in the random utility model," Journal of Economic Theory, Elsevier, vol. 203(C).
    15. Robert Butler & Liam J. A. Lenten & Patrick Massey, 2020. "Bonus incentives and team effort levels: Evidence from the “Field”," Scottish Journal of Political Economy, Scottish Economic Society, vol. 67(5), pages 539-550, November.
    16. Nicolau, Juan L., 2012. "The effect of winning the 2010 FIFA World Cup on the tourism market value: The Spanish case," Omega, Elsevier, vol. 40(5), pages 503-510.
    17. Xie, Erhao, 2021. "Empirical properties and identification of adaptive learning models in behavioral game theory," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 798-821.
    18. Manuel Frondel & Stefanie Schubert, 2016. "Sieg der Defensive? Evidenz für die 1. Deutsche Fußball-Liga [Victory of the defense? Evidence from the 1. German Football League]," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(4), pages 225-246, December.
    19. S. Cerreia-Vioglio & F. Maccheroni & M. Marinacci & A. Rustichini, 2017. "Multinomial logit processes and preference discovery: inside and outside the black box," Working Papers 615, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    20. Ziv Hellman & Yehuda John Levy, 2020. "Equilibria Existence in Bayesian Games: Climbing the Countable Borel Equivalence Relation Hierarchy," Working Papers 2020_15, Business School - Economics, University of Glasgow.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:snopef:v:4:y:2023:i:3:d:10.1007_s43069-023-00247-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.