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

Paramahansa Pramanik () and Alan M. Polansky ()
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Paramahansa Pramanik: University of South Alabama
Alan M. Polansky: Northern Illinois University

SN Operations Research Forum, 2023, vol. 4, issue 3, 1-39

Abstract: 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.

Keywords: Liouville-like quantum gravity; Soccer game; Infinitary logic and quantum formula; Stochastic goal dynamics; Lefschetz-Hopf fixed point theorem; Feynman-type path integral; Primary 60H05; Secondary 81Q30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s43069-023-00247-y

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