On the one-shot two-person zero-sum game in football from a penalty kickerâ€™s perspective
Virtue Ekhosuehi ()
Operations Research and Decisions, 2018, vol. 3, 17-27
This paper models a penalty kickerâ€™s problem in football. The study takes into consideration the different directions in which the ball can be struck and goalkeepersâ€™ success at defending shots. The strategic form of the game that can be used to predict how the kicker should optimally randomise his strategies is modelled as a non-linear game-theoretic problem from a professional kickerâ€™s viewpoint. The equilibrium of the game (i.e., the pair of mutually optimal mixed strategies) is obtained from the game-theoretic problem by reducing it to a linear programming problem and the two-phase simplex method is adopted to solve this problem. The optimal solution to the game indicates that the kicker never chooses to kick the ball off target, to the goalpost or to the crossbar, but rather chooses to kick the ball in the opposite direction to the one where the goalkeeper is most likely to successfully defend from past history.
Keywords: linear programming; mixed strategy; penalty kick; strategic game; two-person zero-sum game. (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:wut:journl:v:3:y:2018:p:17-27:id:1375
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