Issue: 2018/Vol.28/No.3, Pages 17-27
ON THE ONE-SHOT TWO-PERSON ZERO-SUM GAME IN FOOTBALL FROM A PENALTY KICKER’S PERSPECTIVE
Virtue Ekhosuehi
Cite as: V. Ekhosuehi. On the one-shot two-person zero-sum game in football from a penalty kicker’s perspective. Operations Research and Decisions 2018: 28(3), 17-27. DOI 10.5277/ord180302
Abstract
A penalty kicker’s problem in football has been modelled. The study took into consideration different directions in which the ball can be struck and goalkeepers’ success at defending shots. The strategic form of the game that can be used to predict how the kicker should optimally randomise his strategies has been modelled as a non-linear game-theoretic problem from a professional kicker’s viewpoint. The equilibrium of the game (i.e., the pair of mutually optimal mixed strategies) was obtained from the game-theoretic problem by reducing it to a linear programming problem and the two-phase simplex method was 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
Received: 3 March 2018 Accepted: 15 August 2018