Mixed-Strategy Nash Equilibrium and Soccer Players A Case Study of Penalty Kicks

Subject Areas : Labor and Demographic Economics

morteza sameti ^{1 *} , mehdi fath abadi ² , kamran kasraei ³

1 - استاد دانشگاه اصفهان
2 - دانشجوی دکتری دانشگاه آزاد واحد خوراسگان
3 - دانشجوی دکتری دانشگاه آزاد اسلامی واحد خوراسگان

Received: 2015-04-21 Accepted : 2015-04-21 Published : 2011-04-01

Keywords: Soccer, Game Theory Mixed Strategy, Nash equilibrium, Penalty Kicks,

Abstract :

 Mixed strategy Nash equilibrium (MSNE) is a concept commonly used in Game Theory. The game between the kicker and goalkeeper in soccer penalty kicks is a real game used to examine the application of the MSNE concept or the rate of its accuracy. The data were collected on the direction of kicks and jumps in 106 penalties kicked in Premier League of Iran and the predictions of the model analyzed. The observations represented that given the probability distribution of kick direction, the optimal strategy for goalkeepers is to stay in the center of the goal; but the goalkeepers, almost always, jumped to the right or left. Finally, the “left-left” pattern is the most frequent and have the greatest number of observations.

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