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Soccer Penalty and Game Theory

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Submitted By dichou
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Strategic interaction in sports

Penatly kicks in soccer

This short paper will explain how penalty kicks in soccer can be a example of strategic interaction. Strategic interaction[1] is a term that is broadly used to identify a process that seeks to involve several parties in achieving a common goal, relying heavily on effective communication to make progress in pursuing that goal. Everyday, people interact between each other and most of the time when people make a decision they think about the others and how they can react. Some decisions that one take depends sometimes on the choice of others. This paper is going to link social interaction with an economic principle.
Soccer being a low-scoring game, matches often finish on a draw and need to be decided by penalties. In soccer, penalty kicks put the goal keeper against a striker in a tough mental contest. Indeed, it takes less than a half second for the ball to touch the net unless the goalkeeper succeed in intercepting it which is definitely not enough time for the goalkeeper to analyze the trajectory of the ball. He must guess where the striker will shoot unless he does not have any chances.
Both striker and keeper must make delicate decisions. A left-footed strike will make a better shot to the left. The keeper will anticipate the shot and the striker would sometimes shot to the right because a even a weaker shot is better where the keeper does not stand. Same if the striker decide to toss a coin, the keeper would dive to the right side because he cannot guess where the ball will go and it is better to dive where the weak shot is coming. However, the striker should favorize his stronger feet again.
The two players participate in a zero-sum game with well defined strategies for both of them. The kicker's possibilities are to kick right, left or in the middle; the goalkeeper's actions can be to jump

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