Mixed Strategy Paper

# Mixed Strategy Paper - Ryan Ingalls Introduction This test...

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Ryan Ingalls Introduction This test is looking at the soccer penalty shot. These penalty shots are a one on one game, shooter against goal keeper; the shooter trying to guess which side the goalkeeper will not defend, and the goalkeeper trying to guess the side the shooter will shoot. Another nice simplicity of this game is that it occurs simultaneously; the ball only takes .2-.3 seconds from the kick to reach the net, so if the goalie were to make a decision after the kick it would be too late. For data we have 372 penalty shots taken, either taken to left or the right, and we are going to see if the success probabilities are the same for shooting to either side of the net. Mixing Probability Success Probabilities Goalie Left Goalie Right Kick Left .632 .941 Kick Right .895 .44 Best Responses Goalies Best Response Shooters Best Response If Shooter Goalie Goes If Goalie Shooter Goes Goes Left Left Goes Left Right Goes Right Right Goes Right Left No Combination has both parties choosing the best response

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## This note was uploaded on 10/17/2011 for the course ISS 328 taught by Professor Martin during the Spring '10 term at Michigan State University.

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Mixed Strategy Paper - Ryan Ingalls Introduction This test...

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