3. Consider the case of a penalty kick in football. Suppose that the striker has only...

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3. Consider the case of a penalty kick in football. Suppose that the striker has only three choices: to kick the ball to the left, right, or center of the goal. Suppose the goalkeeper has only three options: to dive to the left or right, or stay in the center. Suppose that whenever the goalkeeper correctly guesses the striker's choice, he stops the penalty. In any other case, a goal is scored. Suppose that if the goal is scored, the payoffs are 1 for the striker and -1 for the goalkeeper 1 and that if the penalty is stopped, the payoffs are 1 for the goalkeeper and -1 for the striker. Represent this situation as a simultaneous-move game in normal form, determine the best re- sponses of both players and find all their dominant strategies. 3. Consider the case of a penalty kick in football. Suppose that the striker has only three choices: to kick the ball to the left, right, or center of the goal. Suppose the goalkeeper has only three options: to dive to the left or right, or stay in the center. Suppose that whenever the goalkeeper correctly guesses the striker's choice, he stops the penalty. In any other case, a goal is scored. Suppose that if the goal is scored, the payoffs are 1 for the striker and -1 for the goalkeeper 1 and that if the penalty is stopped, the payoffs are 1 for the goalkeeper and -1 for the striker. Represent this situation as a simultaneous-move game in normal form, determine the best re- sponses of both players and find all their dominant strategies.

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The scenario described in the question is a typical example of a zerosum game in game theory In this game the striker and the goalkeeper are the two p... View the full answer