Consider a situation of after-match penalty shoot-out. The striker can target either East or West side of the goal. If he targets West, with 80% chance he shoots on target. If he shoots East, he is accurate with 75%. The goalkeeper has to choose the corner to jump to. If he does not guess the corner correctly and the shot is on target, then the striker scores. If the striker shoots West, the shot is on target and the goalkeeper jumps West, then with 75% chance he saves the goal. If the striker shoots East, the shot is on target and the goalkeeper jumps East, then with chance of 2/3 he saves the goal. Suppose, that it is a zero-sum game and if the striker scores his payoﬀ is 1, otherwise it is 0. 1. Formulate this situation as a strategic game and Find all Nash equilibria of the game.

Consider a situation of after-match penalty shoot-out. The striker can target either East or West side of the goal. If he targets West, with 80% chance he shoots on target. If he shoots East, he is accurate with 75%. The goalkeeper has to choose the corner to jump to. If he does not guess the corner correctly and the shot is on target, then the striker scores. If the striker shoots West, the shot is on target and the goalkeeper jumps West, then with 75% chance he saves the goal. If the striker shoots East, the shot is on target and the goalkeeper jumps East, then with chance of 2/3 he saves the goal. Suppose, that it is a zero-sum game and if the striker scores his payoﬀ is 1, otherwise it is 0. 1. Formulate this situation as a strategic game and Find all Nash equilibria of the game.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.3P

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