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Pehalty kickS Ih Soccer. Let's consider a situation where a football player has to faceoff the goalkeeper in a penalty kickoff. Standing infront of the goalpost, the Kicker (player 1) has several angle which he could kick the ball to the goalpost. Let's say he could kick the ball in the Left corner of the goalpost, Right corner of the goalpost or shoot straight through the Center. And, same as the player, the goalkeeper (player 2) also has three options to predict which direction the player would kick the ball and try to stop it. This game can be represented using the following 3 × 3 matrix: Left Center Right 63 37 94 6 95 5 Left 100' 100 100' 100 700' 100 91 9 100 94 6 Center (100' 100 100' 100 100 100 94 6 93 7 60 40 Right (100' 100 100 100 100' 100 In the above matrix, the payoff of the kicker is the probability that he scores and the payoff of the goalkeeper is the probability that the kicker doesn't score. We know that the total probability of an event is 1, therefore, all the payoffs sum up to 1. 1. Find a mixed strategy o, = (p, P2. (1 – p1 - P2) for Player 1 that will make Player 2 indifferent about playing Left, Center or Right. 2. Find a mixed strategy o, = (q , 92, (1 – 91 - 92)) for Player 2 that will make Player 1 indifferent about playing Left, Center or Right. 3. What is the probability that the Kicker(player 1) scored a goal, or in other words what is the expected utility for player 1.

Pehalty kickS Ih Soccer. Let's consider a situation where a football player has to faceoff the goalkeeper in a penalty kickoff. Standing infront of the goalpost, the Kicker (player 1) has several angle which he could kick the ball to the goalpost. Let's say he could kick the ball in the Left corner of the goalpost, Right corner of the goalpost or shoot straight through the Center. And, same as the player, the goalkeeper (player 2) also has three options to predict which direction the player would kick the ball and try to stop it. This game can be represented using the following 3 × 3 matrix: Left Center Right 63 37 94 6 95 5 Left 100' 100 100' 100 700' 100 91 9 100 94 6 Center (100' 100 100' 100 100 100 94 6 93 7 60 40 Right (100' 100 100 100 100' 100 In the above matrix, the payoff of the kicker is the probability that he scores and the payoff of the goalkeeper is the probability that the kicker doesn't score. We know that the total probability of an event is 1, therefore, all the payoffs sum up to 1. 1. Find a mixed strategy o, = (p, P2. (1 – p1 - P2) for Player 1 that will make Player 2 indifferent about playing Left, Center or Right. 2. Find a mixed strategy o, = (q , 92, (1 – 91 - 92)) for Player 2 that will make Player 1 indifferent about playing Left, Center or Right. 3. What is the probability that the Kicker(player 1) scored a goal, or in other words what is the expected utility for player 1.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Penalty kicks in soccer. Let's consider a situation where a football player has to faceoff the goalkeeper in a penalty kickoff. Standing infront of the goalpost, the Kicker (player 1) has several angle which he could kick the ball to the goalpost. Let's say he could kick the ball in the Left corner of the goalpost, Right corner of the goalpost or shoot straight through the Center. And, same as the player, the goalkeeper (player 2) also has three options to predict which direction the player would kick the ball and try to stop it. This game can be represented using the following 3 x 3 matrix: Left Center Right 63 37 94 95 Left 100' 100 100' 100 100' 100 100. 6 100' 100 91 9 94 Center 100' 100 100' 100 94 6 93 7 60 40 Right 100' 100 100' 100 100' 100 In the above matrix, the payoff of the kicker is the probability that he scores and the payoff of the goalkeeper is the probability that the kicker doesn't score. We know that the total probability of an event is 1, therefore, all the payoffs sum up to 1. 1. Find a mixed strategy o, = (p1, P2, (1 – P1 - P2)) for Player 1 that will make Player 2 indifferent about playing Left, Center or Right. 2. Find a mixed strategy o, = (91, 92, (1 – 9, - 9,)) for Player 2 that will make Player 1 indifferent about playing Left, Center or Right. 3. What is the probability that the Kicker(player 1) scored a goal, or in other words what is the expected utility for player 1.
Transcribed Image Text:Penalty kicks in soccer. Let's consider a situation where a football player has to faceoff the goalkeeper in a penalty kickoff. Standing infront of the goalpost, the Kicker (player 1) has several angle which he could kick the ball to the goalpost. Let's say he could kick the ball in the Left corner of the goalpost, Right corner of the goalpost or shoot straight through the Center. And, same as the player, the goalkeeper (player 2) also has three options to predict which direction the player would kick the ball and try to stop it. This game can be represented using the following 3 x 3 matrix: Left Center Right 63 37 94 95 Left 100' 100 100' 100 100' 100 100. 6 100' 100 91 9 94 Center 100' 100 100' 100 94 6 93 7 60 40 Right 100' 100 100' 100 100' 100 In the above matrix, the payoff of the kicker is the probability that he scores and the payoff of the goalkeeper is the probability that the kicker doesn't score. We know that the total probability of an event is 1, therefore, all the payoffs sum up to 1. 1. Find a mixed strategy o, = (p1, P2, (1 – P1 - P2)) for Player 1 that will make Player 2 indifferent about playing Left, Center or Right. 2. Find a mixed strategy o, = (91, 92, (1 – 9, - 9,)) for Player 2 that will make Player 1 indifferent about playing Left, Center or Right. 3. What is the probability that the Kicker(player 1) scored a goal, or in other words what is the expected utility for player 1.
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