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 theLeft corner of the goalpost, Right corner of the goalpost or shoot straight through the Center. And, same as the player, the goalkeeper (player 2) alsohas 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 3matrix:Le ftCenterRightLe ft60 40100 10094 6100' 100- 93 7100 ' 10095100 10091 9100 ' 1005100Center100 ' 100Right(91 9100 ' 10094100 ' 10063 37100 ' 100In 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'tscore. We know that the total probability of an event is 1, therefore, all the payoffs sum up to 1.1. Find a mixed strategy o1 = (P1, P2, (1 – P1 – P2 jor Player 1 that will make Player 2 indifferent about playing LeftCenteror Right2. Find a mixed strategy o2 = (41, 42, (1 – 41 – 42 for Player 2 that will make Player 1 indifferent about playing Le ftCenteror Right3. What is the probability that the Kicker(player 1) scored a goal, or in other words what is the expected utility for player 1.If you are using decimal numbers instead of fractions, use at least six digits after decimal point.

Given two players, a Kicker (Player 1) and a Goalkeeper (Player 2). Player 1 has three options,…

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 3matrix: