Question

Left Center Right
Left ( 63100,37100 ) ( 94100,6100 ) ( 94100,6100 )
Center ( 95100,5100 ) ( 0100,100100 ) ( 94100,6100 )
Right ( 95100,5100 ) ( 90100,10100 ) ( 62100,38100 )
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.

Find a mixed strategy σ1=(p1,p2,(1−p1−p2)) for Player 1 that will make Player 2 indifferent about playing Left , Center or Right .
Find a mixed strategy σ2=(q1,q2,(1−q1−q2)) for Player 2 that will make Player 1 indifferent about playing Left , Center or Right .
What is the probability that the Kicker(player 1) scored a goal, or in other words what is the expected utility for player 1.

Answer 1

Answer:

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Answer 2

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