Consider the penalty kick game covered in class, where the Kicker is kicking a penalty shot and Goalkeeper is defending.

The Kicker can kick to the left, center or right, whereas the goalie can defend left, center or right.

The matrix presented below denotes the payoffs for the kicker and goalkeeper from the possible strategies, where the kicker's payoffs represent the probability that she scores, whereas the goalkeeper's payoffs capture the probability that the kicker does not score.

Goalie

Left Center Right

Kicker Left 0.65, 0.35 0.95, 0.05 0.95, 0.05

Center 0.95, 0.05 0, 1 0.95, 0.05

Right 0.95, 0.05 0.95, 0.05 0.65, 0.35

1. What is the mixed strategy Nash equilibria in this game? What is the expected likelihood that the kicker will score in equilibrium?