3 Choosing the Optimal Mixture: Penalty Kicks (25 points) The following game represents the payoffs for a kicker (player 1) and goalie (player 2). The payoff to the kicker is the probability of scoring a goal while the probability of blocking the goal is the goalie's payoff. Goalie left center right Left 45,55 90,10 90,10 Kicker Center 85,15 0,100 85,15 Right 95.5 95,5 60,40 a) (5 points) There are no PSNE in this game. Explain how you can know that. b) (15 points) Solve for the MSNE in this game. Let the kicker mix with probabilities pr, pc, and pa while the goalie mixes with probabilites p, pe, and pr. Be sure to tell what are each of the 6 prbabilities just listed. c) (5 points) When both players are playing their MSNE, what is the expected payoff to each player. 'We'll call him a "goalie" and not a "keeper" because now you can abbreviate the players with K and G if you like