Consider the soccer penalty kicks game where striker shoots on a goal defended by keeper, moves are simultaneous and payoffs are given by the table below: Keeper Shooter Left 1\0 0\1 Left Right a. Is there a pure-strategy Nash Equilibrium in this game? b. In the mixed-strategy game, if the keeper's strategy is {30% Left, 70% Right}, what is (are) the striker's best response(s)? c. Find Nash Equilibrium in mixed strategies. Does it exist? Is it unique? Right 01 1\0 Now, assume the game consists of two penalty kicks, one after another. Keeper's and striker's payoffs in each stage are characterized by the table above. Total game payoff is the sum. d. Describe strategy spaces in this game. e. Characterize the equilibrium as sharply as you can. Now assume there are two types of strikers: left-eyed (with better left eye) and right- eyed (better right eye). A left-eyed striker has 20% chance of missing when shooting at right corner even when there is no goalie there. He does not miss when shooting right. The opposite characterizes a right-eyed striker. Population proportions of the two types are 50/50. KS Left Right Payoffs when S lefteyed: Left 10 0.2 0.8 Right 01 1\0 1 KS Left Payoffs when S righteyed: Left 1\0 Right 0.2 0.8 Righ 0\1 1\0 f. If the striker is left-eyed and the keeper knows it, what is the equilibrium? g. What is the equilibrium of the one-shot game where a priori striker knows his type but keeper does not (keeper expects 50/50)? h. As sharply as you can, characterize NBPE (Nash-Bayes Perfect Equilibrium) of the two-shot game where at the beginning keeper does not know striker's type.