Consider the modified game of penalty kick in soccer. There are two players, the Kicker and the Goalie. The Kicker has three possible actions: kick to the goalie's left (L), the goalie's right (R), or kick to the middle (M). The Goalie has two possible actions: move left (l) or move right (r). If the Goalie and Kicker chooses different sides, (L, r) or (R, l), the Kicker scores with probability 0.9. If both of them chooses the same side, (R, r) or (L, l), then the Kicker scores with probability 0.4. If the Kicker kicks to the middle, M, then he scores with probability 0.6 independently of the side Goalie chooses. The payoff for the Kicker is his probability of scoring and the payoff for the Goalie is just the negative of that. For example, if Goalie chooses l and the Kicker chooses L, then the payoff of the Kicker is 0.4 and the payoff of the Goalie is 0.4. (a) Formulate this situation as a matrix game. (b) Show that this game does not have a pure strategy Nash equilibrium. (c) Find all mixed strategy Nash equilibria of this game.