In the game of baseball, a pitcher throws a ball towards a batter who tries to hit it. In our simplied version of the game, the pitcher can pitch high or pitch low, and the batter can swing high or swing low. The ball moves so fast that the batter has to commit to swinging high or swinging low before the ball is released. Let us suppose that if the pitcher throws high and batter swings low, or the pitcher throws low and the batter swings high, the batter misses the ball, so the pitcher wins. If the pitcher throws high and the batter swings high, the batter always connects. If the pitcher throws low and the batter swings low, the batter will connect only 60% of the time. This story leads us to the following payoff matrix, where if the batter hits the ball he gets a payoff of 1 and the pitcher gets 0, and if the batter misses, the pitcher gets a payoff of 1 and the batter gets 0. Batter Swing High (SH) Swing Low (SL) Pitch High (PH) 0, 1 1, 0 Pitcher Pitch Low (PL) 1,0 0.4, 0.6 a. Does this game have a pure-strategy Nash equilibrium? If so, nd it. [2 mark] b. Does this game have a mixed-strategy equilibrium? If so, nd it. [8 marks]