finding nash equilibrium

Consider a baseball game between a pitcher and a batter. The pitcher can either throw a fast or curve ball. The batter can choose to swing or not swing. The game and its payoffs can be represented in the following table: Batter swing not swing fast 5,5 5,0 Pitcher curve -2, 3 3,2 (a) Explain the pitcher's best responses. Does the pitcher have any dominated strategies? (b) Explain the batter's best responses. Does the batter have any dominated strate- gies? (c) What is the pure strategy Nash Equilibrium