Question: 3. A baseball pitcher throws three pitches, a fastball, a slider and a change-up. As a measure of the payoff for this type of confrontation,

3. A baseball pitcher throws three pitches, a fastball, a slider and a change-up. As a measure of the payoff for this type of confrontation, we might use the expected number of runs the batter creates in each situation. (Note: there are other possible measures that take into account the pitcher's abilities). We would expect that for any given pitch, the batter's performance is better if he anticipates the pitch. Let us Finding solutions for Africa SSOA022 QUIZ 1 2021 assume that the batter has four possible strategies. To anticipate either a fastball, a slider or a change-up or not to anticipate any pitch. Pitcher Fastball Change-up Slider Fastball 0.38 0.37 0.39 Batter Change-up 0.25 0.40 0.41 Slider 0.35 0.32 0.45 None 0.38 0.30 0.42 a) Find the reduced payoff matrix (at each iteration, state which row/column is dominated). (02) b) Find the optimal mixed strategy for both players. (06) c) What is the value of the game? (02)

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