Question 3. Suppose an MLB pitcher has two options for each pitch, throw fastball or throw...

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Question 3. Suppose an MLB pitcher has two options for each pitch, throw fastball or throw curveball, and the batter has two options for each pitch, anticipate fastball or anticipate curveball. This game is represented by the following payoff matrix: Batter Pitcher Throw Fastball Throw Curveball Anticipate Fastball (-2,3) (4,-1) Anticipate Curveball (2,-2) (-2,2) The numbers on the left correspond to the payoffs for the pitcher, and the numbers on the right correspond to the payoffs for the batter. a) Show that there is no pure-strategy Nash equilibrium for this game. (Hint: Go through each of the four scenarios and show why one side has an incentive to switch strategies if the other side does not switch.) b) How often should the batter anticipate fastball so that the pitcher will not know whether it is better to throw fastball or throw curveball? (Hint: If the batter anticipates fastball with probability p, then he anticipates curveball with probability (1 p). To solve this problem, the batter will choose p such that the pitcher's payoff from throw fastball is the same as from throw curveball.) c) How often should the pitcher throw fastball such that the batter will not know whether it is better to anticipate fastball or anticipate curveball? (Hint: If the pitcher throws fastball with probability q, then he throws curveball with probability (1-q). To solve this problem, the pitcher will choose q such that the batter's payoff from anticipate fastball is the same as from anticipate curveball.) Question 3. Suppose an MLB pitcher has two options for each pitch, throw fastball or throw curveball, and the batter has two options for each pitch, anticipate fastball or anticipate curveball. This game is represented by the following payoff matrix: Batter Pitcher Throw Fastball Throw Curveball Anticipate Fastball (-2,3) (4,-1) Anticipate Curveball (2,-2) (-2,2) The numbers on the left correspond to the payoffs for the pitcher, and the numbers on the right correspond to the payoffs for the batter. a) Show that there is no pure-strategy Nash equilibrium for this game. (Hint: Go through each of the four scenarios and show why one side has an incentive to switch strategies if the other side does not switch.) b) How often should the batter anticipate fastball so that the pitcher will not know whether it is better to throw fastball or throw curveball? (Hint: If the batter anticipates fastball with probability p, then he anticipates curveball with probability (1 p). To solve this problem, the batter will choose p such that the pitcher's payoff from throw fastball is the same as from throw curveball.) c) How often should the pitcher throw fastball such that the batter will not know whether it is better to anticipate fastball or anticipate curveball? (Hint: If the pitcher throws fastball with probability q, then he throws curveball with probability (1-q). To solve this problem, the pitcher will choose q such that the batter's payoff from anticipate fastball is the same as from anticipate curveball.)

Answer rating: 100% (QA)

a There is no purestrategy Nash equilibrium for this game 1 If ... View the full answer