Reference no: EM13873876

In baseball, pitchers and batters have conflicting goals. Pitchers want to get the ball past batters but batters want to connect with pitched balls. The following ta ble shows the payoffs for a hypothetical game between a pitcher and a batter. The payoffs take into account the fact that fastballs, when anticipated and hit by a batter, yield better hits (more bases) than do similarly anticipated and hit curve balls.

		PITCHER
		Throw curve	Throw fastball
BATIER	Antici pate curlle	2	-1
	Anticipate fastball	-1	4

(a) Verify that there is no pure-strategy equilibrium in this game, and then find the mixed-strategy equilibrium.

(b) Draw the best-response curves for both players, and indicate the mixed­ strategy equilibrium on your diagram.

(c) Can the pitcher improve his expected payoff in the mixed-strategy equi­ librium of this game by slowing down his fastball (thereby making it more similar to a curve ball)? Assume that slowing down the pitched fastball changes the payoff to the hitter in the "anticipate fastball/ throw fastball" cell from 4 to 3. Explain carefully how you determine the an­ swer here and show your work. Also explain why slowing the fastball can or cannot improve the pitcher's expected payoff in the game.