In a World Series game, Jacob deGrom is pitching and Mike Trout is batting. The count on Trout is three balls and two strikes. deGrom has to decide whether to throw a fastball or a curveball. Trout has to decide whether to swing or not swing. If deGrom throws a fastball and Trout doesn’t swing, the pitch will almost certainly be a strike, and Trout will be out. If Trout does swing, however, there is a strong likelihood that he will get a hit. If deGrom throws a curve and Trout swings, there is a strong likelihood that Trout will strike out. But if deGrom throws a curve and Trout doesn’t swing, there is a good chance that it will be ball four and Trout will walk (assume that a walk is as good as a hit in this instance). The following table shows the payoffs from each pair of choices that the two players can make:

a) Is there a Nash equilibrium in pure strategies in this game?
b) Is there a mixed strategy Nash equilibrium in this game? If so, what is it?

Transcribed Image Text:

Jacob Fastball deGrom Curveball Mike Trout Swing -100, 100 100, -100 Do Not Swing 100, -100 -100, 100