In a World Series game, Tim Lincecum is pitching and Joe Mauer is batting. The count on Mauer is 3 balls and 2 strikes. Lincecum has to decide whether to throw a fastball or a curveball. Mauer has to decide whether to swing or not swing. If Lincecum throws a fastball and Mauer doesn't swing, the pitch will almost certainly be a strike, and Mauer will be out. If Mauer does swing, however, there is a strong likelihood that he will get a hit. If Lincecum throws a curve and Mauer swings, there is a strong likelihood that Mauer will strike out. But if Lincecum throws a curve and Mauer doesn't swing, there is a good chance that it will be ball four and Mauer 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?

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Joe Mauer Swing Do Not Swing |-100、100 | 100,-100 Tim Lincecum Fastball Curveball100,-10000,100