10. Say we have two basketball players, Nash and Yao. Nash has the ball 20 feet from the basket and Yao is defending. Nash can either take a jump shot or drive the basket. Yao can either come out and contest the shot, or can stay in and protect the basket. The game looks like this. Yao comes out Yao protects Nash takes jump shot 0.3, 0.7 0.4, 0.6 Nash drives 0.5, 0.5 0.3, 0.7 For example, if Nash takes a jump shot and Yao comes out, then Nash has a 30 percent chance of scoring and Yao has a 70 percent chance of successfully defending. a. Find the mixed strategy Nash equilibrium of this game. In the mixed Nash equilibrium, what is Nash's overall probability of scoring? b. Now say that Nash practices over the summer and improves his jump shot. Now the game looks like this. Yao comes out Yao protects Nash takes jump shot 0.4, 0.6 0.5, 0.5 Nash drives 0.5, 0.5 0.3, 0.7 Find the mixed strategy Nash equilibrium of this new game. In the mixed Nash equilibrium, what is Nash's overall probability of scoring? c. After Nash improves his jump shot, does he go to his jump shot more often? After Nash improves his jump shot, is it more successful? After Nash improves his jump shot, is his drive more successful? Why does an improved jump shot improve other parts of Nash's game