Ryan and Nicholas are chosen to play a game called "Guess 2 3 the average. Each of them chooses a real number on the interval [0, 100]. Denote Ryan's choice as r and Nicholas' choice as n. Whoever chooses the number closest to 2 3 the average of both of the guesses (the average is r+n 2 ) wins $100. 1. Write out Ryan's best response function to Nick's strategies. Write out Nick's best response function to Ryan's strategies. 2. What is the Nash equilibrium of this game? 3. Does this seem like a reasonable prediction for what would happen in this game? Why or why not?