Consider a guessing game with N people, and the person closest to 20 plus one-half of the average is awarded the prize, which is split in the event of a tie. The range of guesses is from 0 to 100. Show that 40 is Nash equilibrium. (Hint: Suppose that N-1 people choose 40 and one person deviates to x < 40. Calculate the target as a function of the deviant’s decision, x. The deviant will lose if the target is greater than the midpoint between x and 40, i.e., if the target is greater than (40 + x)/2. (Check to see if this is the case.)