5: Guess the Average Three players simultaneously pick a point in the interval [0, 1]. The player closest to the average of the three points wins $1. If there is a tie, then the dollar is split equally among the winners. More formally, the players simultaneously choose strategies si from Si = [0, 1]. The average of their choices is s = (s1 s2 s3)/3. Player i's payoff function is: Ui(s1 s2 s3) = 1/t if i argminj |sj s| 0 otherwise where t is the number of players who tie (their choices are equally close to the average). (If only one player is closest to the average, then t = 1 and that player wins the entire $1.) What are the pure-strategy equilibria of this game? What are the mixed-strategy equilibria if the possible strategies are limited to playing 0 or 1, rather than [0, 1]? 3