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 5,- from S,- = [0, 1]. The average of their choices is 3 = (31 | 82 + 53) / 3. Player i's payoff function is: 1/t if i E argminj ISj | U(31 + 32 + 53) = 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.) 0 What are the purestrategy equilibria of this game? 0 What are the mixedstrategy equilibria if the possible strategies are limited to playing 0 or 1, rather than [0, 1]