3. Consider a variation on the beauty contest game from class. Each player must simultaneously choose an integer between 0 and 100 (inclusive). The average of the chosen numbers will be calculated; call this average x. The player whose number is closest to x will win and earn a positive payoff. If two or more players are equally close to x, the winner will be chosen at random among them. Players who do not win earn a payoff of zero. a) What are the pure strategy Nash equilibria if there are two players? b) What are the pure strategy Nash equilibria if there are three players? c) Let the number of players be ‘large’. Let the level 0 strategy be to choose a number at random. Find the outcome when all players are level k reasoners with k > 0.