3. Guess the mean. Each of N players writes an integer between 1 and 10, without showing it to any other player. The players then reveal their numbers. The winner is that person whose number comes closest to equaling half the mean of the numbers supplied by the other players. For example, if there are four players and they write down the numbers 1, 3, 5, and 6. Then the scores for each player are below, and player 2 would win. 1/3+5+6 3 = 1.33 1:1 2 1 2:3 2 (1+5+6) = 1 3:5 - (1+3+6) 1+3+5 = 3.33 4:6 - = 4.5 3 All players strictly prefer winning to tying, and strictly prefer tying to losing. (a) Show that the game is dominance solvable (strictly or weakly?). What is the solution by IEDS? (b) Is the solution you found in (a) a Nash equilibrium? Justify your answer. (10)