4. n players are playing the guessing-the-average game. Each player simultaneously chooses a number from the interval [0,100] (note that a player is allowed to choose a num- ber that is not an integer). Let 1",; denote the guess of player i. Given a strategy prole (3:1,1:2,...,:rn), player is payoff is _$1+:r2+...+3:n (5"a' 2n )2- (a) Suppose n = 2. Find the best reply function of each player. Plot the players' best reply functions in one gure and nd all the Nash equilibrium in pure strategies. Explain your answer. (10%) (b) Suppose 'n. = 3. If player 2's guess is 1172 and player 3's guess is 5:3, what is the best reply of player 1'? Find a symmetric Nash equilibrium. Explain your answer. (10%) (c) Now assume that 'n. > 3. Find a symmetric Nash equilibrium. Explain your answer. (5%)