Consider a game with n players. Simultaneously and independently, the players choose between X and Y. That is, the strategy space for each player i is Si = {X, Y}. The payoff of each player who selects X is  2m_x - m²x + 3, who selects Y is 4 - m_y , where my is the number of players who choose Y. Note that m_x + m_y = n.

(a) For the case of n = 2, represent this game in the normal form and find the pure-strategy Nash equilibria (if any).

(b) Suppose that n = 3. How many Nash equilibria does this game have?

(Note: you are looking for pure-strategy equilibria here.) If your answer is more than zero, describe a Nash equilibrium.

(c) Continue to assume that n = 3. Determine whether this game has a symmetric mixed-strategy Nash equilibrium in which each player selects X with probability p. If you can find such an equilibrium, what is p?