1. Consider a game with n players. Simultaneously and independently, the players choose between X and...

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1. 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 S, = {X,Y). The payoff of each player who selects X is 2m, - m² +3, where m, is the number of players who choose X. The payoff of each player who selects Y is 4-my, where my is the number of players who choose Y. Note that m₂ + my = 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 meted strategy Nash equilibrium in which each player selects X with probability p. If you can find such equilibrium, what is p? 1. 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 S, = {X,Y). The payoff of each player who selects X is 2m, - m² +3, where m, is the number of players who choose X. The payoff of each player who selects Y is 4-my, where my is the number of players who choose Y. Note that m₂ + my = 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 meted strategy Nash equilibrium in which each player selects X with probability p. If you can find such equilibrium, what is p?