1) [65 points] Consider two players, Players 1 and 2. The strategy of player i, i= 1, 2, is denoted z; and can be any nonnegative real number. (Notice that the strategies are continuous.) The payoff function for player 1, denoted by Vi(Z1, Z2), and player 2, V2(Z1, Z2), are defined as: Vi(Z1, Z2)=(60- Z1 - Z2)*Z1 & V2(Z1, Z2)=(60 Z1 Z2)*Z2 - a. [35 points] Assume that Player 1 chooses zi without knowing the decision of Player 2 (i.e., z2) and vice versa. (That is, Player 2 chooses z2 without knowing the decision of Player 1, i.e. z.) i. [20 points] Derive and graph the best-response functions for each player. Make sure to mark the axes and the best-response functions clearly. ii. [10 points] Find the Nash equilibrium. iii. [5 points] Is the Nash equilibrium Pareto efficient? Explain why or why not. b. [25 points] Now assume that the players choose sequentially: Player 1 moves first, chooses zi, Player 2 observes Player 1's choice and then moves to choose z2. Find the Backwards Induction equilibrium of the sequential move game (with perfect information). c. [5 points] Given your findings in parts (a) and (b): Is there a first-mover advantage in this interaction between Player 1 and Player 2? Explain why or why not.