1. Static and Dynamic Game. [28 marks.] Consider the following 2-by-2 game: (a) [2 marks.] Assume for now that a = 2. Using dominant strategies or oth- erwise, nd the pure-strategy Nash equilibria, if any of this game. (There is no need to look for equilibria in mixed strategies) (b) Now, consider the dynamic game in which player 1 moves before player 2, and the payoffs remain unchanged. i. [3 marks.] Draw the game tree for this dynamic game. What are the possible strategies for each player? Recall that a strategy prole for a player not at the initial node of the game tree must specify an action for the player at every node. ii. [2 marks.] Find the backwardinduction solution(s) to this game. iii. [3 marks.] Calculate the equilibrium payoffs for each player. Com- pared to the simultaneous game, is there a rst-mover advantage or a second-mover advantage? (c) Now, assume that a = 0 in the original static game. i. [3 marks.] Find all the Nash equilibria in pure and mixed strategies. ii. [4 marks.] Denoting p the probability player 1 plays A and q the prob ability that player 2 plays C, compute and graph the best-response functions of each player. Show that where the two best response func tions intersect represent the Nash equilibrium or equilibria of the game. iii. [2 marks.] Calculate the equilibrium payoff of each player