5. Consider three firms competing in the market for a homogeneous product and they have the possibility to choose between three levels of production -low (L), medium (M), high (H)-. The profits of each company in euros are presented in the tables below. Firm 1 selects row, firm 2 selects column, firm 3 selects table. H M L H 2, -1, 2 H -2, -2, -2 7,0, 7 M -1, 2, 2 4, 4, 5 5,0, 15 L 0, 7, 7 0, 5, 15 0, 0, 20 H M L M H 2, 2, -1 5,4,4 15, 0, 5 4, 5,4 6,6, 6 9,0.9 0, 15, 5 0,9,9 0, 0, 12 H M L L H 7, 7,0 15, 5, 0 20, 0,0 M 5, 15, 0 9,9, 0 2, 0,0 L 0, 20, 0 0, 12, 0 0,0,0 i. Find the pure strategy Nash equilibria if all three firms choose simultaneously. ii. Now suppose that all three firms choose simultaneously, but firm 3 does not choose strategically, but randomly chooses one of the three output levels, each with probability 1/3. Write the table describing the expected payoffs of the game for firms 1 and 2 and calculate the Nash equilibria of the game (two-player game at this point) in both pure and mixed strategies. iii. Now suppose that firms choose sequentially. For each possible turn, find the Subgame Perfect Nash Equilibria if each firm can observe what has been played before its turn. [Hint: Do you need to do the analysis for all cases separately?] iv. Now suppose that firm 3 chooses before the other two, and then firms 1 and 2 choose simultaneously. Compute the Subgame Perfect Nash Equilibria of this game. V. Suppose now that firms play a repeated game, where the stage game is the simultaneous game of question (i). Find (if any) a Subgame Perfect Nash Equilibria that gives each player an average payoff per round more than 6