Hi, I think there is only one Nash equilibrium which is point E, but how many exactly does it have? please explain It step by step!

* Q17. Suppose we have the same payoff matrix as in the previous problem except now firm 1 gets to move first and knows that firm 2 will see the results of this choice before deciding which type of car to build. Draw the game tree for this sequential game. What is the Nash equilibrium for this game? Write down the payoff matrix of the game. D 400 for Firm 1 Big car 400 for Firm 2 Big car B Firm 2 Small car E 1000 for Firm 1 800 for Firm 2 Firm 1 Big car F 800 for Firm 1 1000 for Firm 2 Small car C Firm 2 Small car G 500 for Firm 1 500 for Firm 2 By backward induction, we have that firm 2's best responses in its two subgames are Small car if firm 1 plays Big car and Big car if firm 1 plays Small car. Then, firm 1 has a strict incentive to play Big car and thus the outcome of the game is (Big car, Small car). The matrix representation of the game has two strategies for firm 1, which are simply the two types of car choices, Small car and Big car. On the other hand, firm 2 has 4 strategies, as firm 2 could play at two different points in the game and has two types of cars to choose from. There are thus 4 combinations of possible actions. Firm Big car Small car Big car no matter what 400 for 1, 400 for 2 800 for 1, 1000 for 2 Big if 1 goes for big, small if 1 goes for small 400 for 1, 400 for 2 500 for 1, 500 for 2 Firm 2 Big if 1 goes for small, small if 1 goes for big 1000 for 1, 800 for 2 800 for 1, 1000 for 2 Small car no matter what 1000 for 1, 800 for 2 500 for 1, 500 for 2 We can find the Nash equilibria here by first identifying all the cells where Firm 1 (who chooses the column) is getting the highest payoff in that row (since otherwise they'll switch columns). Next, we identify all of the cells where Firm 2 (who chooses the row) is getting the highest payoff within the column (because otherwise they'll change rows). Any cell in which both players numbers are highlighted is a Nash equilibrium. Notice that the above matrix has three pure- strategy Nash equilibria, but only the one that is consistent with the subgame perfect equilibrium contains a credible "threat" by firm 2