Problem 1 (3 marks). This question is adapted from our textbook. Firms 1 and 2 must decide whether to enter a new industry.

Problem 1 (3 marks). This question is adapted from our textbook. Firms 1 and 2 must decide whether to enter a new industry. To enter the industry, each firm must choose to build either a plant with a small output capacity (S), or large output capacity (L). A plant with small capacity costs $50 to set up; one with large capacity costs $175. In either case, the marginal cost of production is zero. But firms can also opt not to enter (N), in which case they do not incur in any type of cost. The revenues under the different scenarios are given below.• If neither firm enters, revenues (and hence profits) are zero.• If only one small firm enters, its revenue is $80, the other earns zero.• If two small firms enter, each earns revenue of $70.• If only one large firm enters, its revenue is $200, the other earns zero.• If two large firms enter, each earns revenue of $90.• If one small and one large firm enter, the small firm earns $40 in revenue while the large one earns $160.Suppose both firms play a simultaneous game, choosing between S, L or N. (a) Draw the matrix representation of the simultaneous game.(b) Find all the pure strategy NE of this game.Suppose the firms now play a sequential game with firm 1 moving first. After observing firm1's choice, firm 2 has to choose S, L or N.(c) Draw the extensive form game and write down the set of strategies available to eachfirm.(d) Find the subgame perfect Nash equilibrium (SPNE) of this game.Suppose now that the rules of the game change and, after choosing not to enter the industry and observing firm 2's decision, firm 1 can revisit its choice and decide whether to enter with a small plant or to stay out (firm 1 can no longer choose the large plant at this stage).(e) Draw the extensive form game and write down the set of strategies available to each firm.(f) Find the SPNE of this game.