Question 4: Interaction between three quantity-setting firms Consider a market in which three firms, 1, 2, and 3, produce and sell a good. Firm 's (z = 1,2, 3) production level is denoted by ; > 0. By producing this quantity, the firm incurs the cost C(q;) = cg;, where [0,1). Given the output levels q;, g2, and g3, the market price, p, is given by the inverse demand function p = 1 q; g2 3. Firm i's profit can thus be written as m = pgi C(qi)) = (1cq1 g2 g3) qi- Bach firm i chooses its quantity with the objective of maximizing the own profit. The timing of the game is as follows: (1) firm 1 chooses g;; (2) firms 2 and 3 observe , and they then simultaneously with each other choose their own quantity (i.e., g2 and g3, respectively). (a) Draw a tree that shows the extensive form of the game. (b) Solve for all subgame-perfect Nash equilibria of the game