Two firms in the market agreed verbally to produce 10 units each, thus producing the monopoly output of 20, and sharing resulting profit of 400 equally between them. there were no binding commitment to stop one or both firms from reneging on such an agreement and producing some other amount. suppose that the only action considered by each firm is to produce its capacity output of 12 units. thus, each firm has the action set (10, 12)

a). show the extensive form of the game in which the firms produce and put their outputs onto the market simultaneously.

b). given i =a ,b where a is firm a and b is firm b.
c=cq=qa+qb ( given per unit cost function (c) as 1) and p=41-qi as the demand function where qj=qa+qb
i) drive the expression for the firms profit function
ii). generate the profit pairs for the two firms

c) write the game in its strategic form and determine
i). the dominant strategic for the firm
ii). nash equilibrium of the firm.