(55) Three firms compete in Cournot format by choosing their quantities of production. The inverse demand of the market is P(Q) = 20 - 20, where @ = q1 + 92 + 93. Each firm has a constant marginal cost c = 1. (a) (15) These three firms choose their quantities simultaneously. Solve for the NE. (b) (20) Consider a modified game: firm 1 is the industry leader and chooses its quantity q1 first. Firm 2 and 3 observe q1 and then simultaneously choose q2 and 93 respectively. Find the SPE and the corresponding profits. (c) (20) Consider another modified game: at t = 1, firm 1 first chooses q1. At t = 2, firm 2 and 3 observe q1. Then firm 2 and 3 have the option to merge as one firm. If firm 2 and 3 merge, they act as one firm and equally share their profits. Will they choose to merge or not