Imagine that there are 3 firms in a monopolistic market, F1, F2 and F3. Firms 1 and 2 are incumbent firms and act simultaneously whereas Firm 3 observes the actions of both firms before deciding whether to enter.
All firms face a market price of $P(Q) = 16-q_1-q_2-q_3$. Incumbent firms face a production cost of $C_i (q_i) = 4q_i$ for $i= 1,2$. Firm 3 faces a production cost of $C_3(q_3) = 4 + 4q_3$. Find both firm 3 and firm 1's payoff.
I understand that I need to take firm 3's best response function which is $$0.5 (12-q_2-q_1)$$ but I am not sure where to go from there. Do I substitute this back into the price equation? I tried doing this but it wouldn't yield any definitive answers. Thanks!