Stackleburg Oligopoly 3 firms

Reply Wed 22 May, 2019 05:33 pm
magine 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)=16βˆ’π‘ž1βˆ’π‘ž2βˆ’π‘ž3. Incumbent firms face a production cost of 𝐢𝑖(π‘žπ‘–)=4π‘žπ‘– for 𝑖=1,2. Firm 3 faces a production cost of 𝐢3(π‘ž3)=4+4π‘ž3. Find both firm 3 and firm 1's payoff.

I understand that I need to take firm 3's best response function which is
but I am not sure where to go from there. How would I go about finding each firms predicted quantity? Thanks!
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