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# Stackleburg Oligopoly 3 firms

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 π(π)=16βπ1βπ2βπ3. Incumbent firms face a production cost of πΆπ(ππ)=4ππ for π=1,2. Firm 3 faces a production cost of πΆ3(π3)=4+4π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(12βπ2βπ3)
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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