Advantage Of The Stackelberg Model

This analysis assumes that a maximum of two countries are trading with each other. They both have made negotiations to not to impose a tariff but are thinking to go back on their word and impose a protectionist measure. The analysis also assumes that organisations such as World trade organisation don’t exist and that trading will cease after both countries retaliate.
In order for a country to impose a tariff against another country, it must have a first mover advantage. This refers to the advantage that the player who moves first has. (I.e. the country must gain if it imposes a protectionist first rather than if the country is retaliating) The first mover advantage can be best explained by the Stackelberg model.
The model is a game between

Therefore first we need to analyse firm 2’s moves. The output of firm 1 (q1) is already set. So firm 2 must choose q2. The output of both the firms can be shown on the graph below :

For example if firm 1 chooses to produce qx1, firm 2’s best response would be to produce qx2. Similarly if firm 1 produces qy1, then firm 2 should produce qy2. The equation of the line is: p=a-b(q_1+ q_2) where p= profit which is also the payoff in the game. (Ben Polak, 2008)
However in this game, firm 1 knows that firm 2 will use this equation to determine its response. In other words firm 1 can anticipate what firm 2 will do. Therefore the problem facing Firm 1 is that what quantity should it set, knowing that firm 2 will use the equation to determine its response. It should choose the output that maximises its profits.
So far I know that: p=a-b(q_1+q_2) Profit,i = Pqi – Cqi where P stands for revenue and C stands for costs
Backward induction states that this problem should be first solved in terms of firm 2, taking q1 as given.
Firm 2 wants to maximise q2.
[a-bq_1-bq_2 ] q_2-cq_2
Where:
[a-bq_1-bq_2 ] is the price
[a-bq_1-bq_2 ] q_2 is the revenue cq_2 is the

[a-bq_1-bq_2 ] q_1-cq_1 q_2=(a-c)/2b-q_1/2 [a-bq_1-b((a-c)/2b-q_1/2)-c]