In very general terms, let the price function for the (duopoly) industry be formula_1; price is simply a function of total (industry) output, so is formula_2 where the subscript 1 represents the leader and 2 represents the follower. Suppose firm formula_3 has the cost structure formula_4. The model is solved by backward induction. The leader considers what the best response of the follower is, i.e. how it "will" respond once it has observed the quantity of the leader. The leader then picks a quantity that maximises its payoff, anticipating the predicted response of the follower. The follower actually observes this and in equilibrium picks the expected quantity as a response.