Two firms (1 and 2) produce a homogeneous good at zero marginal cost. They face two types of consumers: a mass N of consumers are informed about the prices, p₁ and p₂ of the two firms and therefore buy from the cheapest firm; a mass M of consumers are uninformed in the sense that they only know the price of one firm and therefore have a demand only for this firm. We assume that M = M₁ +M₂, where Mi is the mass of consumers who can only observe pi and where M₂ > M₁. All consumers have an inelastic demand: they buy at most one unit of the good, as long as the price is not larger than their reservation price R > 0.

1. Suppose that firm 1 sets its price before firm 2. Characterize the subgame- perfect equilibrium of this two-stage game.

2. Repeat the previous question by supposing instead that it is firm 2 that sets its price first.

3. Show that firm 1 has a second-mover advantage, while firm 2 is indifferent between playing first or second.