  We consider a price competition between two sellers of perfect-complement
goods. Each seller posts a price for the good it sells, but the demand is
determined according to the sum of prices. This is a classic model by Cournot
(1838), who showed that in this setting a monopoly that sells both goods is
better for the society than two competing sellers. We show that non-trivial
pure Nash equilibria always exist in this game. We also quantify Cournot's
observation with respect to both the optimal welfare and the monopoly revenue.
We then prove a series of mostly negative results regarding the convergence of
best response dynamics to equilibria in such games.
