Profit loss in Cournot oligopolies

We compare the aggregate profit achieved at a Cournot equilibrium to the maximum possible, which would be obtained if the suppliers were to collude. We establish a lower bound on the profit of Cournot equilibria in terms of a scalar parameter that captures qualitative properties of the inverse demand function and the number of suppliers (or the maximum of the suppliers’ market shares). The lower bounds are tight when the inverse demand function is affine.