Cournot oligopoly with "almost" identical convex costs

M. McManus has shown that a Cournot equilibrium among identical quantity-setting firms with a convex cost function always exists, whatever the inverse demand function. Here the result is extended in two directions: Firstly, the firms may differ in their production capacity. Secondly, the theorem remains valid for a discrete version of the Cournot model where all the outputs are integers.