We examine both quantity and price competition between a number of profit-maximizing firms and a state-controlled enterprise (SCE). The objective function of the latter is strategically defined by a welfare-maximizing government which weighs the SCE’s profits relative to consumer surplus and private profits. Different motives drive the government‘s optimal behavior in the two competitive settings and lead all firms in oligopoly to gain higher profits in Cournot than in Bertrand. The profit ordering is reverted, and social welfare is enhanced, with respect to the purely-mixed market examined by Ghosh and Mitra (2010). In duopoly, aggregate profits are equivalent in Cournot and Bertrand.