Profitability under commitment in cournot and bertrand mixed markets

we examine both quantity and price competition in a mixed oligopoly. In a market in which the adoption of commitment strategies enables the public firm or a government to achieve welfare gains, profits of both the public and the private firms turn out to be higher under Cournot than Bertrand competition. We therefore find that the profit ordering is reversed with respect to the scenario described by Ghosh and Mitra (2010), thus confirming both the higher competitiveness and the higher efficiency of price competition than quantity competition. Moreover, we demonstrate that welfare-maximizing behavior under commitment leads in a duopoly to the same aggregate profits under Cournot and Bertrand.