Comparing Cournot and Bertrand Competition in a Unionized Mixed Duopoly

We investigate a differentiated mixed duopoly in which private and public firms can choose to strategically set prices or quantities by facing a union bargaining process. For the case of a unionized mixed duopoly, only the public firm is able to choose a type of contract irrespective of whether the goods are substitutes or complements in the equilibrium. Thus, we show that social welfare under Bertrand competition is always determined by the public firm's dominant strategy, wherein the Bertrand competition entails higher social welfare than the Cournot competition. Moreover, there are multiple Nash equilibria in the contract stage of the game. Finally, our main results hold irrespective of the nature of goods, with the exception of when a sufficiently large parameter of complements is employed, the ranking of private firm's profit is not reversed, which is contrast to the standard findings.