Extended Games Played by Managerial Firms with Asymmetric Costs

Both demand and cost asymmetries are considered in oligopoly model with managerial delegation. It shows that (i) both efficient and inefficient firms with delegation have second move advantage under quantity setting and first move advantage under price competition; (ii) the extended games under both quantity and price competition have subgame equilibria. Lastly, the social welfare of all strategy combinations is considered to find that when the efficient firm moves first and the inefficient firm moves second under price competition, the social welfare can be higher than Bertrand case, if the efficiency gap between the two firms is huge. 1. Introduction Industrial organization analysis in oligopoly and duopoly usually assumes that firms move either simultaneously or sequentially. Technically speaking, it is Cournot (Bertrand) game or Stackelberg game. In a seminal paper, Singh and Vives [1] show that, in a differentiated duopoly, Cournot competition entails higher prices and profits than Bertrand competition, whereas both firms’ output and social welfare are higher under Bertrand competition. López and Naylor [2] show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition—when the differentiated duopoly game is played in imperfect substitutes—is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences and on the distribution of bargaining power over the input price. Hsu and Wang [3] show that both consumer surplus and total surplus are higher under price competition than under quantity competition, regardless of whether goods are substitutes or complements. Zanchettin [4] shows that both the efficient firm’s profits and industry profits are higher under Bertrand competition when asymmetry is strong and/or products are weakly differentiated. (See Mukherjee [5] for comparison of equilibrium outcome under quantity and price competition in free entry, and in Mukherjee et al. [6], comparison of equilibrium outcome under quantity and price competition is analyzed in a vertical structure with production efficiency. The productivity difference between the downstream firms is the key to their analyses, which enriches Zanchettin [4] because in spite of the homogenous products Mukherjee et al. [6] utilize the productivity differences to justify the cost asymmetry assumed in Zanchettin [4]. Correa-López [7] also makes similar comparisons in a vertical structure but allows the downstream firm to choose either price or