Oligopolistic competition as a common agency game

In applying the common agency framework to the context of an oligopolistic industry, we want to go beyond the classical dichotomy between Cournot and Bertrand competition. We define two games, the oligopolistic game and the corresponding concept of oligopolistic equilibrium, and an associated auxiliary game that can be interpreted as a common agency game and that has the same set of equilibria. The parameterization of the set of (potential) equilibria in terms of competitive toughness is derived from the first order conditions of this auxiliary game. The enforceability of monopolistic competition, of price and quantity competition, and of collusion is examined in this framework. We then describe the (reduced) set of equilibria one would obtain, first in the nonintrinsic case and then in the case where a global approach would be adopted instead of partial equilibrium approach. Finally, we illustrate the use of the concept of oligopolistic equilibrium and of the corresponding parameterization by referring to the standard case of symmetric quadratic utility.