A fundamental problem of oligopoly theory is equilibrium indeterminacy. This indeterminacy is not only of the kind associated with a given equilibrium concept and the possibility of multiple solutions. It is mainly related to the choice of the equilibrium concept itself. This is most simply demonstrated in static models by the choice between quantity competition (usually assimilated to the approach of Cournot, 1838) and price competition (linked to Bertrand's 1883 critique of Cournot). However, this second kind of indeterminacy" is not to be seen as the failure of the theory, but rather as reflecting the variety of observed regimes of oligopolistic competition, with varying degree of toughness resulting from firms more or less coordinated behavior. Certainly this variety of regimes cannot be reduced to the dichotomous choice between Cournot and Bertrand.
Moreover each static concept itself (Cournot, Bertrand, or else) may be seen as the reduced form of various industrial situations, involving different dynamic settings and different norms of conduct for the firms. A good example of this multiplicity is the variety of structural and behavioral justifications for Cournot outcome. It may be based for instance on the way production and sales are organised in time. As well illustrated by Kreps and Scheinkman (1983) for a symmetric duopoly, if firms fix their production (or capacity) levels in advance and then compete in prices, the Cournot outcome obtains as the only subgame perfect equilibrium. Cournot outcome may also be associated with particular "facilitating practices" in the selling policy of firms. If, for example, firms are supposed to use best-price policies ("meet or-release" and "most-favored-customer" clauses) together with advance notification of list price changes and the possibility of discounts below list prices, then Holt and Scheffman (1987) show that Cournot price is the highest equilibrium price. But there are other ways to select the Cournot outcome. As known since Bowley (1924), it can be obtained by assuming appropriate conjectures in the conjectural variation approach, or, as we will see again below, it can be obtained as a particular supply function equilibrium when assuming (as in Grossman, 1981, and Hart, 1982) that firms compete in supply functions. And the latter approach can be explained by having the owners of the firms designing particular types of incentive contracts for their managers as functions of profitability and sales.
The property for a static model of competition to correspond to different dynamic settings and different norms of conducts (including different types of conjectures and commitments) should hold for other competition regimes than the Cournot one. However, we do not pursue this investigation here but, instead, sticking to a static model of competition, we propose a comprehensive concept of oligopolistic equilibrium allowing for a parametrized continuum of competition regimes. This concept remains in the line of Cournot by considering oligopolistic competition as a generalization of monopoly, with firms setting simultaneously both prices and quantities constrained by market demand (which, unlike Cournot, we require to be fully satisfied only at equilibrium), and also constrained by their rivals' anticipated behavior& (implying, as in Cournot, the "necessity" that the selling price be the same for all firms when the good is homogeneous). Hence, each firm, while maximizing its profit both in price and in quantity, is supposed to face two constraints, one relative to the size of the market, the other relative to its share of that market. The type of solution (i.e. the competition regime) will vary according to the values of the Lagrange multipliers associated with each of these two constraints. The proposed parametrization, interpreted in terms of competitive toughness, is based on these values.
The set of oligopolistic equilibria will be shown to include the Cournot solution at one extreme, when competition is extremely soft, as well as the competitive equilibrium at the other extreme, when competition is extremely tough. In the homogeneous case, the intermediate competititon regimes will be characterized as supply function equilibria, with firms strategy spaces restricted to the set of non-decreasing supply functions. Alternatively, the set of oligopolistic equilibria outcomes will be identified as a selected subset of the outcomes obtained by conjectural variations of a particular type (the compensating ones).
The proposed concept of oligopolistic equilibrium is applicable to an industry supplying a group of differentiated products, the homogeneous product being the limit case corresponding to perfect substitutability. These differentiated products are aggregated into a composite commodity, in a similar but more general framework than the popular Dixit-Stiglitz (1977) and Spence (1976a, b) one. Products in such an industry are not necessarily substitutes (perfect complementarity: being actually another limit case). This applies to many man-ufactured good industries, such as the automobile and electronic industry, if we include maintenance, parts and complementary equipments, as well as to many service industries (e.g. hotel bookings and trip organizations in the travel industry). Of course, the present paper does not treat product differentiation in its full generality (horizontal and vertical) and remains in a strict partial equilibrium setting. However, a comprehensive concept of oligopolistic equilibrium, encompassing a large family of competition regimes, can be seen as a building block to be used in a more general, multi-sector setting.
