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.