Competition for market share or for market size: oligopolistic equilibria with varying competitive toughness
We propose a comprehensive concept of oligopolistic equilibrium, allowing for a parametrized continuum of competition regimes, with each firm setting simultaneously both its price and its quantity and facing two constraints: one relative to its share ofthe market, the other relative to the size of the 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. In the homogeneous case, the set of oligopolistic equilibria will be shown to include the Cournot solution at tone extreme, when competition is extremely soft, as well as the competitive equilibrium at the other extreme, when competition is extremely tough. The set of equilibria may be characterized as supply function equilibria, with firms strategy spaces restricted to the set of non-decreasing supply functions, or, alternatively, 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 also applicable to an industry supplying a group of differentiated products, the homogeneous product being the limit case corresponding to perfect substitutability.
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