External conjectural variations in symmetric oligopoly equilibrium

In this paper, we introduce the concept of conjectural variations across sectors called "external conjectural variations" in a pure exchange economy. Three results are obtained. First, the symmetric oligopoly equilibrium coincides with the Cournot equilibrium when the conjectural variations are zero. Second, the symmetric oligopoly equilibrium coincides with the competitive equilibrium when the conjectural variations take the value of the competitive market equilibrium price. Third, the optimal strategies of agents between sectors are complements (substitutes) when the conjectural variation is negative (positive).