Unrestricted Duopoly Competition: Equilibrium and Survival

This paper is inspired by the ever lasting discussions over Bertrand's (1883) price-deviation critique of Cournot's (1838) duopoly analysis. We consider a homogenous good duopoly with constant marginal costs and no capacity constraints, but we allow firms to set either a quantity, a price, or both. We derive two main results. First, this model has two duopoly equilibria, one where firms commit only to prices (Bertrand behavior) and one where they commit only to quantities (Cournot behavior), and it has equilibria supporting a perfect contestable market where one firm supplies the entire market at a price equal to marginal costs. Second, the Cournot behavior is best fit for survival in terms of evolutionary stability. This provides an argument for the existence of quantity-commitment institutions like auctions in oligopolistic markets for homogenous goods.