On pure strategy Nash equilibria in price quantity games
This paper examines the existence and characteristics of pure strategy Nash equilibria in oligopoly models in which firms set both prices and quantities. Existence is proved for a broad and natural class of price quantity games. With differentiated products, the equilibrium outcome is similar to that of a price only model. With undifferentiated products and limited spillover demand, there are rationing equilibria in which combined production falls short of market demand. Moreover, there might again be an equilibrium reflecting the outcome of a price game. Competition in price and quantity may thus yield Bertrand outcomes under a variety of market conditions.