Endogenous strategy spaces in sequential- and simultaneous-move duopoly games

Duopoly markets are widely discussed in industrial economics under the assumptions of quantity and price competition in sequential- and simultaneous-move duopoly games with differentiated goods. We compare Nash and Stackelberg equilibria in which the firms endogenously choose to behave as a price or quantity setter. Using the utility function introduced by Dixit (1979), we generalize the model of Boyer and Moreaux (1987) by allowing different market sizes and show that it is always more profitable to strategically set the price (quantity) if the goods are complements (substitutes). For every degree of product differentiation, consumer surplus and total welfare are highest under the standard Bertrand equilibrium, followed by the price Stackelberg, the quantity Stackelberg, and the Cournot equilibrium. In a generalized framework of Boyer and Moreaux (1987), we show that there is no unique ranking of prices, quantities, and profits of the leader and follower depending on the degree of product differentiation and the type of competition. Furthermore, we show that the price (quantity) Stackelberg equilibrium is bounded by the Bertrand and the mixed Nash equilibrium in which Firm 1 sets the price (quantity) and Firm 2 the quantity (price).