Endogeneous Strategy Spaces: Simultaneous Move vs. Sequential Move Games
24 Pages Posted: 18 Dec 2019
Date Written: December 4, 2019
In a horizontal differentiated duopoly we compare Nash and Stackelberg equilibria in which the firms endogeneously 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) and show that it is always more profitable to stategically set the price (quantity) if the goods are complements (subsitutes). For every degree of product differentiation, consumer surplus and total welfare are maximal in the standard Bertrand equilibrium, followed by the price Stackelberg, the quantity Stackelberg and the Cournot equilibrium. In contrast to Boyer and Moreaux 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).
Keywords: Stackelberg equilibrium, Cournot, Bertrand, strategy space
JEL Classification: C72, D43, L13
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