The location model with two periods of price competition

In this paper we characterize the subgame perfect Nash equilibria of a location-then-price game where firms first choose locations and after that compete for prices in two subsequent periods. Locations are thus seen as long term commitments. There are two types of consumers, each with different valuations for the variants offered by the firms. Due to changes in the fractions of the consumer types, competition in both periods differs. Firms anticipate that their location choice in uences price competition in both periods and therefore maximize their lifetime profit. Although we cannot give explicit expressions for the firms' location choices, we can prove the existence of a unique subgame perfect Nash equilibrium.