Competitive pricing by a price leader

We examine the problem of pricing in a market where one brand acts as a price leader. We develop a procedure to estimate a leader's price rule, which is optimal given a sales target objective, and allows for the inclusion of demand forecasts. We illustrate our estimation procedure by calibrating this optimal price rule for both the leader and the follower using data on past sales and prices from the mid-size sedan segment of the U.S. automobile market. Our results suggest that a leader-follower system (Stackelberg) seems more consistent with the pricing behavior in this market, than a mutually independent pricing rule (Nash). We also find that our optimal price rule explains this market data better than other pricing schemes that do not account for optimizing behavior on the part of the leader and the follower.

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