Stackelberg equilibria in a multiperiod vertical contracting model with uncertain and price-dependent demand
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Date
2012-02Metadata
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Abstract
In this paper, we consider Stackelberg games in a multiperiod vertical contracting model with uncertain demand.
Demand has a distribution with a mean and variance that depend on the current retail price, and this dependence
may vary from period to period. We focus on a class of problems in which the market has a memory-based scaling
of demand, and the mean scaling is a function of previous retail prices. This leads to a strategic game in which the
parties must balance high immediate profits with reduced future earnings. We propose a complete solution to this
multiperiod Stackelberg game, covering cases with finite and infinite horizons. The theory is illustrated by using a
Cobb-Douglas demand function with an additive, normally distributed random term, but the theory applies to more
general settings.