Uncertain Spatial Demand and Price Flexibility: A State Space Approach to Duopoly

In spatial competition firms are likely to be uncertain about demand when launching products either because of shifting demographics or of asymmetric information about preferences. This paper considers two types of prices: those set on prior information and flexible prices which adjust across states. The existing literature requires uniformly distributed consumers in each state, restricts the uncertainty to the mean of consumer locations ("demand location uncertainty") and requires finite support. We generalize this approach by allowing distributions of consumer tastes to vary across states with the effect that the support and other moments (besides the mean) of the consumer distribution are allowed to be uncertain. The support of the state parameter is only assumed to be convex. We provide conditions for a unique price equilibrium depending only on the distribution of the uncertainty and the state distributions. Comparative statics for the Normal-Quadratic case show ex-ante prices increase faster in uncertainty than expected ex-post prices. We also briefly consider efficiency and endogenous locations for the symmetric case.