Uncertainty in Spatial Duopoly with Possibly Asymmetric Distributions : A State Space Approach

In spatial competition iuml;B01rms are likely to be uncertain about consumer locations when launching products either because of shifting demographics or of asymmetric information about preferences. Realistically distributions of consumer locations should be allowed to vary over states and need not be uniform. However, the existing literature models location uncertainty as an additive shock to a uniform consumer distribution. The additive shock restricts uncertainty to the mean of the consumers locations. We generalize this approach to a state space model in which a vector of parameters gives rise to different distributions of consumer tastes in different states, allowing other moments (besides the mean) of the consumer distribution to be uncertain. We illustrate our model with an asymmetric consumer distribution and obtain a unique subgame perfect equilibrium with an explicit, closed-form solution. An equilibrium existence result is then given for the general case. For symmetric distributions, the unique subgame perfect equilibrium in the general case can be described by a simple closed-form solution