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

In spatial competition firms are likely to be uncertain about consumer locations when launching products either because of shifting demograph- ics or of asymmetric information about preferences. Realistically distri- butions 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 loca- tions. We generalize this approach to a state space model in which a vector of parameters gives rise to different distributions of consumer tastes in dif- ferent 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.