We study a model of spatial duopoly competition with sequential entry on a segment in the choice of locations (stage 1 of the game) and then simultaneous competition in delivery prices (stage 2). The second mover at stage one has incomplete information on the marginal cost (high or low) of the first mover. Hence, we obtain a signalling game in which there exist natural constraints on the range of possible signals. The focus of the analysis is the identification and characterization of perfect Bayesian equilibria robust to some refinements criteria (the intuitive criterion and D1) when the constraints on the signals are tight. The main result is that the separating equilibrium is no longer the only equilibrium surviving the D1 criterion. An important consequence of this result is that the robust equilibria become highly sensitive to the prior beliefs of the players. For a given interval of locations, the higher the cost difference between the low type and the high type of first movers, the more often the constraints will be tight. The characterization of the role of these constraints requires a systematic description of all the equilibria and of their dependence on prior beliefs.
Spatial competition and distortions of localization under incomplete information
3 April 2018