Non-cooperative game of a duopoly under asymmetric information on consumer location

We consider a single inventoried product that is sold by two competing firms (i.e. a duopoly). The two firms are located at both endpoints of a straight line. We assume the firms are unequal in their access to information on consumer locations, that is, only one of the two firms has full information about consumer location. By modelling the profit maximisation problem as a non-cooperative game, we obtain the best response function of the firm who does not have access to accurate consumer information. We show that this response function is translated into a unique, global solution. Through an extensive numerical example, we conclude that asymmetric information on consumer location has a significant effect on the profit gap between the competing firms and on the market share that each firm is able to attract. We conclude that when one firm inaccurately estimates consumer information about location, this can cause a significant deterioration in the profits of both firms and the consumers are the ones who gain from this information asymmetry. This conclusion encourages information sharing with the uninformed firm. Surprisingly, it also emerges from our computation that the higher the travelling costs the higher profits both firms obtain.