Asymmetric information and exchange of information about product differentiation

We introduce asymmetric information about consumers' transportation costs (i.e., the degree of product differentiation) in the model of Hotelling (1929). When the transportation costs are high, both firms have lower profits than in the case of perfect information. Contrarily, both firms may prefer the asymmetric information case if the transportation costs are low (the informed firm always prefers the informational advantage, while the uninformed firm may or may not prefer to remain uninformed). Information sharing is ex-ante advantageous for the firms, but ex-post damaging in the case of low transportation costs. If the information is not verifiable, the informed firm always tends to announce that the transportation cost is high. To induce truthful revelation: (i) the uninformed firm must pay for the informed firm to confess that the transportation costs are low; and (ii) the informed firm must make a payment (to the uninformed firm or to a third party) for the uninformed firm to believe that the transportation costs are high.