History-based price discrimination with imperfect information accuracy and asymmetric market shares

The paper considers a duopoly model in which firms inherited asymmetric market shares and history-based price discrimination is viable. However, firms can identify only a share of their own consumers depending to the degree of information accuracy. We derive the pricing strategies and we analyze the relationship between information accuracy and asymmetric market shares, showing under which circumstances there exists an equilibrium in pure strategies. We show that history-based price discrimination makes the dominant firm’s profits always lower than those of the rival, with an ambiguous effect of the information accuracy on industry profits. Moreover, we prove that the level of information accuracy has a decreasing effect on social welfare, while it affects consumer surplus non-monotonically, according to the size of asymmetry in the inherited market shares.