Imperfect history-based price discrimination with asymmetric market shares

We consider a duopoly model with history-based price discrimination where firms inherit asymmetric shares of consumers that they might partly recognize according to the degree of information completeness. We analyze the impact of the amount of information on market configuration, profits and welfare. With high degrees of information completeness and sufficiently small asymmetries in the market shares, firms are more likely to use aggressive pricing strategies, both poaching rival's consumers. Otherwise, firms adopt different pricing strategies and price discrimination is enforced only by the smaller firm. Greater information completeness has a non-monotonic effect on profits and a decreasing effect on welfare. Finally, we show that the case with perfect information is a special case whose results do not hold when even a small degree of uncertainty is introduced in the game.