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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.

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In this study, we investigate firms' ability to collude when price discrimination based on the inherited market is possible, but the information accuracy about the inherited market is imperfect. We show that the level of information accuracy affects collusion sustainability nonmonotonically, according to the starting level of information and the consumers' reservation price. Moreover, we show that banning price discrimination might increase the sustainability of tacit collusion.

We study an infinitely repeated oligopoly game in which firms compete on quantity and one of them is capacity-constrained. We show that collusion sustainability is non-monotonic in the size of the capacity-constrained firm, which has little incentive to deviate from a cartel. We also present conditions for the emergence of a partial cartel, with the capacity-constrained firm being excluded by the large firms or self-excluded. In the latter case, we show under which circumstances the small firm induces a partial conspiracy that is Pareto-dominant. Implications for cartel identification and enforcement are finally discussed.