The posterior price-matching is a mechanism where a firm reimburses the price difference to a customer who has purchased a product before a markdown. Thus, it is unlikely for a monopolist seller to mark down in a market where consumers are homogeneous (i.e., no room for price discrimination) and there is no inventory to reduce. The purpose of this paper is to offer a novel behavioral explanation for the reason why such posterior price-matching system should be adopted, study the role of consumer boundedly rational expectations in this mechanism, and offer managerial guidelines for the implementation of dynamic markdown policy when customers are boundedly rational.

Under the posterior price-matching policy, there is a common assumption of “rational expectations” of the firm and its consumers in relation to each other’s strategies. However, in real-life practice, while a firm has abundant information, its consumers only have scarce chances to learn the firm’s markdown strategy. A new model capturing consumer boundedly rational expectations should be adopted so as to allow sellers to make profit under a price-matching policy.

This paper adopts a simple model enabling the isolation and focus on the impact of customer boundedly rational expectations on using posterior price matching. Under this basic model, while the firm has perfect information regarding its consumers’ strategies, consumers make their decisions according to the sampled outcome (i.e., anecdote). It is found that consumer boundedly rationality alone may justify the employment of posterior price matching, coupled with probabilistic markdowns. Even though it is uncertain as to whether a firm can indeed make a profit by the adoption of such price-matching mechanism, ignoring consumer bounded rationality is likely to lead to a substantial profit loss. Therefore, the role of customer boundedly rational expectations is crucial for firms when considering whether to adopt posterior price matching.

When customers are proved as having boundedly rational expectations, it is beneficial for firms to dynamically manage and adjust their markdown probability over the long run. Instead of committing to a fixed probability of markdowns, offering dynamic markdowns – such as providing markdown probability in each season or offering personalized pricing strategy to each individual consumer – is a more feasible and beneficial option for firms. A dynamic programming model is hence built to characterize its optimal policy. It is evident that a cyclic policy shifting between a high and low markdown probability is generally seen as the most favorable for exploiting customer boundedly rational expectations due to the submodularity of the firm profit function. It is also demonstrated that the more boundedly rational customers are, the higher degree of flexibility such dynamic markdown policy may be carried out with. So long as customers have multiple samples, the firm can still make a substantial profit by the employment of such dynamic markdown policy.