In many applications the sale of perishable products is characterized by competitive settings and incomplete information. While prices of sellers are typically observable, the inventory levels of firms are mutually not observable. In this paper, we analyze stochastic dynamic pricing models in a finite horizon duopoly with partial information. We use a Hidden Markov Model approach to compute strategies that are applicable when the competitor’s inventory level is not observable. Our approach utilizes feedback pricing strategies that are optimal if the competitor’s inventory level is observable. We show that price reactions are balancing two effects: (i) to slightly undercut the competitor’s price to sell more items, and (ii) to use high prices to promote a competitor’s run-out and to act as a monopolist for the rest of the time horizon. Moreover, we compute heuristic strategies that can be applied when the number of competitors is large and their strategies are unknown. We find that expected profits are hardly affected by different information structures as long as the firms’ information is symmetric.