Dynamic Pricing Strategies in a Finite Horizon Duopoly with Partial Information

Abstract

In many applications the sale of perishable products is characterized by competitive settings, e.g. the airline industry. While prices of sellers are typically observable, the inventory levels of firms are mutually not observable. We analyze stochastic dynamic pricing models in a finite horizon duopoly with partial information. Based on the feedback pricing strategies that are optimal for case in which the competitor’s inventory level is observable, we use a Hidden Markov Model approach to compute strategies that are applicable when the competitor’s inventory level is not 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 not known. We find that expected profits are hardly affected by different information structures as long as the firms’ information is symmetric.