Dynamic Pricing Competition with Unobservable Inventory Levels: A Hidden Markov Model Approach
Many markets are characterized by competitive settings and incomplete information. While offer prices of sellers are often observable, the competitors’ inventory levels are mutually not observable. In this paper, we study stochastic dynamic pricing models in a finite horizon duopoly model with partial information. To be able to derive effective pricing strategies when the competitor’s inventory level is not observable, we use a Hidden Markov Model. Our approach is based on feedback pricing strategies that are optimal, if the competitor’s inventory level is observable. Optimized 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. For the case that a competitor’s strategy is unknown, we derive robust heuristic strategies. Comparing duopolies with different information structures, we find that expected sales results are quite similar as long as the firms’ information is symmetric. By evaluating asymmetric pairs of strategies, we study to which extent the value of additional information is affected by the consumers’ price sensitivity or the competitors’ price response times.
KeywordsDynamic pricing Duopoly competition Response strategies Hidden Markov Model Asymmetric information
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