We analyze a dynamic oligopoly model with strategic sellers and buyers/consumers over a finite horizon. Each seller has private information described by a finite-state Markov process; the Markov processes describing the sellers' information are mutually independent. At the beginning of each time/stage t the sellers simultaneously post the prices for their good; subsequently, consumers make their buying decisions; finally, after the buyers' decisions are made, a public signal, indicating the buyers' consumption experience from each seller's good becomes available and the whole process moves to stage t + 1. The sellers' prices, the buyers' decisions and the signal indicating the buyers' consumption experience are common knowledge among buyers and sellers. This dynamic oligopoly model arises in online shopping and dynamic spectrum sharing markets. The model gives rise to a stochastic dynamic game with asymmetric information. Using ideas from the common information approach (developed in [1] for decentralized decision-making), we prove the existence of common information based equilibria. We obtain a sequential decomposition of the game and we provide a backward induction algorithm to determine common information-based equilibria that are perfect Bayesian equilibria. We illustrate our results with an example.