Dynamic oligopoly games with private Markovian dynamics

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.