Revenue management with incomplete information dynamic competition

This paper discusses revenue maximization problems for multi-retailers competition, each retailer has a stock of items and sells them with dynamic pricing based on her/his own stock and other retailers´ stock during a finite time horizon. At any time, each retailer does not know the accurate stock of other retailer, but knows their distribution. A differential game model for the competitive revenue management problem is constructed, and some properties of the retailer´s equilibrium revenue and pricing strategy are obtained. Moreover, a non-competition model is constructed to obtain the up-bound of the equilibrium revenue of competition problem.