Dynamic pricing with online learning of customer arrival rate and acceptable price

In many industries, the price of commodities are adjusted by taking into account the current level of inventory and the distribution of future demand. This has motivated studies in the area of dynamic pricing, which among others have been successfully applied in airline industry. A common assumption in these studies is that the distribution of future demand is known in advance. While sometimes this
distribution can be learned from historical data in advance, there are cases where the selling scenario has unique characteristics and the learning can only be achieved as the selling process is going on. In this note we will use Bayesian learning to update our belief about two distributions: The distribution of customer arrivals and the distribution of acceptable price for customers.