Competitive dynamic pricing under demand uncertainty

We consider a multi-seller dynamic pricing problem with unknown demand models. In this problem, each seller offers prices sequentially to a stream of potential customers. Each customer considers only the lowest price among all sellers, and the probability of making a purchase is governed by an unknown demand model that can take a finite number of possible forms. The problem is formulated as a repeated game with incomplete information. We develop a dynamic pricing strategy that leads to an efficient subgame perfect equilibrium and offers a finite regret with respect to the ideal case of a known demand model.