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Revenue maximization through dynamic pricing under unknown market behaviour

We consider the scenario of a multimodal memoryless market to sell one product, where a customer’s probability to actually buy the product depends on the price. We would like to set the price for each customer in a way that maximizes our overall revenue. In this case, an exploration vs. exploitation problem arises. If we explore customer responses to different prices, we get a pretty good idea of what customers are willing to pay. On the other hand, this comes at the cost of losing a customer (when we set the price too high) or selling the product too cheap (when we set the price too low). The goal is to infer the true underlying probability curve as a function of the price (market behaviour) while maximizing the revenue at the same time. This paper focuses on learning the underlying market characteristics with as few data samples as possible by exploiting the knowledge gained from both exploring potentially profitable areas with high uncertainty and optimizing the trade-off between knowledge gained and revenue exploitation. The response variable being binary by nature, classification methods such as logistic regression and Gaussian processes are explored. Two new policies adapted to non parametric inference models are presented, one based on the efficient global optimization (EGO) algorithm and the second based on a dynamic programming approach. Series of simulations of the evolution of the proposed model are finally presented to summarize the achieved performance of the policies.