Active Learning and Dynamic Pricing Policies

In this paper, we address the problem of dynamic pricing to optimize the revenue coming from the sales of a limited inventory in a finite time-horizon. A priori, the demand is assumed to be unknown. The seller must learn on the fly. We first deal with the simplest case, involving only one class of product for sale. Furthermore the general situation is considered with a finite number of product classes for sale. In particular, a case in point is the sale of tickets for events related to culture and leisure; in this case, typically the tickets are sold months before the event, thus, uncertainty over actual demand levels is a very a common occurrence. We propose a heuristic strategy of adaptive dynamic pricing, based on experience gained from the past, taking into account, for each time period, the available inventory, the time remaining to reach the horizon, and the profit made in previous periods. In the computational simulations performed, the demand is updated dynamically based on the prices being offered, as well as on the remaining time and inventory. The simulations show a significant profit over the fixed-price strategy, confirming the practical usefulness of the proposed strategy. We develop a tool allowing us to test different dynamic pricing strategies designed to fit market conditions and seller s objectives, which will facilitate data analysis and decision-making in the face of the problem of dynamic pricing

Pricing with Limited Knowledge of Demand

How should a firm price a new product for which little is known about demand? We propose a pricing rule that can be used if the firm can estimate (even roughly) the maximum price it can charge and still expect to sell some units, and the firm need not know in advance the quantity it will sell. The rule is simple: Set price as though the demand curve were linear. We show that if the true demand curve is one of many commonly used demand functions, or even a more complex function, and if marginal cost is known and constant, the firm can expect its profit to be close to what it would earn if it knew the true demand curve. We derive analytical performance bounds for a variety of demand functions, calculate expected profit performance for randomly generated demand curves, and evaluate the welfare implications of our pricing rule

Real-time dynamic pricing in a non-stationary environment using model-free reinforcement learning.

This paper examines the problem of establishing a pricing policy that maximizes the revenue for selling a given inventory by a fixed deadline. This problem is faced by a variety of industries, including airlines, hotels and fashion. Reinforcement learning algorithms are used to analyze how firms can both learn and optimize their pricing strategies while interacting with their customers. We show that by using reinforcement learning we can model the problem with inter-dependent demands. This type of model can be useful in producing a more accurate pricing scheme of services or products when important events affect consumer preferences. This paper proposes a methodology to optimize revenue in a model-free environment in which demand is learned and pricing decisions are updated in real-time. We compare the performance of the learning algorithms using Monte-Carlo simulation