Pricing a product with network effects for sale to a fixed population of customers
研究一种具有网络效应的产品在固定异质客户群体中的动态定价问题，提出需求模型和启发式方法，发现固定价格策略在网络效应强或时间跨度长时表现不佳。
Abstract We consider a deterministic dynamic pricing problem for a product that exhibits network effects and that is sold to a fixed heterogeneous population of customers. We begin by introducing a demand model wherein those customers are arrayed over two‐dimensional space according to a bivariate probability distribution. Each customer's location in space provides a description of that customer's intrinsic value for the product as well as the extent to which the customer is influenced by the network effect. In the pricing problem, as sales accumulate over time, the set of customers who have already purchased the product grows, while the set of customers who have not yet purchased the product shrinks. The total customer population remains fixed. Those who have not yet purchased constitute the remaining population of potential buyers of the product. As time moves forward, the mix of customers that remain as potential buyers evolves endogenously. The demand model yields a geometric interpretation of the remaining population of potential buyers, and gives rise to a dynamic program with states that are sets in two‐dimensional space. It is not practical to solve the dynamic pricing problem to optimality, so we present bounds and comparative statics results that help us identify tractable heuristics and obtain rigorous performance guarantees. In numerical experiments, we find that fixed‐price policies may perform poorly, especially when the network effect is strong or the time horizon is long. We also introduce a stochastic version of the problem that uses a spatial Poisson process to describe the customers, and we develop and analyze a heuristic approach for that formulation.