Customer Heterogeneity and Strategic Behavior in Revenue Management: a Martingale Approach

This paper studies the effects of customer heterogeneity and strategic behavior on dynamic pricing strategies. We assume that heterogenous customers arrive during a fixed season according to a Poisson process with intensity as a function of price. We obtain an implicit optimal pricing policy by solving a HJB equation. Our results show that optimal prices follow a submartingale (supermartingale) if price sensitivity is constant or decreasing (increasing) in time. We also demonstrate martingale properties for the arrival intensity and consumer surplus processes. Finally, we build heterogenous customer profiles, composed of value of time and price sensitivity, and show that an increasing (decreasing) value of time function results in increasing (decreasing) prices and decreasing (increasing) customer price sensitivity over the course of the season. Date: November 2, 2004. Email: [email protected] and [email protected].