Bayesian Dynamic Pricing with Two-Sided Censored Customer Willingness-to-Pay Data

We consider a Bayesian dynamic pricing problem with an unknown distribution of customer willingness to pay (WTP). The posted price serves as either a leftor right-censoring point of the customer’s true WTP. This two-sided censoring effect makes the Bayesian dynamic pricing problem difficult to analyze. Little is known in the literature about how to solve this problem in its general form. In this paper, we develop computational strategies to tackle this challenge. We first quantify the loss of informational value due to censoring and derive the first-order derivative for the problem. Leveraging on these results, we derive a sequence of lower and upper bounds for the value function of the problem. We then propose three easy-to-compute heuristics based on the bound results. Our numerical studies show that one of the proposed heuristics is near optimal in all cases. We further discuss several interesting insights obtained from our analytical and numerical analysis.