Sample-Based Optimal Pricing

Pricing is central to many industries and academic disciplines ranging from Operations Research to Computer Science and Economics. In the present paper, we study data-driven optimal pricing in low informational environments. We analyze the following fundamental problem: how should a decision-maker optimally price based on a single sample of the willingness-to-pay (WTP) of customers. The decision-maker's objective is to select a general pricing policy with maximum competitive ratio when the WTP distribution is only known to belong to some broad set. We characterize optimal performance across a spectrum of non-parametric families of distributions, α-strongly regular distributions, two notable special cases being regular and monotone hazard rate distributions. We develop a general approach to obtain structural lower and upper bounds on the maximin ratio characterized by appropriate dynamic programming value functions. In turn, we develop a tractable procedure to evaluate these bounds. The bounds allow to characterize the maximin ratio up to 1.3% across a spectrum of values of α.