# Sample-Based Optimal Pricing

64 Pages Posted: 19 Mar 2019 Last revised: 12 Jul 2019

See all articles by Amine Allouah

## Amine Allouah

Columbia University - Columbia Business School

## Omar Besbes

Columbia Business School - Decision Risk and Operations

Date Written: February 25, 2019

### Abstract

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, $\alpha$-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 novel dynamic programming value functions. In turn, we develop a tractable procedure to obtain near-optimal mechanisms and near-worst-case distributions, allowing to characterize the maximin ratio for all values of $\alpha$ in $[0,1]$.

Keywords: pricing, data-driven decision-making, value of information, monotone hazard rate, regular, $\alpha$-strongly regular distributions, competitive ratio

Suggested Citation

Allouah, Amine and Besbes, Omar, Sample-Based Optimal Pricing (February 25, 2019). Available at SSRN: https://ssrn.com/abstract=3334650 or http://dx.doi.org/10.2139/ssrn.3334650

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