# Learning Revenue Maximization using Posted Prices for Stochastic Strategic Patient Buyers

arXiv: https://arxiv.org/abs/2202.06143 · HTML: https://mlsanity.com/paper/2202.06143/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 12 Feb 2022.

## Builds on (most cited first, 12 of 12)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Learning Prices for Repeated Auctions with Strategic Buyers](https://mlsanity.com/paper/1311.6838/) (2013)
- [Learning Simple Auctions](https://mlsanity.com/paper/1604.03171/) (2016)
- [Generalizing Complex Hypotheses on Product Distributions: Auctions, Prophet Inequalities, and Pandora's Problem](https://mlsanity.com/paper/1911.11936/) (2019)
- [Majorizing Measures, Sequential Complexities, and Online Learning](https://mlsanity.com/paper/2102.01729/) (2021)
- [Making the Most of Your Samples](https://mlsanity.com/paper/1407.2479/) (2014)
- [Efficient Empirical Revenue Maximization in Single-Parameter Auction Environments](https://mlsanity.com/paper/1610.09976/) (2016)
- [Bandits with Movement Costs and Adaptive Pricing](https://mlsanity.com/paper/1702.07444/) (2017)
- [Multi-Armed Bandits with Metric Movement Costs](https://mlsanity.com/paper/1710.08997/) (2017)
- [Computing Stackelberg Equilibria of Large General-Sum Games](https://mlsanity.com/paper/1909.03319/) (2019)
- [Optimal Mechanism Design for Single-Minded Agents](https://mlsanity.com/paper/2002.06329/) (2020)
- [The menu complexity of "one-and-a-half-dimensional" mechanism design](https://mlsanity.com/paper/1711.02165/) (2017)

## Abstract (arXiv)

We consider a seller faced with buyers which have the ability to delay their decision, which we call patience. Each buyer's type is composed of value and patience, and it is sampled i.i.d. from a distribution. The seller, using posted prices, would like to maximize her revenue from selling to the buyer. In this paper, we formalize this setting and characterize the resulting Stackelberg equilibrium, where the seller first commits to her strategy, and then the buyers best respond. Following this, we show how to compute both the optimal pure and mixed strategies. We then consider a learning setting, where the seller does not have access to the distribution over buyer's types. Our main results are the following. We derive a sample complexity bound for the learning of an approximate optimal pure strategy, by computing the fat-shattering dimension of this setting. Moreover, we provide a general sample complexity bound for the approximate optimal mixed strategy. We also consider an online setting and derive a vanishing regret bound with respect to both the optimal pure strategy and the optimal mixed strategy.