# Competitive and Revenue-Optimal Pricing with Budgets

arXiv: https://arxiv.org/abs/2310.03692 · HTML: https://mlsanity.com/paper/2310.03692/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2023.

## Built on by (most cited first, 1 of 1)

- [Autobidding Arena: unified evaluation of the classical and RL-based autobidding algorithms](https://mlsanity.com/paper/2510.19357/) (2025)

## Abstract (arXiv)

In markets with budget-constrained buyers, competitive equilibria need not be efficient in the utilitarian sense, or maximise the seller's revenue. We consider a setting with multiple divisible goods. Competitive equilibrium outcomes, and only those, are constrained utilitarian efficient, a notion of utilitarian efficiency that respects buyers' demands and budgets. Our main contribution establishes that, when buyers have linear valuations, competitive equilibrium prices are unique and revenue-optimal for a zero-cost seller.