Graph Pricing with Limited Supply
Zachary Friggstad, Maryam Mahboub

TL;DR
This paper develops approximation algorithms for graph pricing with limited supply and customer budgets, focusing on maximizing revenue without envy-free constraints, and provides bounds for various capacity scenarios.
Contribution
It introduces new approximation algorithms for capacitated graph pricing, including local search and LP-rounding techniques, with improved bounds for different capacity regimes.
Findings
Achieves an 8-approximation for the capacitated case.
Provides a 7.8096-approximation for simple graphs with uniform capacities.
Offers a $(4+ ext{epsilon})$-approximation for large capacities using LP rounding.
Abstract
We study approximation algorithms for graph pricing with vertex capacities yet without the traditional envy-free constraint. Specifically, we have a set of items and a set of customers where each customer has a budget and is interested in a bundle of items with . However, there is a limited supply of each item: we only have copies of item to sell for each . We should assign prices to each and chose a subset of customers so that each can afford their bundle () and at most chosen customers have item in their bundle for each item . Each customer pays for the bundle they purchased: our goal is to do this in a way that maximizes revenue. Such pricing problems have been studied from the perspective of envy-freeness…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
