# The Competition Complexity of Prophet Inequalities

arXiv: https://arxiv.org/abs/2402.11084 · HTML: https://mlsanity.com/paper/2402.11084/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2024.

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

- [The Competition Complexity of Prophet Inequalities with Correlations](https://mlsanity.com/paper/2409.06868/) (2024)

## Abstract (arXiv)

We study the classic single-choice prophet inequality problem through a resource augmentation lens. Our goal is to bound the (1-varepsilon)-competition complexity of different types of online algorithms. This metric asks for the smallest k such that the expected value of the online algorithm on k copies of the original instance, is at least a (1-varepsilon)-approximation to the expected offline optimum on a single copy. We show that block threshold algorithms, which set one threshold per copy, are optimal and give a tight bound of k = Theta(log log 1/varepsilon). This shows that block threshold algorithms approach the offline optimum doubly-exponentially fast. For single threshold algorithms, we give a tight bound of k = Theta(log 1/varepsilon), establishing an exponential gap between block threshold algorithms and single threshold algorithms. Our model and results pave the way for exploring resource-augmented prophet inequalities in combinatorial settings. In line with this, we present preliminary findings for bipartite matching with one-sided vertex arrivals, as well as in XOS combinatorial auctions. Our results have a natural competition complexity interpretation in mechanism design and pricing applications.