Non-Adaptive Matroid Prophet Inequalities

TL;DR

This paper introduces the first truly non-adaptive constant-factor prophet inequality for graphic matroids, advancing auction design by enabling order-oblivious posted prices.

Contribution

It provides the first non-adaptive constant-factor prophet inequality specifically for graphic matroids, addressing a gap in auction mechanism design.

Findings

First non-adaptive constant-factor prophet inequality for graphic matroids

Enables order-oblivious posted pricing in auctions

Improves applicability of prophet inequalities in multi-dimensional settings

Abstract

We investigate non-adaptive algorithms for matroid prophet inequalities. Matroid prophet inequalities have been considered resolved since 2012 when [KW12] introduced thresholds that guarantee a tight 2-approximation to the prophet; however, this algorithm is adaptive. Other approaches of [CHMS10] and [FSZ16] have used non-adaptive thresholds with a feasibility restriction; however, this translates to adaptively changing an item's threshold to infinity when it cannot be taken with respect to the additional feasibility constraint, hence the algorithm is not truly non-adaptive. A major application of prophet inequalities is in auction design, where non-adaptive prices possess a significant advantage: they convert to order-oblivious posted pricings, and are essential for translating a prophet inequality into a truthful mechanism for multi-dimensional buyers. The existing matroid prophet inequalities do not suffice for this application. We present the first non-adaptive constant-factor prophet inequality for graphic matroids.