Non-Adaptive Matroid Prophet Inequalities

Abstract

We consider the problem of matroid prophet inequalities. This problem has been ex- tensively studied in case of adaptive prices, with [KW12] obtaining a tight 2-competitive mechanism for all the matroids. However, the case non-adaptive is far from resolved, although there is a known constant- competitive mechanism for uniform and graphical matroids (see [Cha+20]). We improve on constant-competitive mechanism from [Cha+20] for graphical matroids, present a separate mechanism for cographical matroids, and combine those to obtain constant-competitive mechanism for all regular matroids.