Benchmark Problems for Totally Unimodular Set System Auction

TL;DR

This paper introduces benchmark problems for auctions involving totally unimodular set systems, extending previous bounds and aiding in the analysis of truthful auction mechanisms' frugality ratios.

Contribution

It generalizes and strengthens existing bounds for benchmarks in set system auctions with totally unimodular matrices, advancing the theoretical understanding.

Findings

Generalized bounds for set system auction benchmarks

Strengthened theoretical results for frugality ratios

Applicable to a broad class of linear programming problems

Abstract

We consider a generalization of the $k$-flow set system auction where the set to be procured by a customer corresponds to a feasible solution to a linear programming problem where the coefficient matrix and right-hand-side together constitute a totally unimodular matrix. Our results generalize and strengthen bounds identified for several benchmarks, which form a crucial component in the study of frugality ratios of truthful auction mechanisms.