Better Approximation for Interdependent SOS Valuations

TL;DR

This paper introduces a new truthful mechanism for interdependent SOS valuations that improves the approximation ratio from 4 to 3.315, advancing the design of efficient auctions in complex valuation settings.

Contribution

It presents a novel, simple truthful mechanism achieving a better approximation ratio for interdependent SOS valuations, narrowing the gap to the lower bound.

Findings

Achieves a 3.315-approximation ratio

Improves upon the previous 4-approximation mechanism

Provides insights into truthful auction design for interdependent valuations

Abstract

Submodular over signal (SOS) defines a family of interesting functions for which there exist truthful mechanisms with constant approximation to the social welfare for agents with interdependent valuations. The best-known truthful auction is of $4$-approximation and a lower bound of 2 was proved. We propose a new and simple truthful mechanism to achieve an approximation ratio of 3.315.