Better Approximation for Interdependent SOS Valuations

Pinyan Lu, Enze Sun, Chenghan Zhou

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. In particular, we first generalize the random sampling auction in [9]. Then, we proposed a brand new auction that is simple, efficient to implement and easy to verify the truthfulness. We call our mechanism the contribution-based mechanism. Our proposed mechanism with better approximation runs a convex combination of the above two mechanisms. Since the random sampling mechanism performs well when the second largest value is comparable to the largest one while contribution-based mechanism performs well when the largest one is much larger than all other values, their combination achieves a good balance for all instances. The approximation of our final mechanism is 3.315. This improves the previous 4-approximation mechanism for the first time. Besides the new auction, we also investigate the relation with SOS and strong-SOS, a stronger notion of SOS which was also introduced in [9]. We build a reduction and prove that strong-SOS is as difficult as SOS in terms of approximation ratio for single item setting. This means that it is fine to design mechanisms for strong-SOS valuation only if it is easier since the mechanism can be transformed to a mechanism for general SOS valuations with almost same approximation ratio. The full version of our paper can be found here: https://arxiv.org/abs/2210.06507.

External IDs:dblp:conf/wine/LuSZ22