Approximation algorithm and mechanism design for bisubmodular welfare maximization problem

Abstract

In a combinatorial auction, m indivisible items are sold to multiple buyers. This paper explores the welfare maximization problem in combinatorial auctions with bisubmodular buyers. When buyers' valuations are public, we give a simple greedy algorithm that outputs an allocation achieving 2-approximation, and we prove a hardness result for the bisubmodular welfare maximization problem. When buyers are strategic individuals with valuations as private information, we give a dominant-strategy incentive compatible (DSIC) mechanism that can motivate buyers to provide truthful information and outputs an allocation achieving $O\left(\sqrt{m}\right)$-approximation.