Combinatorial Auctions with Interdependent Valuations: SOS to the Rescue

• 成果类型: Article; Early Access
• 署名作者: Eden, Alon; Feldman, Michal; Fiat, Amos; Goldner, Kira; Karlin, Anna R.
• 署名单位: Hebrew University of Jerusalem; Tel Aviv University; Boston University; University of Washington; University of Washington Seattle
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.1371
• 发表日期: 2023
• 关键词: design

摘要

We study combinatorial auctions with interdependent valuations, where each agent i has a private signal si that captures her private information and the valuation function of every agent depends on the entire signal profile, s = (s1,...,sn). The literature in economics shows that the interdependent model gives rise to strong impossibility results and identifies assumptions under which optimal solutions can be attained. The computer science literature provides approximation results for simple single-parameter settings (mostly single-item auctions or matroid feasibility constraints). Both bodies of literature focus largely on valuations satisfying a technical condition termed single crossing (or variants thereof). We consider the class of submodular over signals (SOS) valuations (without imposing any single crossing-type assumption) and provide the first welfare approximation guarantees for multidimensional combinatorial auctions achieved by universally ex post incentive compatible, individually rational mechanisms. Our main results are (i) four approximation for any single-parameter downward-closed setting with single-dimensional signals and SOS valuations; (ii) four approximation for any combinatorial auction with multidimensional signals and separable-SOS valuations; and (iii) (k + 3) and (2 log(k) + 4) approximation for any combinatorial auction with single-dimensional signals, with k-sized signal space, for SOS and strong-SOS valuations, respectively. All of our results extend to a parameterized version of SOS, d-approximate SOS, while losing a factor that depends on d.