Combinatorial Auctions with Interdependent Valuations: SOS to the Rescue

Abstract

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, [Formula: see text]. 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. Funding: A. Eden was partially supported by NSF Award IIS-2007887, the European Research Council (ERC) under the European Union's Seventh Framework Programme [FP7/2007-2013]/ERC Grant Agreement 337122, by the Israel Science Foundation [Grant 317/17], and by an Amazon research award. M. Feldman received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program [Grant Agreement 866132], by the Israel Science Foundation [Grant 317/17], by an Amazon research award, and by the NSF-BSF [Grant 2020788]. The work of K. Goldner was supported partially by NSF awards DMS-1903037 and CNS-2228610 and a Shibulal Family Career Development Professorship. A. R. Karlin was supported by the NSF-CCF [Grant 1813135].