Abstract

We study combinatorial auctions with interdependent valuations. In such settings, each agent $i$ has a private signal $s_i$ that captures her private information, and the valuation function of every agent depends on the entire signal profile, ${\bf s}=(s_1,\ldots,s_n)$. 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 {\em single crossing} (or variants thereof). We consider the class of {\em submodular over signals} (SOS) valuations (without imposing any single-crossing type assumption), and provide the first welfare approximation guarantees for multi-dimensional combinatorial auctions, achieved by universally ex-post IC-IR mechanisms. Our main results are: $(i)$ 4-approximation for any single-parameter downward-closed setting with single-dimensional signals and SOS valuations; $(ii)$ 4-approximation for any combinatorial auction with multi-dimensional signals and {\em 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, $d$-SOS, while losing a factor that depends on $d$.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.