  The celebrated model of auctions with interdependent valuations, introduced
by Milgrom and Weber in 1982, has been studied almost exclusively under private
signals $s_1, \ldots, s_n$ of the $n$ bidders and public valuation functions
$v_i(s_1, \ldots, s_n)$. Recent work in TCS has shown that this setting admits
a constant approximation to the optimal social welfare if the valuations
satisfy a natural property called submodularity over signals (SOS). More
recently, Eden et al. (2022) have extended the analysis of interdependent
valuations to include settings with private signals and private valuations, and
established $O(\log^2 n)$-approximation for SOS valuations. In this paper we
show that this setting admits a constant factor approximation, settling the
open question raised by Eden et al. (2022).
