  We explore the approximation power of deterministic obviously strategy-proof
mechanisms in auctions, where the objective is welfare maximization. A trivial
ascending auction on the grand bundle guarantees an approximation of
$\min\{m,n\}$ for all valuation classes, where $m$ is the number of items and
$n$ is the number of bidders. We focus on two classes of valuations considered
"simple": additive valuations and unit-demand valuations. For additive
valuations, Bade and Gonczarowski [EC'17] have shown that exact welfare
maximization is impossible. No impossibilities are known for unit-demand
valuations.
  We show that if bidders' valuations are additive or unit-demand, then no
obviously strategy-proof mechanism gives an approximation better than
$\min\{m,n\}$. Thus, the aforementioned trivial ascending auction on the grand
bundle is the optimal obviously strategy-proof mechanism. These results
illustrate a stark separation between the power of dominant-strategy and
obviously strategy-proof mechanisms. The reason for it is that for both of
these classes the dominant-strategy VCG mechanism does not only optimize the
welfare exactly, but is also "easy" both from a computation and communication
perspective.
  In addition, we prove tight impossibilities for unknown single-minded bidders
in a multi-unit auction and in a combinatorial auction. We show that in these
environments as well, a trivial ascending auction on the grand bundle is
optimal.
