  The simultaneous multiple-round auction (SMRA) and the combinatorial clock
auction (CCA) are the two primary mechanisms used to sell bandwidth. Under
truthful bidding, the SMRA is known to output a Walrasian equilibrium that
maximizes social welfare provided the bidder valuation functions satisfy the
gross substitutes property. Recently, it was shown that the combinatorial clock
auction (CCA) provides good welfare guarantees for general classes of valuation
functions. This motivates the question of whether similar welfare guarantees
hold for the SMRA in the case of general valuation functions.
  We show the answer is no. But we prove that good welfare guarantees still
arise if the degree of complementarities in the bidder valuations are bounded.
In particular, if bidder valuations functions are $\alpha$-near-submodular
then, under truthful bidding, the SMRA has a welfare ratio (the worst case
ratio between the social welfare of the optimal allocation and the auction
allocation) of at most $(1+\alpha)$. The special case of submodular valuations,
namely $\alpha=1$, and produces individually rational solutions. However, for
$\alpha>1$, this is a bicriteria guarantee, to obtain good welfare under
truthful bidding requires relaxing individual rationality.
  Finally, we examine what strategies are required to ensure individual
rationality in the SMRA with general valuation functions. First, we provide a
weak characterization, namely \emph{secure bidding}, for individual
rationality. We then show that if the bidders use a profit-maximizing secure
bidding strategy the welfare ratio is at most $1+\alpha$. Consequently, by
bidding securely, it is possible to obtain the same welfare guarantees as
truthful bidding without the loss of individual rationality.
