  We study the asymptotic average-case efficiency of static and anonymous
posted prices for $n$ agents and $m(n)$ multiple identical items with
$m(n)=o\left(\frac{n}{\log n}\right)$.
  When valuations are drawn i.i.d from some fixed continuous distribution (each
valuation is a vector in $\Re_+^m$ and independence is assumed only across
agents) we show: (a) for any "upper mass" distribution there exist posted
prices such that the expected revenue and welfare of the auction approaches the
optimal expected welfare as $n$ goes to infinity; specifically, the ratio
between the expected revenue of our posted prices auction and the expected
optimal social welfare is $1-O\left(\frac{m(n)\log n}{n}\right)$, and (b) there
do not exist posted prices that asymptotically obtain full efficiency for most
of the distributions that do not satisfy the upper mass condition.
  When valuations are complete-information and only the arrival order is
adversarial, we provide a "tiefree" condition that is sufficient and necessary
for the existence of posted prices that obtain the maximal welfare. This
condition is generically satisfied, i.e., it is satisfied with probability $1$
if the valuations are i.i.d.~from some continuous distribution.
