  We consider descending price auctions for selling $m$ units of a good to unit
demand i.i.d. buyers where there is an exogenous bound of $k$ on the number of
price levels the auction clock can take. The auctioneer's problem is to choose
price levels $p_1 > p_2 > \cdots > p_{k}$ for the auction clock such that
auction expected revenue is maximized. The prices levels are announced prior to
the auction. We reduce this problem to a new variant of prophet inequality,
which we call \emph{batched prophet inequality}, where a decision-maker chooses
$k$ (decreasing) thresholds and then sequentially collects rewards (up to $m$)
that are above the thresholds with ties broken uniformly at random. For the
special case of $m=1$ (i.e., selling a single item), we show that the resulting
descending auction with $k$ price levels achieves $1- 1/e^k$ of the
unrestricted (without the bound of $k$) optimal revenue. That means a
descending auction with just 4 price levels can achieve more than 98\% of the
optimal revenue. We then extend our results for $m>1$ and provide a closed-form
bound on the competitive ratio of our auction as a function of the number of
units $m$ and the number of price levels $k$.
