Descending Price Auctions with Bounded Number of Price Levels and Batched Prophet Inequality

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Tác giả: Saeed Alaei, Ali Makhdoumi, Azarakhsh Malekian, Rad Niazadeh

Ngôn ngữ: eng

Ký hiệu phân loại: 018.3 +Catalogs arranged by author, main entry, date, or register number

Thông tin xuất bản: 2022

Mô tả vật lý:

Bộ sưu tập: Metadata

ID: 194595

 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 $k$.
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