广义置换面体与最优拍卖
Generalized permutahedra and optimal auctions
摘要：
我们研究了一族凸多胞体，称为SIM体，由Giannakopoulos和Koutsoupias（2018）引入，用于分析所谓的直套拍卖。首先，我们证明了SIM体属于广义置换面体类。其次，我们证明了在确定性拍卖中的直夹克拍卖的最优性结果。第三，我们采用计算机代数方法和数学软件来明确确定最优价格和收入。
英文摘要：
We study a family of convex polytopes, called SIM-bodies, which were introduced by Giannakopoulos and Koutsoupias (2018) to analyze so-called Straight-Jacket Auctions. First, we show that the SIM-bodies belong to the class of generalized permutahedra. Second, we prove an optimality result for the Straight-Jacket Auctions among certain deterministic auctions. Third, we employ computer algebra methods and mathematical software to explicitly determine optimal prices and revenues.
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