The polyhedral geometry of truthful auctions

被引:0
|
作者
Joswig, Michael [1 ,2 ]
Klimm, Max [3 ]
Spitz, Sylvain [3 ]
机构
[1] Tech Univ Berlin, Discrete Math Geometry, Str 17 Juni 136, D-10623 Berlin, Germany
[2] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany
[3] Tech Univ Berlin, Discrete Optimizat, Str 17 Juni 136, D-10623 Berlin, Germany
关键词
MULTIDIMENSIONAL MECHANISM DESIGN; COMBINATORIAL AUCTIONS; MONOTONICITY; ALGORITHMS;
D O I
10.1007/s10107-024-02168-y
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
The difference set of an outcome in an auction is the set of types that the auction mechanism maps to the outcome. We give a complete characterization of the geometry of the difference sets that can appear for a dominant strategy incentive compatible multi-unit auction showing that they correspond to regular subdivisions of the unit cube. Similarly, we describe the geometry for affine maximizers for n players and m items, showing that they correspond to regular subdivisions of the m-fold product of (n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n-1)$$\end{document}-dimensional simplices. These observations are then used to construct mechanisms that are robust in the sense that the sets of items allocated to the players change only slightly when the players' reported types are changed slightly.
引用
收藏
页码:539 / 566
页数:28
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