Product-Mix Auctions and Tropical Geometry
Product-Mix Auctions and Tropical Geometry
复制标题
产品组合拍卖和热带几何
DOI：
10.1287/moor.2018.0975
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Josephine Yu
中科院分区：
文献类型：
--
作者：
N. Tran;Josephine Yu
在最近和正在进行的一项工作中，鲍德温和克伦佩雷尔探索了热带几何和经济学之间的联系。给出了不可分商品的产品组合拍卖中存在竞争均衡的充分条件。这个结果，我们称之为么正定理，也可以追溯到Danilov，Koshevoy和Murota在离散凸分析中的工作。利用整数规划中经典的么正定理，给出了么正定理的一个新的证明。我们用热带几何统一地处理了这些结果，并给出了只有两类产品时竞争均衡的一个新的充分条件。我们的定理在高维空间的推广等价于代数几何中Oda猜想的各种形式。
In a recent and ongoing work, Baldwin and Klemperer explore a connection between tropical geometry and economics. They give a sufficient condition for the existence of competitive equilibrium in product-mix auctions of indivisible goods. This result, which we call the unimodularity theorem, can also be traced back to the work of Danilov, Koshevoy, and Murota in discrete convex analysis. We give a new proof of the unimodularity theorem via the classical unimodularity theorem in integer programming. We give a unified treatment of these results via tropical geometry and formulate a new sufficient condition for competitive equilibrium when there are only two types of products. Generalizations of our theorem in higher dimensions are equivalent to various forms of the Oda conjecture in algebraic geometry.
DOI：
10.2139/ssrn.2643086
发表时间：
2018-10
期刊：
Microeconomics: General Equilibrium & Disequilibrium Models eJournal
影响因子：
--
作者：
E. Baldwin;P. Klemperer
通讯作者：
E. Baldwin;P. Klemperer