英文标题：
《Product-Mix Auctions and Tropical Geometry》
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作者：
Ngoc Mai Tran and Josephine Yu
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最新提交年份：
2017
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英文摘要：
In a recent and ongoing work, Baldwin and Klemperer explored a connection between tropical geometry and economics. They gave 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 product. Generalizations of our theorem in higher dimensions are equivalent to various forms of the Oda conjecture in algebraic geometry.
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中文摘要：
在最近正在进行的一项研究中，鲍德温和克伦佩尔探索了热带几何学与经济学之间的联系。他们给出了不可分割商品的产品组合拍卖存在竞争均衡的充分条件。这个结果，我们称之为单模性定理，也可以追溯到Danilov、Koshevoy和Murota在离散凸分析中的工作。通过整数规划中的经典单模性定理，给出了单模性定理的一个新证明。我们通过热带几何学对这些结果进行了统一处理，并在只有两类产品的情况下给出了竞争平衡的一个新的充分条件。我们的定理在高维上的推广等价于代数几何中各种形式的Oda猜想。
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分类信息：

一级分类：Computer Science 计算机科学
二级分类：Computer Science and Game Theory 计算机科学与博弈论
分类描述：Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.
涵盖计算机科学和博弈论交叉的所有理论和应用方面，包括机制设计的工作，游戏中的学习（可能与学习重叠），游戏中的agent建模的基础（可能与多agent系统重叠），非合作计算环境的协调、规范和形式化方法。该领域还涉及博弈论在电子商务等领域的应用。
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一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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