热带几何与机制设计
Tropical Geometry and Mechanism Design
摘要：
我们开发了一个新的框架来构建和分析有限值，多维机制，使用热带凸几何。我们几何特征的激励相容性使用细胞的热带凸包的类型集。这些细胞是激励相容的支付的集合，形成热带单纯形，通过生成数量等于单纯形的维度的支付来跨越。通过热带单纯形及其生成支付的激励相容机制的收集的分析促进了几何技术的使用。我们使用这种观点来获得一个新的几何特征的收入等价，但也显示了如何处理多维的收入等价的情况下的机制。
英文摘要：
We develop a novel framework to construct and analyze finite valued, multidimensional mechanisms using tropical convex geometry. We geometrically characterize incentive compatibility using cells in the tropical convex hull of the type set. These cells are the sets of incentive compatible payments and form tropical simplices, spanned by generating payments whose number equals the dimension of the simplex. The analysis of the collection of incentive compatible mechanisms via tropical simplices and their generating payments facilitates the use of geometric techniques. We use this view to derive a new geometric characterization of revenue equivalence but also show how to handle multidimensional mechanisms in the absence of revenue equivalence.
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