منابع مشابه
Product-Mix Auctions and Tropical Geometry
In a recent and ongoing work, Baldwin and Klemperer found 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. We introduce auction theory for a mat...
متن کاملTropical geometry and amœbas
The objective of this course (ALGANT course, M2, Bordeaux, January-April 2012) was originally to present various facets of the so-called “tropical calculus”, as it appeared in various mathematical domains, including theoretical as applied ones (algebraic geometry, optimization and control theory, dynamical systems, etc., see [Gaub] for a wide panorama in such applied directions). The original i...
متن کاملTropical Geometry
Tropical geometry still is a rather young field of mathematics which nevertheless over the past couple of years has proved to be rather powerful for tackling questions in enumerative geometry (see e.g. [Mik05], [GM08], [IKS04]). It also has been used to provide alternative algorithmic means to eliminate variables (see [StY08]). People from applied mathematics such as optimisation or control the...
متن کاملTropical Geometry and Mechanism Design
We use tropical geometry to analyze finite valued mechanisms. We geometrically characterize all mechanisms on arbitrary type spaces, derive geometric and algebraic criteria for weak monotonicity, incentive compatibility and revenue equivalence. As corollaries we obtain various results known in the literature and shed new light on their nature.
متن کاملGeometry and product states
As separable states are a convex combination of product states, the geometry of the manifold of product states, Σ is studied. Prior results by Sanpera, Vidal and Tarrach are extended. Furthermore, it is proven that states in the set tangent to Σ at the maximally mixed state are separable; the set normal constains, among others, all maximally entangled states. A canonical decomposition is given....
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ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2019
ISSN: 0364-765X,1526-5471
DOI: 10.1287/moor.2018.0975