Product-Mix Auctions and Tropical Geometry

Ngoc Mai Tran; Josephine Yu

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arXiv · 1505.05737

Product-Mix Auctions and Tropical Geometry

Ngoc Mai Tran·Josephine Yu

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Abstract

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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Ngoc Mai Tran, Josephine Yu. 2015-05-15. Product-Mix Auctions and Tropical Geometry. https://arxiv.org/abs/1505.05737

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