The Algebraic Geometry of Competitive Equilibrium

1992 ◽  
pp. 53-66 ◽  
Author(s):  
Lawrence E. Blume ◽  
William R. Zame
Keyword(s):  
Algebraic Geometry ◽  
Competitive Equilibrium

scholarly journals Product-Mix Auctions and Tropical Geometry

2019 ◽  
Vol 44 (4) ◽  
pp. 1396-1411 ◽  
Author(s):  
Ngoc Mai Tran ◽  
Josephine Yu
Keyword(s):  
Algebraic Geometry ◽  
Competitive Equilibrium ◽  
Tropical Geometry ◽  
Higher Dimensions ◽  
Sufficient Condition ◽  
Indivisible Goods ◽  
Product Mix ◽  
Ongoing Work ◽  
Discrete Convex Analysis ◽  
Discrete Convex

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.

Sign in / Sign up

Export Citation Format

Share Document