A simplex-like algorithm for fisher markets

Authors:
Bharat Adsul;Ch. Sobhan Babu;Jugal Garg;Ruta Mehta;Milind Sohoni
Affiliations:
Indian Institute of Technology, Bombay;Indian Institute of Technology, Hyderabad;Indian Institute of Technology, Bombay;Indian Institute of Technology, Bombay;Indian Institute of Technology, Bombay
Venue:
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Year:
2010

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Abstract

We propose a new convex optimization formulation for the Fisher market problem with linear utilities. Like the Eisenberg-Gale formulation, the set of feasible points is a polyhedral convex set while the cost function is non-linear; however, unlike that, the optimum is always attained at a vertex of this polytope. The convex cost function depends only on the initial endowments of the buyers. This formulation yields an easy simplex-like pivoting algorithm which is provably strongly polynomial for many special cases.