A Simplex-like Algorithm for Linear Fisher Markets
نویسندگان
چکیده
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 algorithm which is provably strongly polynomial for many special cases. The algorithm can also be interpreted as a complementary pivot algorithm resembling the classical LemkeHowson algorithm for computing Nash equilibrium of two person bimatrix games.
منابع مشابه
A Simplex-Like Algorithm for Fisher Markets
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. Thi...
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