A perfect price discrimination market model with production, and a (Rational) convex program for it

Abstract

Recent results showed PPAD-completeness of the problem of computing an equilibrium for Fisher's market model under additively separable, piecewise-linear, concave utilities. We show that introducing perfect price discrimination in this model renders its equilibrium polynomial time computable. Moreover, its set of equilibria are captured by a convex program that generalizes the classical Eisenberg-Gale program, and always admits a rational solution. We also introduce production into our model; our goal is to carve out as big a piece of the general production model as possible while still maintaining the property that a single (rational) convex program captures its equilibria, i.e., the convex program must optimize individually for each buyer and each firm. © 2010 Springer-Verlag Berlin Heidelberg.