A Perfect Price Discrimination Market Model with Production, and a (Rational) Convex Program for It

Recent results showing PPAD-completeness of the problem of computing an equilibrium for Fisher’s market model under additively separable, piecewise-linear, concave utilities (plc utilities) have dealt a serious blow to the program of obtaining efficient algorithms for computing equilibria in “traditional” market models and has prompted a search for alternative models that are realistic as well as amenable to efficient computation. In this paper we show that introducing perfect price discrimination into the Fisher model with plc utilities 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. Next, we introduce production into our model, and 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....

• Type: Journal
• Year: 2010
• Where: SAGT
• Authors: Gagan Goel, Vijay V. Vazirani
• Keywords: Convex Program, Game Theory, Market Model, Plc Utilities, SAGT 2010