Auction algorithms for market equilibrium

Abstract

In this paper we study algorithms for computing market equilibrium in markets with linear utility functions. The buyers in the market have an initial endowment given by a portfolio of items. The market equilibrium problem is to compute a price vector which ensures market clearing, i.e. the demand of a good equals its supply, and given the prices, each buyer maximizes its utility. The problem is of considerable interest in Economics. This paper presents a formulation of the market equilibrium problem as a parameterized linear program. We construct the dual of these parametrized linear programs. We show that finding the market equilibrium is the same as finding a linear-program from the family of programs where the optimal dual solution satisfies certain properties. The market clearing conditions arise naturally from complementary slackness conditions. We then define an auction mechanism which computes prices such that approximate market clearing is achieved. The algorithm we obtain outperforms previously known methods.