An Auction-Based Market Equilbrium Algorithm for the Separable Gross Substitutibility Case

In this paper we study the problem of market equilibrium. Firstly we consider the model (Fischer model) where there is a supply of money associated with each buyer and a quantity associated with each item. 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 subject to his endowment, each buyer maximizes his utility. Each item has a utility for a given buyer. We assume that the utility function is an increasing, differentiable, concave function. We show that under the assumptions of gross substitutibility, an auction algorithm can determine approximate market clearing. Not only does this algorithm extends the class of utility functions for which market equilibrium can be determined polynomially, the auction algorithm is efficient and in this model O(n) faster than the auction algorithm for the case of linear utilities in the Arrow-Debreu model. We outline an extension of our method to the Arrow-Debreu method.