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. The problem is of considerable interest in Economics. We formulate the market equilibrium problem as a non-linear program. We construct the dual of this non-linear formulation and define conditions under which prices achieve market clearing. These conditions arise naturally from complementary slackness conditions.
We then define an auction mechanism, which computes prices such that approximate market clearing is achieved, i.e. the surplus is cleared to within a small factor of the total final endowment.
By: Rahul Garg and Sanjiv Kapoor
Published in: RI03011 in 2003
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