A Simple Approximation Algorithm for Computing Arrow-Debreu Prices

We consider the Arrow-Debreu market with linear utilities in which there is a set G of divisible goods and a set B of buyers. Each buyer starts with an initial endowment of goods. The buyer’s utility function is a linearly separable function of the goods that the buyer purchases. We develop a simple and efficient algorithm for determining an approximate market equilibrium. Our algorithm finds an …-approximate solution in O4n/…4—B——G—55 time, where n = —B— + —G—. The running time can be further improved to O4n/…4m+—B— log —B—55 where m is the number of pairs 4i1 j5 such that buyer i has some utility for purchasing good j .