# A polynomial time algorithm for computing an Arrow-Debreu market equilibrium for linear utilities

@article{Jain2004APT, title={A polynomial time algorithm for computing an Arrow-Debreu market equilibrium for linear utilities}, author={Kamal Kumar Jain}, journal={45th Annual IEEE Symposium on Foundations of Computer Science}, year={2004}, pages={286-294} }

We provide the first polynomial time exact algorithm for computing an Arrow-Debreu market equilibrium for the case of linear utilities. Our algorithm is based on solving a convex program using the ellipsoid algorithm and simultaneous diophantine approximation. As a side result, we prove that the set of assignments at equilibria is convex and the equilibria prices themselves are log-convex. Our convex program is explicit and intuitive, which allows maximizing a concave function over the set of… Expand

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