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}
}
  • K. Jain
  • Published 2004
  • Mathematics, Computer Science
  • 45th Annual IEEE Symposium on Foundations of Computer Science
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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A Polynomial Time Algorithm for Computing the Arrow-Debreu Market Equilibrium for Linear Utilities
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  • Mathematics, Computer Science
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A. Wald has presented a model of production and a model of exchange and proofs of the existence of an equilibrium for each of them. Here proofs of the existence of an equilibrium are given for anExpand
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