On the approximation and smoothed complexity of Leontief market equilibria

Authors:
Li-Sha Huang;Shang-Hua Teng
Affiliations:
State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China;Computer Science Department, Boston University, Boston, Massachusetts and Akamai Technologies Inc., Cambridge, Massachusetts
Venue:
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Year:
2007

Citing 9
Cited 5

On the complexity of the parity argument and other inefficient proofs of existence

Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Playing large games using simple strategies

Proceedings of the 4th ACM conference on Electronic commerce
On the complexity of price equilibria

Journal of Computer and System Sciences - STOC 2002
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time

Journal of the ACM (JACM)
Leontief economies encode nonzero sum two-player games

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The complexity of computing a Nash equilibrium

Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Settling the Complexity of Two-Player Nash Equilibrium

FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Computing Nash Equilibria: Approximation and Smoothed Complexity

FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Exchange market equilibria with leontief’s utility: freedom of pricing leads to rationality

WINE'05 Proceedings of the First international conference on Internet and Network Economics

Settling the complexity of computing two-player Nash equilibria

Journal of the ACM (JACM)
Market equilibria with hybrid linear-Leontief utilities

Theoretical Computer Science
Smoothed analysis: an attempt to explain the behavior of algorithms in practice

Communications of the ACM - A View of Parallel Computing
Spending Is Not Easier Than Trading: On the Computational Equivalence of Fisher and Arrow-Debreu Equilibria

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Market equilibrium under separable, piecewise-linear, concave utilities

Journal of the ACM (JACM)

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we resolve two open questions on the computation and approximation of an Arrow-Debreu equilibrium in a Leontief exchange economy: - We prove that the Leontief market exchange problem does not have a fully polynomial-time approximation scheme, unless PPAD ⊆ P. - We show that the smoothed complexity of any algorithm for computing a market equilibrium in a Leontief economy, is not polynomial, unless PPAD ⊆ RP.