The complexity of non-monotone markets

Authors:
Xi Chen;Dimitris Paparas;Mihalis Yannakakis
Affiliations:
Columbia University, New York, NY, USA;Columbia University, New York, NY, USA;Columbia University, New York, NY, USA
Venue:
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Year:
2013

Citing 18
Cited 0

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
Applied General Equilibrium Modeling with MPSGE as a GAMS Subsystem: AnOverview of the Modeling Framework and Syntax

Computational Economics - Special issue on programming languages
On the complexity of price equilibria

Journal of Computer and System Sciences - STOC 2002
Market equilibrium via the excess demand function

Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the polynomial time computation of equilibria for certain exchange economies

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Leontief economies encode nonzero sum two-player games

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A path to the Arrow–Debreu competitive market equilibrium

Mathematical Programming: Series A and B
A Polynomial Time Algorithm for Computing an Arrow-Debreu Market Equilibrium for Linear Utilities

SIAM Journal on Computing
Market equilibrium via a primal--dual algorithm for a convex program

Journal of the ACM (JACM)
Market Equilibria in Polynomial Time for Fixed Number of Goods or Agents

FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Settling the complexity of computing two-player Nash equilibria

Journal of the ACM (JACM)
The Complexity of Computing a Nash Equilibrium

SIAM Journal on 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
Settling the Complexity of Arrow-Debreu Equilibria in Markets with Additively Separable Utilities

FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Spending Constraint Utilities with Applications to the Adwords Market

Mathematics of Operations Research
On the Complexity of Nash Equilibria and Other Fixed Points

SIAM Journal on Computing
Market equilibrium under separable, piecewise-linear, concave utilities

Journal of the ACM (JACM)
Market equilibrium for CES exchange economies: existence, multiplicity, and computation

FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce the notion of non-monotone utilities, which covers a wide variety of utility functions in economic theory. We show that it is PPAD-hard to compute an approximate Arrow-Debreu market equilibrium in markets with linear and non-monotone utilities. Building on this result, we settle the long-standing open problem regarding the computation of an approximate Arrow-Debreu market equilibrium in markets with CES utilities, by proving that it is PPAD-complete when the Constant Elasticity of Substitution parameter, ρ, is any constant less than -1.