On total functions, existence theorems and computational complexity
Theoretical Computer Science
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Leontief economies encode nonzero sum two-player games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Exchange market equilibria with Leontief's utility: Freedom of pricing leads to rationality
Theoretical Computer Science
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)
The computation of approximate competitive equilibrium is PPAD-hard
Information Processing Letters
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
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
On the approximation and smoothed complexity of Leontief market equilibria
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
On the Complexity of Nash Equilibria and Other Fixed Points
SIAM Journal on Computing
A perfect price discrimination market model with production, and a (rational) convex program for it
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
A Perfect Price Discrimination Market Model with Production, and a Rational Convex Program for It
Mathematics of Operations Research
The notion of a rational convex program, and an algorithm for the Arrow-Debreu Nash bargaining game
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The notion of a rational convex program, and an algorithm for the arrow-debreu Nash bargaining game
Journal of the ACM (JACM)
A complementary pivot algorithm for markets under separable, piecewise-linear concave utilities
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A Simple Approximation Algorithm for Computing Arrow-Debreu Prices
Operations Research
The complexity of non-monotone markets
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We consider Fisher and Arrow--Debreu markets under additively separable, piecewise-linear, concave utility functions and obtain the following results. For both market models, if an equilibrium exists, there is one that is rational and can be written using polynomially many bits. There is no simple necessary and sufficient condition for the existence of an equilibrium: The problem of checking for existence of an equilibrium is NP-complete for both market models; the same holds for existence of an ε-approximate equilibrium, for ε = O(n−5). Under standard (mild) sufficient conditions, the problem of finding an exact equilibrium is in PPAD for both market models. Finally, building on the techniques of Chen et al. [2009a] we prove that under these sufficient conditions, finding an equilibrium for Fisher markets is PPAD-hard.