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
On the complexity of equilibria
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Market Equilibrium via a Primal-Dual-Type Algorithm
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
Auction algorithms for market equilibrium
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A Polynomial Time Algorithm for Computing the Arrow-Debreu Market Equilibrium for Linear Utilities
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Market equilibrium via the excess demand function
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On the polynomial time computation of equilibria for certain exchange economies
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the computational complexity of Nash equilibria for (0, 1) bimatrix games
Information Processing Letters
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
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
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Pricing for fairness: distributed resource allocation for multiple objectives
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The computation of approximate competitive equilibrium is PPAD-hard
Information Processing Letters
A FPTAS for Computing a Symmetric Leontief Competitive Economy Equilibrium
WINE '08 Proceedings of the 4th International Workshop 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
Algorithmic Game Theory: A Snapshot
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
The Complexity of Models of International Trade
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
On the approximation and smoothed complexity of Leontief market equilibria
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
A note on equilibrium pricing as convex optimization
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Extending polynomial time computability to markets with demand correspondences
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Computing market equilibrium: beyond weak gross substitutes
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Market equilibrium under separable, piecewise-linear, concave utilities
Journal of the ACM (JACM)
Distributed algorithms via gradient descent for fisher markets
Proceedings of the 12th ACM conference on Electronic commerce
Economies with non-convex production and complexity equilibria
Proceedings of the 12th ACM conference on Electronic commerce
How profitable are strategic behaviors in a market?
ESA'11 Proceedings of the 19th European conference on Algorithms
An interior-point path-following algorithm for computing a Leontief economy equilibrium
Computational Optimization and Applications
Making economic theory operational
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Market equilibria with hybrid linear-leontief utilities
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
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
Buy-sell auction mechanisms in market equilibrium
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Tatonnement in ongoing markets of complementary goods
Proceedings of the 13th ACM Conference on Electronic Commerce
The complexity of non-monotone markets
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
ACM Transactions on Algorithms (TALG)
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We consider Leontief exchange economies, i.e., economies where the consumers desire goods in fixed proportions. Unlike bimatrix games, such economies are not guaranteed to have equilibria in general. On the other hand, they include suitable restricted versions which always have equilibria.We give a reduction from two-player games to a special family of Leontief exchange economies, which are guaranteed to have equilibria, with the property that the Nash equilibria of any game are in one-to-one correspondence with the equilibria of the corresponding economy.Our reduction exposes a potential hurdle inherent in solving certain families of market equilibrium problems: finding an equilibrium for Leontief economies (where an equilibrium is guaranteed to exist) is at least as hard as finding a Nash equilibrium for two-player nonzero sum games.As a corollary of the one-to-one correspondence, we obtain a number of hardness results for questions related to the computation of market equilibria, using results already established for games [17]. In particular, among other results, we show that it is NP-hard to say whether a particular family of Leontief exchange economies, that is guaranteed to have at least one equilibrium, has more than one equilibrium.Perhaps more importantly, we also prove that it is NP-hard to decide whether a Leontief exchange economy has an equilibrium. This fact should be contrasted against the known PPAD-completeness result of [30], which holds when the problem satisfies some standard sufficient conditions that make it equivalent to the computational version of Brouwer's Fixed Point Theorem.On the algorithmic side, we present an algorithm for finding an approximate equilibrium for some special Leontief economies, which achieves quasi-polynomial time whenever each trader does not demand too much more of any good than some other good.