SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the complexity of market equilibria with maximum social welfare
Information Processing Letters
Variational Inequalities and Economic Equilibrium
Mathematics of Operations Research
Exchange market equilibria with Leontief's utility: Freedom of pricing leads to rationality
Theoretical Computer Science
Theoretical Computer Science
Proportional response dynamics leads to market equilibrium
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An experimental study of different approaches to solve the market equilibrium problem
Journal of Experimental Algorithmics (JEA)
Market equilibrium via a primal--dual algorithm for a convex program
Journal of the ACM (JACM)
The complexity of equilibria: Hardness results for economies via a correspondence with games
Theoretical Computer Science
A Fast and Simple Algorithm for Computing Market Equilibria
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Market equilibria with hybrid linear-Leontief utilities
Theoretical Computer Science
Proportional Response Dynamics in the Fisher Market
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On the complexity of market equilibria with maximum social welfare
Information Processing Letters
A note on equilibrium pricing as convex optimization
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Market equilibrium with transaction costs
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Proportional response dynamics in the Fisher market
Theoretical Computer Science
A revealed preference approach to computational complexity in economics
Proceedings of the 12th ACM conference on Electronic commerce
Distributed algorithms via gradient descent for fisher markets
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
Discrete Fixed Points: Models, Complexities, and Applications
Mathematics of Operations Research
Price roll-backs and path auctions: an approximation scheme for computing the market equilibrium
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
Computing equilibrium prices: does theory meet practice?
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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
A fixed point approach for the computation of market equilibria
WINE'05 Proceedings of the First international conference on Internet and Network Economics
A practical algorithm for the computation of market equilibrium with logarithmic utility functions
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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
Incentive ratios of fisher markets
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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
A combinatorial polynomial algorithm for the linear arrow-debreu market
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We present polynomial-time interior-point algorithms for solving the Fisher and Arrow–Debreu competitive market equilibrium problems with linear utilities and n players. Both of them have the arithmetic operation complexity bound of $${O(n^{4}log(1/\epsilon}$$)) for computing an $${\epsilon}$$ -equilibrium solution. If the problem data are rational numbers and their bit-length is L, then the bound to generate an exact solution is O(n4L) which is in line with the best complexity bound for linear programming of the same dimension and size. This is a significant improvement over the previously best bound $$O(n^{8}log(1/\epsilon$$)) for approximating the two problems using other methods. The key ingredient to derive these results is to show that these problems admit convex optimization formulations, efficient barrier functions and fast rounding techniques. We also present a continuous path leading to the set of the Arrow–Debreu equilibrium, similar to the central path developed for linear programming interior-point methods. This path is derived from the weighted logarithmic utility and barrier functions and the Brouwer fixed-point theorem. The defining equations are bilinear and possess some primal-dual structure for the application of the Newton-based path-following method.