Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
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
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Market equilibrium via the excess demand function
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Auction Algorithms for Market Equilibrium
Mathematics of Operations Research
Eisenberg-Gale markets: algorithms and structural properties
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A path to the Arrow–Debreu competitive market equilibrium
Mathematical Programming: Series A and B
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
Computing equilibrium prices: does theory meet practice?
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Advertising network formation based on stochastic diffusion search and market equilibria
Proceedings of the 28th ACM International Conference on Design of Communication
Distributed algorithms via gradient descent for fisher markets
Proceedings of the 12th ACM conference on Electronic commerce
Tatonnement beyond gross substitutes?: gradient descent to the rescue
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We give a new mathematical formulation of market equilibriausing an indirect utility function : the function of pricesand income that gives the maximum utility achievable. Theformulation is a convex program and can be solved when theindirect utility function is convex in prices. We illustrate thatmany economies including Homogeneous utilities of degreeα ∈ [0,1] in Fisher economies — thisincludes Linear, Leontief, Cobb-Douglas Resource allocation utilities like multi-commodityflows satisfy this condition and can be efficiently solved.Further, we give a natural and decentralized price-adjustingalgorithm in these economies. Our algorithm, mimics the naturaltâtonnement dynamics for the markets as suggested by Walras:it iteratively adjusts a good's price upward when the demand forthat good under current prices exceeds its supply; and downwardwhen its supply exceeds its demand. The algorithm computes anapproximate equilibrium in a number of iterations that isindependent of the number of traders and is almost linear in the number of goods. Interestingly, our algorithm applies tocertain classes of utility functions that are not weak grosssubstitutes .