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
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
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
Dynamics of bid optimization in online advertisement auctions
Proceedings of the 16th international conference on World Wide Web
Proportional response dynamics leads to market equilibrium
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
Fast-converging tatonnement algorithms for one-time and ongoing market problems
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Distributed algorithms via gradient descent for fisher markets
Proceedings of the 12th ACM conference on Electronic commerce
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In this paper, we show that the proportional response dynamics, a utility based distributed dynamics, converges to the market equilibrium in the Fisher market with constant elasticity of substitution (CES) utility functions. By the proportional response dynamics, each buyer allocates his budget proportional to the utility he receives from each good in the previous time period. Unlike the tâtonnement process and its variants, the proportional response dynamics is a large step discrete dynamics, and the buyers do not solve any optimization problem at each step. In addition, the goods are always cleared and assigned to the buyers proportional to their bids at each step. Despite its simplicity, the dynamics converges fast for strictly concave CES utility functions, matching the best upperbound of computing the market equilibrium via solving a global convex optimization problem.