Paper Info
Title
Computing Walrasian Equilibria: Fast Algorithms and Structural Properties.
Abstract
We present the first polynomial time algorithm for computing Walrasian equilibrium in an economy with indivisible goods and general buyer valuations having only access to an aggregate demand oracle, i.e., an oracle that given prices on all goods, returns the aggregated demand over the entire population of buyers. For the important special case of gross substitute valuations, our algorithm queries the aggregate demand oracle Õ(n) times and takes Õ(n3) time, where n is the number of goods. At the heart of our solution is a method for exactly minimizing certain convex functions which cannot be evaluated but for which the subgradients can be computed. We also give the fastest known algorithm for computing Walrasian equilibrium for gross substitute valuations in the value oracle model. Our algorithm has running time Õ((mn + n3)TV) where TV is the cost of querying the value oracle. A key technical ingredient is to regularize a convex programming formulation of the problem in a way that subgradients are cheap to compute. En route, we give necessary and sufficient conditions for the existence of robust Walrasian prices, i.e., prices for which each agent has a unique demanded bundle and the demanded bundles clear the market. When such prices exist, the market can be perfectly coordinated by solely using prices.
Year
DOI
Venue
2017
10.1007/s10107-018-1334-9
SODA
Keywords
Field
DocType
Walrasian equilibrium,Convex optimization,Gross substitutes,90C25 (Convex programming),91B26 (Market models)
Population,Mathematical optimization,Mathematical economics,Algorithm,Oracle,Convex function,Aggregate demand,Time complexity,General equilibrium theory,Convex optimization,Mathematics,Special case
Conference
Volume
Issue
ISSN
179
1
0025-5610
ISBN
Citations 
PageRank 
978-1-61197-503-1
1
0.37
References 
Authors
8
2
Name
Order
Citations
PageRank
renato paes133136.45
Sam Chiu-wai Wong2746.68