Max-Planck-Institut für Informatik
max planck institut
informatik
mpii logo Minerva of the Max Planck Society
 

MPI-INF or MPI-SWS or Local Campus Event Calendar

<< Previous Entry Next Entry >> New Event Entry Edit this Entry Login to DB (to update, delete)
What and Who
Title:Computation of Fisher-Gale equilibrium by auction
Speaker:Vladimir Shikhman
coming from:Catholic University of Louvain (UCL), Belgium
Speakers Bio:http://www.uclouvain.be/vladimir.shikhman
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1, D2, D3, D4, D5, RG1, SWS, MMCI
We use this to send out email in the morning.
Level:AG Audience
Language:English
Date, Time and Location
Date:Tuesday, 24 November 2015
Time:13:00
Duration:45 Minutes
Location:Saarbrücken
Building:E1 4
Room:024
Abstract
We study the Fisher model of a competitive market from the algorithmic perspective. For that, the related convex optimization problem due to Gale and Eisenberg is used. The latter problem is known to yield a Fisher equilibrium under some structural assumptions on consumers’ utilities, e.g. homogeneity of degree 1, homotheticity etc. Our goal is to examine the applicability of the convex optimization framework by departing from these traditional assumptions. We just assume the concavity of consumers’ utility functions. For this case we suggest a novel concept of Fisher-Gale equilibrium by introducing consumers’ utility prices. The prices of utility transfer the utility of a consumption bundle to a common numéraire. We develop a subgradient-type algorithm from Convex Analysis to compute a Fisher-Gale equilibrium by Gale's approach. In order to decentralize prices, we additionally implement the auction design, i.e. consumers settle and update their individual prices and producers sell at the highest offer price. Our price adjustment is based on a tâtonnement procedure, i.e. the prices change proportionally to consumers’ individual excess supplies. Historical averages of consumption are shown to clear the market of goods. Our algorithm enjoys a convergence rate. In worst case, the number of price updates needed to achieve the E-tolerance is proportional to 1/E^2.
Contact
Name(s):Jugal Garg
Video Broadcast
Video Broadcast:NoTo Location:
Tags, Category, Keywords and additional notes
Note:
Attachments, File(s):
Created by:Jugal Garg, 10/08/2015 11:47 PMLast modified by:Uwe Brahm/MPII/DE, 11/24/2016 04:13 PM
  • Jugal Garg, 10/08/2015 11:47 PM -- Created document.