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What and Who
Title:Computation of Fisher-Gale equilibrium by auction
Speaker:Vladimir Shikhman
coming from:Catholic University of Louvain (UCL), Belgium
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1, D2, D3, D4, D5, RG1, SWS, MMCI
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Level:AG Audience
Date, Time and Location
Date:Tuesday, 24 November 2015
Duration:45 Minutes
Building:E1 4
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.
Name(s):Jugal Garg
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  • Jugal Garg, 10/08/2015 11:47 PM -- Created document.