Eisenberg–Gale markets: Algorithms and game-theoretic properties

We define a new class of markets, the Eisenberg–Gale markets. This class contains Fisher's linear market, markets from the resource allocation framework of Kelly [Kelly, F.P., 1997. Charging and rate control for elastic traffic. Europ. Transactions Telecommunications 8, 33–37], as well as numer...

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Bibliographic Details
Published in:Games and economic behavior Vol. 70; no. 1; pp. 84 - 106
Main Authors: Jain, Kamal, Vazirani, Vijay V.
Format: Journal Article
Language:English
Published: Elsevier Inc 01.09.2010
Elsevier
Series:Games and Economic Behavior
Subjects:
Ascending price auctions
Auctions
Combinatorial algorithm
Competition monotonicity
Convex program
Equilibrium models
Equilibrium theory
Fairness
Fisher market model
General economic equilibrium
General equilibrium theory
General equilibrium theory Fisher market model Combinatorial algorithm Primal-dual algorithm Convex program Resource allocation Ascending price auctions Weak gross substitutability Competition monotonicity Fairness
Market theory
Price theory
Primal-dual algorithm
Resource allocation
Weak gross substitutability
C63
General equilibrium theory
Primal-dual algorithm
C68
Ascending price auctions
Fisher market model
Combinatorial algorithm
Resource allocation
Fairness
Competition monotonicity
Convex program
C62
Weak gross substitutability
ISSN:0899-8256, 1090-2473
Online Access:Get full text
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Summary:We define a new class of markets, the Eisenberg–Gale markets. This class contains Fisher's linear market, markets from the resource allocation framework of Kelly [Kelly, F.P., 1997. Charging and rate control for elastic traffic. Europ. Transactions Telecommunications 8, 33–37], as well as numerous interesting new markets. We obtain combinatorial, strongly polynomial algorithms for several markets in this class. Our algorithms have a simple description as ascending price auctions. Our algorithms lead to insights into game-theoretic properties of these markets, such as efficiency, fairness, and competition monotonicity. They also help determine if these markets always have rational equilibria. A classification of Eisenberg–Gale markets w.r.t. these properties reveals a surprisingly rich set of possibilities.
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ISSN:0899-8256
1090-2473
DOI:10.1016/j.geb.2008.11.011