Proceedings of the 2018 ACM Conference on Economics and Computation 2018
DOI: 10.1145/3219166.3219189
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Dynamics of Distributed Updating in Fisher Markets

Abstract: A major goal in Algorithmic Game Theory is to justify equilibrium concepts from an algorithmic and complexity perspective. One appealing approach is to identify natural distributed algorithms that converge quickly to an equilibrium. This paper established new convergence results for two generalizations of Proportional Response in Fisher markets with buyers having CES utility functions. The starting points are respectively a new convex and a new convexconcave formulation of such markets. The two generalizations… Show more

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Cited by 17 publications
(15 citation statements)
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“…Our proof of Theorem 4 consists of two major steps. In the first, we derive a convex program that captures the market equilibrium (ME) spending of the quasi-linear Fisher market via the approach of [5,24,17]. In the second, we show that a general Mirror Descent (MD) algorithm converges to the optimal solution of this convex program; PR-QLIN is an instantiation of this MD algorithm.…”
Section: Our Main Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…Our proof of Theorem 4 consists of two major steps. In the first, we derive a convex program that captures the market equilibrium (ME) spending of the quasi-linear Fisher market via the approach of [5,24,17]. In the second, we show that a general Mirror Descent (MD) algorithm converges to the optimal solution of this convex program; PR-QLIN is an instantiation of this MD algorithm.…”
Section: Our Main Resultsmentioning
confidence: 99%
“…In contrast, when firms ignore their market power and act as price-takers, the outcomes can be more stable. A line of recent works [51,52,5,16,15,17,9,18] showed that natural adaptive algorithms, including tâtonnement and proportional response, lead to stable adjustments in many families of Fisher markets, where they converge to market equilibria.…”
Section: Introductionmentioning
confidence: 99%
“…Birnbaum, Devanur, and Xiao [7] interpret proportional as mirror descent on the convex program of Shmyrev [64] that captures equilibria in Fisher markets with linear utilities, and also extends it to some other markets. Cheung, Cole, and Tao [18] extend the approach in [7] to show that proportional response converges for the entire range of CES utilities including complements, with linear utilities on one extreme and Leontief utilities on the other extreme. Cheung, Hoefer, and Nakhe [19] show that the dynamics stays close to equilibrium even when the market parameters are changing slowly over time, once again for CES utilities.…”
Section: Previous Workmentioning
confidence: 97%
“…The strongest convergence results for proportional response dynamics in Fisher markets are achieved via the mirror descent interpretation on suitable convex programs [7,18]. Devanur, Garg, and Végh [28] show a similar (but more complicated) convex program for linear utilities in exchange markets.…”
Section: Difficulties and Techniquesmentioning
confidence: 99%
“…Birnbaum, Devanur, and Xiao [BDX11] interpret proportional response as mirror descent on the convex program of Shmyrev [Shm09] that captures equilibria in Fisher markets with linear utilities, and also extends it to some other markets. Cheung, Cole, and Tao [CCT18] extend the approach in [BDX11] to show that proportional response converges for the entire range of CES utilities including complements, with linear utilities on one extreme and Leontief utilities on the other extreme. Cheung, Hoefer, and Nakhe [CHN19] show that the dynamics stays close to equilibrium even when the market parameters are changing slowly over time, once again for CES utilities.…”
Section: Previous Workmentioning
confidence: 97%