Proportional Dynamics in Exchange Economies

Brânzei, Simina; Devanur, Nikhil R.; Rabani, Yuval

doi:10.1145/3465456.3467644

Cited by 12 publications

(11 citation statements)

References 69 publications

(53 reference statements)

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“…The main result in [WZ07] is that when the valuations are symmetric 1 the dynamic converges to market equilibria for all non-degenerate starting configurations. The work in [BDR19] further showed the tit-for-tat dynamic cycles in exchange economies with non-symmetric valuations.…”

Section: Related Workmentioning

confidence: 91%

“…In each round, the players split their budget into bids on the goods, then each good is allocated to each player in proportion to the bid amount and the seller collects the money made from selling. In the exchange economy, each player updates their bids on the goods in proportion to the contribution of each good in their utility; there, the dynamic converges to market equilibria [BDR19] for any economy with additive valuations. In Fisher markets, proportional response converges to market equilibria, which was shown for additive valuations in [Zha11] and for all CES valuations by [CCT18].…”

Section: Related Workmentioning

confidence: 99%

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Tit-for-Tat Dynamics and Market Volatility

Brânzei¹

2019

Preprint

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We study the tit-for-tat dynamic in production markets, where each player can make a good given as input various amounts of goods in the system. In the tit-for-tat dynamic, each player allocates its good to its neighbors in fractions proportional to how much they contributed in its production in the last round. Tit-for-tat does not use money and was studied before in pure exchange settings [WZ07].We study the phase transitions of this dynamic when the valuations are symmetric (i.e. each good has the same worth to everyone) by characterizing which players grow or vanish over time. We also study how the fractions of their investments evolve in the long term, showing that in the limit the players invest only on players with optimal production capacity.

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Section: Related Workmentioning

confidence: 91%

Section: Related Workmentioning

confidence: 99%

Tit-for-Tat Dynamics and Market Volatility

Brânzei¹

2019

Preprint

Self Cite

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“…(6b) and (6c). • Proportional sharing (PS) [28], which allocates a portion of every resource proportionally to the buyer's budget. • Social welfare maximization (SWM) [29], which maximizes the total utility of all the buyers subject to the available supply, without considering the budget constraint.…”

Section: A Market Equilibriummentioning

confidence: 99%

Knowledge Sharing in AI Services: A Market-Based Approach

Mohammed

Naas

Sigg

et al. 2023

IEEE Internet Things J.

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Today's deep neural networks (DNNs) are very accurate when trained on a large amount of data. However, suitable input might not be available or may require extensive data collection. Data sharing is one option to address these issues, but it is generally impractical because of privacy concerns or due to the problematic process of finding a sharing agreement. Instead, this work considers knowledge sharing by first exchanging the weights of pre-trained DNNs and then applying transfer learning. Specifically, it addresses the economics of knowledge sharing in AI services by taking a market-based approach. In detail, a model based on Fisher's market is devised for optimal knowledge sharing, defined as the gain in inference accuracy from exchanging DNN weights. The proposed approach is shown to reach a market equilibrium and to satisfy important economic properties, including Pareto optimality. A technique for weight fusion is also introduced to merge acquired knowledge with the existing one. Finally, an extensive evaluation is conducted in a distributed intelligence scenario. The obtained results show that the proposed solution is efficient and that weight fusion with transfer learning significantly increases inference accuracy compared to the original DNN, without the overhead of federated learning.

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“…, v n ) T . As is standard in the literature (Cheung et al, 2013;Brânzei et al, 2021), we assume that for all buyers i ∈ [n], X i = R m + . Once a utility function class is fixed, an exchange economy is referred to with the name of the utility function, and can be sampled as a tuple (V , E) ∈ R n×m × R n×m for linear, Cobb-Douglas, and Leontief exchange economies, and as a tuple (V , ρ, E) ∈ R n×m × R n × R n×m for CES exchange economies.…”

Section: Arrow-debreu Exchange Economiesmentioning

confidence: 99%

Generative Adversarial Equilibrium Solvers

Denizalp¹,

Parkes²,

Gemp³

et al. 2023

Preprint

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We introduce the use of generative adversarial learning to compute equilibria in general gametheoretic settings, specifically the generalized Nash equilibrium (GNE) in pseudo-games, and its specific instantiation as the competitive equilibrium (CE) in Arrow-Debreu competitive economies. Pseudo-games are a generalization of games in which players' actions affect not only the payoffs of other players but also their feasible action spaces. Although the computation of GNE and CE is intractable in the worst-case, i.e., PPAD-hard, in practice, many applications only require solutions with high accuracy in expectation over a distribution of problem instances. We introduce Generative Adversarial Equilibrium Solvers (GAES): a family of generative adversarial neural networks that can learn GNE and CE from only a sample of problem instances. We provide computational and sample complexity bounds, and apply the framework to finding Nash equilibria in normal-form games, CE in Arrow-Debreu competitive economies, and GNE in an environmental economic model of the Kyoto mechanism.

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Proportional Dynamics in Exchange Economies

Cited by 12 publications

References 69 publications

Tit-for-Tat Dynamics and Market Volatility

Tit-for-Tat Dynamics and Market Volatility

Knowledge Sharing in AI Services: A Market-Based Approach

Generative Adversarial Equilibrium Solvers

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