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Asynchronous Proportional Response Dynamics in Markets with Adversarial Scheduling

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  • Yoav Kolumbus
  • Menahem Levy
  • Noam Nisan

Abstract

We study Proportional Response Dynamics (PRD) in linear Fisher markets where participants act asynchronously. We model this scenario as a sequential process in which in every step, an adversary selects a subset of the players that will update their bids, subject to liveness constraints. We show that if every bidder individually uses the PRD update rule whenever they are included in the group of bidders selected by the adversary, then (in the generic case) the entire dynamic converges to a competitive equilibrium of the market. Our proof technique uncovers further properties of linear Fisher markets, such as the uniqueness of the equilibrium for generic parameters and the convergence of associated best-response dynamics and no-swap regret dynamics under certain conditions.

Suggested Citation

  • Yoav Kolumbus & Menahem Levy & Noam Nisan, 2023. "Asynchronous Proportional Response Dynamics in Markets with Adversarial Scheduling," Papers 2307.04108, arXiv.org, revised Jan 2024.
    • Handle: RePEc:arx:papers:2307.04108
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    References listed on IDEAS

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    5. Sergiu Hart & Andreu Mas-Colell, 2013. "Simple Adaptive Strategies:From Regret-Matching to Uncoupled Dynamics," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8408.
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