Asynchronous Proportional Response Dynamics: Convergence in Markets with Adversarial Scheduling

Yoav Kolumbus, Menahem Levy, Noam Nisan

Keywords: Asynchronous Dynamics, Fisher Markets, Proportional Response, Best Response, Game Dynamics, Competitive Equilibrium, Convergence

TL;DR: We study asynchronous dynamics in Fisher markets under adversarial scheduling and prove convergence properties of proportional response, best response, and regret minimization dynamics.

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 at each step, an adversary selects a subset of the players to update their bids, subject to liveness constraints. We show that if every bidder individually applies 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 reveals additional properties of linear Fisher markets, such as the uniqueness of the market equilibrium for generic parameters and the convergence of associated no swap regret dynamics and best response dynamics under certain conditions.

Submission Number: 8479