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We study Proportional Response Dynamics (PRD) in linear Fisher markets whereparticipants act asynchronously. We model this scenario as a sequential processin which in every step, an adversary selects a subset of the players that willupdate their bids, subject to liveness constraints. We show that if everybidder individually uses the PRD update rule whenever they are included in thegroup of bidders selected by the adversary, then (in the generic case) theentire dynamic converges to a competitive equilibrium of the market. Our prooftechnique uncovers further properties of linear Fisher markets, such as theuniqueness of the equilibrium for generic parameters and the convergence ofassociated best-response dynamics and no-swap regret dynamics under certainconditions.

Asynchronous Proportional Response Dynamics in Markets with Adversarial Scheduling