Asynchronous Proportional Response Dynamics in Markets with Adversarial Scheduling

TL;DR

This paper analyzes how asynchronous proportional response dynamics in Fisher markets with adversarial scheduling still lead to market equilibrium, revealing convergence properties and equilibrium uniqueness.

Contribution

It introduces a model of asynchronous PRD under adversarial scheduling and proves convergence to equilibrium, highlighting new stability and uniqueness results.

Findings

Convergence of asynchronous PRD to market equilibrium

Uniqueness of equilibrium for generic parameters

Convergence of best-response and no-swap regret 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 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.