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.

翻译：我们研究线性费希尔市场中的比例响应动力学（PRD），其中参与者异步行动。我们将该场景建模为一个序列过程，在此过程中，每一步由对抗方在满足活跃性约束的条件下，选择一部分玩家更新其报价。我们证明，如果每个竞标者在被对抗方选中的群体中时，均单独使用PRD更新规则，则（在一般情况下）整个动态过程收敛至市场的竞争均衡。我们的证明技术揭示了线性费希尔市场的进一步性质，例如一般参数下均衡的唯一性，以及在特定条件下相关最优回应动力学和无交换遗憾动力学的收敛性。