Fisher markets are those where buyers with budgets compete for scarce items, a natural model for many real world markets including online advertising. A market equilibrium is a set of prices and allocations of items such that supply meets demand. We show how market designers can use taxes or subsidies in Fisher markets to ensure that market equilibrium outcomes fall within certain constraints. We show how these taxes and subsidies can be computed even in an online setting where the market designer does not have access to private valuations. We adapt various types of fairness constraints proposed in existing literature to the market case and show who benefits and who loses from these constraints, as well as the extent to which properties of markets including Pareto optimality, envy-freeness, and incentive compatibility are preserved. We find that some prior discussed constraints have few guarantees in terms of who is made better or worse off by their imposition.

翻译：费雪市场是指买家拥有预算并竞争稀缺商品的市场，这是包括在线广告在内的许多现实市场的自然模型。市场均衡是一组价格和商品分配，使得供需匹配。我们展示了市场设计者如何在费雪市场中运用税收或补贴，以确保市场均衡结果满足特定约束。我们证明了即使在市场设计者无法获取私人估值的在线环境中，这些税收与补贴仍可被计算。我们调整了现有文献中提出的多种公平性约束类型以适用于市场情境，并分析了这些约束对受益方与受损方的影响，以及市场特性（如帕累托最优性、无嫉妒性和激励相容性）的保留程度。研究发现，部分此前讨论的约束在实施时对参与方的利益增减无法提供充分保障。