公平动态配给

V. Manshadi, Rad Niazadeh, Scott Rodilitz
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引用次数: 31

摘要

我们研究了政府和非营利组织在需要(需求)顺序实现且可能相关的代理人之间公平有效地分配社会产品时所面临的分配挑战。例如,在COVID-19大流行的早期,联邦紧急事务管理局面临着来自不同州的压倒性、暂时分散、先验不确定和相关的医疗用品需求。为了在这种情况下更好地实现公平和效率的双重目标,社会规划者打算最大化各个代理的最小填充率,其中每个代理的填充率必须在其到达时不可撤销地决定。对于任意相关的需求序列,我们建立了任何策略可实现的期望最小填充率(事后公平)和最小期望填充率(事前公平)的上界。我们的边界是由代理数量和预期需求供给比参数化的,它们揭示了在动态配给中实现公平的限制。进一步,我们证明了对于任何一组参数,一个简单的预测比例分配的自适应策略,无论事后还是事前,都能达到最好的公平保证。我们的策略是透明且易于实施的,因为它不依赖于超出第一条件时刻的分布信息。尽管它很简单,但我们通过描述依赖于完全分布知识的最优策略的性能,证明了该策略比非自适应目标填充率策略提供了显著的改进。我们通过在相应的value-to-go上归纳设计下界函数来获得(i)我们提出的自适应策略的性能保证,以及(ii)通过建立与垄断定价优化问题的有趣联系来获得最优目标填充率策略。此外,我们将我们的结果扩展到考虑可选择的目标函数和分配多种类型的资源。我们以白宫使用的预测需求模型为基础,对COVID-19医疗用品配给进行了数值研究,以补充我们的理论发展。在这种情况下,我们的简单自适应策略明显优于其理论保证和最优目标填充率策略。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fair Dynamic Rationing
We study the allocative challenges that governmental and nonprofit organizations face when tasked with equitable and efficient rationing of a social good among agents whose needs (demands) realize sequentially and are possibly correlated. As one example, early in the COVID-19 pandemic, the Federal Emergency Management Agency faced overwhelming, temporally scattered, a priori uncertain, and correlated demands for medical supplies from different states. To better achieve their dual aims of equity and efficiency in such contexts, social planners intend to maximize the minimum fill rate across agents, where each agent's fill rate must be irrevocably decided upon its arrival. For an arbitrarily correlated sequence of demands, we establish upper bounds on both the expected minimum fill rate (ex-post fairness) and the minimum expected fill rate (ex-ante fairness) achievable by any policy. Our bounds are parameterized by the number of agents and the expected demand-to-supply ratio, and they shed light on the limits of attaining equity in dynamic rationing. Further, we show that for any set of parameters, a simple adaptive policy of projected proportional allocation achieves the best possible fairness guarantee, ex post as well as ex ante. Our policy is transparent and easy to implement, as it does not rely on distributional information beyond the first conditional moments. Despite its simplicity, we demonstrate that this policy provides significant improvement over the class of non-adaptive target-fill-rate policies by characterizing the performance of the optimal such policy, which relies on full distributional knowledge. We obtain the performance guarantees of (i) our proposed adaptive policy by inductively designing lower-bound functions on its corresponding value-to-go, and (ii) the optimal target-fill-rate policy by establishing an intriguing connection to a monopoly-pricing optimization problem. Further, we extend our results to considering alternative objective functions and to rationing multiple types of resources. We complement our theoretical developments with a numerical study motivated by the rationing of COVID-19 medical supplies based on a projected-demand model used by the White House. In such a setting, our simple adaptive policy significantly outperforms its theoretical guarantee as well as the optimal target-fill-rate policy.
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