Dominant Resource Fairness with Meta-Types

Abstract

Inspired by the recent COVID-19 pandemic, we study a generalization of the multi-resource allocation problem with heterogeneous demands and Leontief utilities. Unlike existing settings, we allow each agent to specify requirements to only accept allocations from a subset of the total supply for each resource. These requirements can take form in location constraints (e.g. A hospital can only accept volunteers who live nearby due to commute limitations). This can also model a type of substitution effect where some agents need 1 unit of resource A \emph{or} B, both belonging to the same meta-type. But some agents specifically want A, and others specifically want B. We propose a new mechanism called Dominant Resource Fairness with Meta Types which determines the allocations by solving a small number of linear programs. The proposed method satisfies Pareto optimality, envy-freeness, strategy-proofness, and a notion of sharing incentive for our setting. To the best of our knowledge, we are the first to study this problem formulation, which improved upon existing work by capturing more constraints that often arise in real life situations. Finally, we show numerically that our method scales better to large problems than alternative approaches.

Recommendations as treatments

“…Several practical counterfactual estimators have been developed that exploit the combinatorial structures in these interfaces (McInerney et al 2020; Swaminathan et al 2017). Ongoing research uses ideas from doubly‐robust estimation and non‐parametric statistics (Bibaut et al 2019; Su et al 2020; Yin and Wang 2020) to further tune the bias‐variance trade‐off of these kinds of estimators and provide a plug‐and‐play practical solution for realistic recommendation interfaces (Dimakopoulou et al 2019; Ma et al 2020a).…”

Sub-game perfect Nash equilibrium under loser reporting

“…Kalinowski et al [14] further studied the impact of strategic behavior on the complete-information extensive-form game of such sequential allocation procedures. Yin et al [15] proposed a new called Group Dominant Resource Fairness which determines the allocations by solving a small number of linear programs. Baklanov et al [16] proved that a PROPm allocation is guaranteed to exist for all instances, independent of the number of agents or goods.…”