Matching Market Design with Constraints

Aziz, Haris; Bíró, Péter; Yokoo, Makoto

doi:10.1609/aaai.v36i11.21495

Cited by 10 publications

(4 citation statements)

References 52 publications

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“…We should like to consider these multiple constraints in matching problems. [27,28], and to provide efficient market-clearing mechanisms. [29] explores the fairness in matching market from the perspective of bandit learning.…”

Section: Related Workmentioning

confidence: 99%

Subgroup fairness in two-sided markets

2023

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It is well known that two-sided markets are unfair in a number of ways. For example, female drivers on ride-hailing platforms earn less than their male colleagues per mile driven. Similar observations have been made for other minority subgroups in other two-sided markets. Here, we suggest a novel market-clearing mechanism for two-sided markets, which promotes equalization of the pay per hour worked across multiple subgroups, as well as within each subgroup. In the process, we introduce a novel notion of subgroup fairness (which we call Inter-fairness), which can be combined with other notions of fairness within each subgroup (called Intra-fairness), and the utility for the customers (Customer-Care) in the objective of the market-clearing problem. Although the novel non-linear terms in the objective complicate market clearing by making the problem non-convex, we show that a certain non-convex augmented Lagrangian relaxation can be approximated to any precision in time polynomial in the number of market participants using semidefinite programming, thanks to its “hidden convexity”. This makes it possible to implement the market-clearing mechanism efficiently. On the example of driver-ride assignment in an Uber-like system, we demonstrate the efficacy and scalability of the approach and trade-offs between Inter- and Intra-fairness.

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Section: Related Workmentioning

confidence: 99%

Subgroup fairness in two-sided markets

2023

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“…The paper has spawned richer matching models and resulted in new algorithmic work (see, e.g., Manlove [45]). Our work is an extension of these models and falls in the general umbrella of matching markets with various kinds of distributions constraints (see, e.g., Aziz et al [9,12,24,25,36,42]).…”

Section: Related Workmentioning

confidence: 99%

Cutoff stability under distributional constraints with an application to summer internship matching

2022

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We introduce a new two-sided stable matching problem that describes the summer internship matching practice of an Australian university. The model is a case between two models of Kamada and Kojima on matchings with distributional constraints. We study three solution concepts, the strong and weak stability concepts proposed by Kamada and Kojima, and a new one in between the two, called cutoff stability. Kamada and Kojima showed that a strongly stable matching may not exist in their most restricted model with disjoint regional quotas. Our first result is that checking its existence is NP-hard. We then show that a cutoff stable matching exists not just for the summer internship problem but also for the general matching model with arbitrary heredity constraints. We present an algorithm to compute a cutoff stable matching and show that it runs in polynomial time in our special case of summer internship model. However, we also show that finding a maximum size cutoff stable matching is NP-hard, but we provide a Mixed Integer Linear Program formulation for this optimisation problem.

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“…To this extent, several works studied the manipulability of these class of problems [31,32], the fairness [33], and the envy-freeness [34]. We refer to [35] for a comprehensive survey.…”

Section: Introductionmentioning

confidence: 99%

Edge Manipulations for the Maximum Vertex-Weighted Bipartite b-matching

Auricchio,

Ma,

Zhang

2023

Preprint

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MDFS, and MAP – that, given an MVbM problem as input, return a b-matching. We weighted b-Matching (MVbM) problem on bipartite graphs (A∪T,E). The setAcomprises agents,while T represents tasks. The set E, which connects A and T , is the private information of either agents or tasks. In this framework, we investigate three mechanisms – MBFS, MDFS, and MAP – that, given an MVbM problem as input, return a b-matching. We examine scenarios in which either agents or tasks are strategic and report their adjacent edges to one of the three mechanisms. In both cases, we assume that the strategic entities are bounded by their statements: they can hide edges, but they cannot report edges that do not exist. First, we consider the case in which agents can manipulate. In this framework,MBFS and MDFS are optimal but not truthful. By characterizing the Nash Equilibria induced by MBFS and MDFS, we reveal that both mechanisms have a Price of Anarchy (PoA) and Price of Stability (PoS) of 2. These efficiency guarantees are tight; no deterministic mechanism can achieve a lower PoA or PoS. In contrast, the third mechanism, MAP , is not optimal, but truthful and its approximation ratio is 2. We demonstrate that this ratio is optimal; no deterministic and truthful mechanism can outperform it. We then shift our focus to scenarios where tasks can exhibit strategic behaviour. In this case,MBFS,MDFS, and MAP all maintain truthfulness, making MBFS and MDFS truthful and optimal mechanisms. In conclusion, we investigate the manipulability of MBFS and MDFS through experiments on randomly generated graphs. We observe that (i) MBFS is less prone to be manipulated by the first agent than MDFS; (ii) MBFS is more manipulable on instances in which the total capacity of the agents is equal to the number of tasks; (iii) randomizing the agents’ order reduces the agents’ ability to manipulate MBFS.

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Matching Market Design with Constraints

Cited by 10 publications

References 52 publications

Subgroup fairness in two-sided markets

Subgroup fairness in two-sided markets

Cutoff stability under distributional constraints with an application to summer internship matching

Edge Manipulations for the Maximum Vertex-Weighted Bipartite b-matching

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