On the Convergence of Swap Dynamics to Pareto-Optimal Matchings

Brandt, Felix; Wilczynski, Anaëlle

doi:10.1007/978-3-030-35389-6_8

“…For unrestricted preferences, the Top Trading Cycle algorithm (Shapley and Scarf, 1974) is the only one that satisfies Pareto optimality, individual rationality, and strategyproofness. For single-peaked preferences, however, other rules satisfying these properties are known (Bade, 2019;Beynier et al, 2020), and swap dynamics have been studied for this restricted domain (Beynier et al, 2021;Brandt and Wilczynski, 2019).…”

Section: Matching and Assignmentmentioning

confidence: 99%

Preference Restrictions in Computational Social Choice: A Survey

Elkind¹,

Lackner²,

Peters³

2022

Preprint

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Social choice becomes easier on restricted preference domains such as single-peaked, single-crossing, and Euclidean preferences. Many impossibility theorems disappear, the structure makes it easier to reason about preferences, and computational problems can be solved more efficiently. In this survey, we give a thorough overview of many classic and modern restricted preference domains and explore their properties and applications. We do this from the viewpoint of computational social choice, letting computational problems drive our interest, but we include a comprehensive discussion of the economics and social choice literatures as well. Particular focus areas of our survey include algorithms for recognizing whether preferences belong to a particular preference domain, and algorithms for winner determination of voting rules that are hard to compute if preferences are unrestricted.

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“…Gourvès, Lesca, and Wilczynski (Gourvès, Lesca, and Wilczynski 2017) considered the problem of determining whether a target item allocation can be reached via rational swaps on a social network. Furthermore, they considered that the problem of determining whether some specified agent can get a target item via rational swaps (see also (Brandt and Wilczynski 2019;Huang and Xiao 2020)).…”

Section: Related Workmentioning

confidence: 99%

Reforming an Envy-Free Matching

Ito

¹

,

Iwamasa

²

,

Kakimura

³

et al. 2022

AAAI

1

0

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We consider the problem of reforming an envy-free matching when each agent is assigned a single item. Given an envy-free matching, we consider an operation to exchange the item of an agent with an unassigned item preferred by the agent that results in another envy-free matching. We repeat this operation as long as we can. We prove that the resulting envy-free matching is uniquely determined up to the choice of an initial envy-free matching, and can be found in polynomial time. We call the resulting matching a reformist envy-free matching, and then we study a shortest sequence to obtain the reformist envy-free matching from an initial envy-free matching. We prove that a shortest sequence is computationally hard to obtain even when each agent accepts at most four items and each item is accepted by at most three agents. On the other hand, we give polynomial-time algorithms when each agent accepts at most three items or each item is accepted by at most two agents. Inapproximability and fixed-parameter (in)tractability are also discussed.

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“…Gourvès, Lesca, and Wilczynski [10] considered the problem of determining whether a target item allocation can be reached via rational swaps on a social network. Furthermore, they considered that the problem of determining whether some specified agent can get a target item via rational swaps (see also [4,11]).…”

Section: Related Workmentioning

confidence: 99%

“…We construct an instance of the decision version of the shortest reformist sequence problem as follows (see Figure 7). For each edge e ∈ E, we prepare four agents e 1 , e 2 , e 3 , e 4 , and for each vertex v ∈ V , we prepare eight agents v 1 , v 2 , . .…”

Section: Shortest Reformist Sequence: Hardnessmentioning

confidence: 99%

Reforming an Envy-Free Matching

Ito¹,

Iwamasa²,

Kakimura³

et al. 2022

Preprint

0

View full text Add to dashboard Cite

We consider the problem of reforming an envy-free matching when each agent is assigned a single item. Given an envy-free matching, we consider an operation to exchange the item of an agent with an unassigned item preferred by the agent that results in another envy-free matching. We repeat this operation as long as we can. We prove that the resulting envy-free matching is uniquely determined up to the choice of an initial envy-free matching, and can be found in polynomial time. We call the resulting matching a reformist envy-free matching, and then we study a shortest sequence to obtain the reformist envy-free matching from an initial envy-free matching. We prove that a shortest sequence is computationally hard to obtain even when each agent accepts at most four items and each item is accepted by at most three agents. On the other hand, we give polynomial-time algorithms when each agent accepts at most three items or each item is accepted by at most two agents. Inapproximability and fixed-parameter (in)tractability are also discussed.

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On the Convergence of Swap Dynamics to Pareto-Optimal Matchings

Cited by 8 publications

References 25 publications

Preference Restrictions in Computational Social Choice: A Survey

Preference Restrictions in Computational Social Choice: A Survey

Reforming an Envy-Free Matching

Reforming an Envy-Free Matching

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