Fair solutions to the random assignment problem

Basteck, Christian

doi:10.1016/j.jmateco.2018.02.006

Cited by 5 publications

(2 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Subsequently, the literature considered various generalizations of the model and/or applications of TTC: the case of no ownership [36,67,65], the case where some agents may own nothing (generalizing the two previous cases) [2,63,65,49,53], fairer probabilistic rules [1,8,6,11,15,16,22,21,23,35,41] allowing for indifferences in preferences [4,9,14,37,52,54,56,64], School Choice [3,29,48,28,47,46], and dynamic environments [40,58]. Several authors considered manipulation not by preference misreport but by the merging/splitting/withholding of endowments [7,18].…”

Section: Related Literaturementioning

confidence: 99%

On the parameterized complexity of manipulating Top Trading Cycles

Phan¹,

Purcell²

2018

Preprint

View full text Add to dashboard Cite

We study the problem of exchange when 1) agents are endowed with heterogeneous indivisible objects, and 2) there is no money. In general, no rule satisfies the three central properties Pareto-efficiency, individual rationality, and strategy-proofness [62]. Recently, it was shown that Top Trading Cycles is NP-hard to manipulate [32], a relaxation of strategy-proofness. However, parameterized complexity is a more appropriate framework for this and other economic settings. Certain aspects of the problem -number of objects each agent brings to the table, goods up for auction, candidates in an election [25], legislative figures to influence [24] -may face natural bounds or are fixed as the problem grows. We take a parameterized complexity approach to indivisible goods exchange for the first time. Our results represent good and bad news for TTC. When the size of the endowments k is a fixed constant, we show that the computational task of manipulating TTC can be performed in polynomial time. On the other hand, we show that this parameterized problem is W[1]-hard, and therefore unlikely to be fixed parameter tractable.

show abstract

Section: Related Literaturementioning

confidence: 99%

On the parameterized complexity of manipulating Top Trading Cycles

Phan¹,

Purcell²

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…See for example,Basteck [2018] for an extensive analysis of logical relationships between various fairness concepts in the present context.23 Loosely speaking, this means that agents cannot change to "too much" the random assignments of other agents (in terms of probability shares) as the market becomes large.24 RSD is regular, provided the number of copies for each object type grows at the same rate as the number of agents, e.g., in replica economies.…”

mentioning

confidence: 99%