NDLI: Manipulation of stable matchings using minimal blacklists

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Manipulation of stable matchings using minimal blacklists

Content Provider	ACM Digital Library
Author	Gonczarowski, Yannai A.
Abstract	Gale and Sotomayor [1985] have shown that in the Gale-Shapley matching algorithm [1962], the proposed-to side W (referred to as women there) can strategically force the W-optimal stable matching as the M-optimal one by truncating their preference lists, each woman possibly blacklisting all but one man. As Gusfield and Irving have already noted in 1989, no results are known regarding achieving this feat by means other than such preference-list truncation, i.e. by also permuting preference lists. We answer Gusfield and Irving's open question by providing tight upper bounds on the amount of blacklists and their combined size, that are required by the women to force a given matching as the M-optimal stable matching, or, more generally, as the unique stable matching. Our results show that the coalition of all women can strategically force any matching as the unique stable matching, using preference lists in which at most half of the women have nonempty blacklists, and in which the average blacklist size is less than 1. This allows the women to manipulate the market in a manner that is far more inconspicuous, in a sense, than previously realized. When there are less women than men, we show that in the absence of blacklists for men, the women can force any matching as the unique stable matching without blacklisting anyone, while when there are more women than men, each to-be-unmatched woman may have to blacklist as many as all men. Together, these results shed light on the question of how much, if at all, do given preferences for one side a priori impose limitations on the set of stable matchings under various conditions. All of the results in this paper are constructive, providing efficient algorithms for calculating the desired strategies.
Ending Page	449
Page Count	1
Starting Page	449
File Format	PDF
ISBN	9781450325653
DOI	10.1145/2600057.2602840
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-06-01
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Matching Stability Manipulation Blacklist Deferred acceptance Game theory
Content Type	Text
Resource Type	Article

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