Dartmouth College Computer Science
Technical Report series
TR search TR listserv
|By author:||A B C D E F G H I J K L M N O P Q R S T U V W X Y Z|
|By number:||2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, 1997, 1996, 1995, 1994, 1993, 1992, 1991, 1990, 1989, 1988, 1987, 1986|
This paper addresses strategies for the stable roommates problem, assuming that a stable matching is chosen at random. We investigate how a cheating man should permute his preference list so that he has a higher-ranking roommate probabilistically.
In the first part of the paper, we identify a necessary condition for creating a new stable roommate for the cheating man. This condition precludes any possibility of his getting a new roommate ranking higher than all his stable roommates when everyone is truthful. Generalizing to the case that multiple men collude, we derive another impossibility result: given any stable matching in which a subset of men get their best possible roommates, they cannot cheat to create a new stable matching in which they all get strictly better roommates than in the given matching.
Our impossibility result, considered in the context of the stable marriage problem, easily re-establishes the celebrated Dubins-Freedman Theorem. The more generalized Demange-Gale-Sotomayor Theorem states that a coalition of men and women cannot cheat to create a stable matching in which everyone of them gets a strictly better partner than in the Gale-Shapley algorithm (with men proposing). We give a sharper result: a coalition of men and women cannot cheat together so that, in a newly-created stable matching, every man in the coalition gets a strictly better partner than in the Gale-Shapley algorithm while none of the women in the coalition is worse off.
In the second part of the paper, we present two cheating strategies that guarantee that the cheating man's new probability distribution over stable roommates majorizes the original one. These two strategies do not require the knowledge of the probability distribution of the cheating man. This is important because the problem of counting stable matchings is \#P-complete. Our strategies only require knowing the set of stable roommates that the cheating man has and can be formulated in polynomial time. Our second cheating strategy has an interesting corollary in the context of stable marriage with the Gale-Shapley algorithm. Any woman-optimal strategy will ensure that every woman, cheating or otherwise, ends up with a partner at least as good as when everyone is truthful.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
Or copy and paste:
Chien-Chung Huang, "Cheating to Get Better Roommates in a Random Stable Matching." Dartmouth Computer Science Technical Report TR2006-582, December, 2006.
Notify me about new tech reports.
Search the technical reports.
To receive paper copy of a report, by mail, send your address and the TR number to reports AT cs.dartmouth.edu
Copyright notice: The documents contained in this server are included by the contributing authors as a means to ensure timely dissemination of scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.
Technical reports collection maintained by David Kotz.