Impossibilities for Roommate Problems

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Impossibilities for Roommate Problems ? I˙pek Ozkal Sanver † November 28, 2009 Abstract We establish three impossibility results for roommate problems. First, no single valued solution is Pareto optimal and anonymous. Next, no solution satisfies Pareto optimality, anonymity and converse consistency. Finally, no pseudo refinement of the core satisfies consis- tency. ?This research dates back to 2001, when I was a visiting graduate student at the University of Rochester. I owe special thanks to William Thomson. I thank Burak Can and Bettina Klaus for their helpful comments. A preliminary version of this paper has been presented at the 30th Bosphorus Workshop on Economic Design, Bodrum, 2008, and at the Annual Meeting of Association of Southern European Economic Theorists (ASSET), I˙stanbul, 2009. I thank the participants for several useful comments. †I˙stanbul Bilgi University, Department of Economics, 34440 Dolapdere, I˙stanbul, Turkey; e-mail: 1

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matching µ ?

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pareto optimality

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Impossibilities

∗ for Roommate Problems

˙ ¨ † Ipek Ozkal Sanver

November 28, 2009

Abstract We establish three impossibility results for roommate problems. First, no single valued solution is Pareto optimal and anonymous. Next, no solution satisﬁes Pareto optimality, anonymity and converse consistency. Finally, no pseudo reﬁnement of the core satisﬁes consis-tency.

∗ This research dates back to 2001, when I was a visiting graduate student at the University of Rochester. I owe special thanks to William Thomson. I thank Burak Can and Bettina Klaus for their helpful comments. A preliminary version of this paper has been th presented at the 30 Bosphorus Workshop on Economic Design, Bodrum, 2008, and at the Annual Meeting of Association of Southern European Economic Theorists (ASSET), ˙ Istanbul, 2009. I thank the participants for several useful comments. † ˙ ˙ Istanbul Bilgi University, Department of Economics, 34440 Dolapdere, Istanbul, Turkey; e-mail: isanver@bilgi.edu.tr

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