Impossibilities for roommate problems

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 consistency. ∗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 30 Bosphorus Workshop on Economic Design, Bodrum, 2008, and at the Annual Meeting of Association of Southern European Economic Theorists (ASSET), İstanbul, 2009. I thank the participants for several useful comments. †İstanbul Bilgi University, Department of Economics, 34440 Dolapdere, İstanbul, Turkey; e-mail: [email protected]