Consistency and its Converse for Roommate Markets
For marriage markets with equal numbers of men and women and where all men find all women acceptable and all women find all men acceptable, Sasaki and Toda (1992) characterize the core by anonymity, Pareto optimality, consistency, and converse consistency. In a recent paper, Nizamogullari and Özkal-Sanver (2012) generalize this result to the full domain of marriage markets by adding individual rationality and by replacing anonymity with gender fairness. We generalize both results by characterizing the core on the domain of no odd rings roommate markets by individual rationality, anonymity, Pareto optimality, consistency, and converse consistency. We also prove that extending this characterization to the domain of solvable roommate markets is not possible.
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- Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
- Ozkal-Sanver, Ipek, 2004. "A note on gender fairness in matching problems," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 211-217, March.
- Manabu Toda, 2006. "Monotonicity and Consistency in Matching Markets," International Journal of Game Theory, Springer, vol. 34(1), pages 13-31, April.
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