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Farsighted Stability for Roommate Markets
Author(s) -
KLAUS BETTINA,
KLIJN FLIP,
WALZL MARKUS
Publication year - 2011
Publication title -
journal of public economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.809
H-Index - 32
eISSN - 1467-9779
pISSN - 1097-3923
DOI - 10.1111/j.1467-9779.2011.01525.x
Subject(s) - von neumann architecture , singleton , mathematical economics , matching (statistics) , independent set , stability (learning theory) , dominance (genetics) , set (abstract data type) , economics , rationality , von neumann–morgenstern utility theorem , mathematics , combinatorics , computer science , pure mathematics , graph , expected utility hypothesis , chemistry , law , genetics , biology , biochemistry , machine learning , political science , programming language , pregnancy , statistics , gene
We study farsighted stability for roommate markets. We show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this characterization of indirect dominance, we investigate von Neumann–Morgenstern farsightedly stable sets. We show that a singleton is von Neumann–Morgenstern farsightedly stable if and only if the matching is stable (Theorem 1). We also present a roommate market without a von Neumann–Morgenstern farsightedly stable set (Example 1) and a roommate market with a nonsingleton von Neumann–Morgenstern farsightedly stable set (Example 2).