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    A note on roommate problems with a limited number of rooms
    (Springer Heidelberg, 2022) Nizamogullari, Duygu; Ozkal-Sanver, Ipek
    Classical roommate problems define individual rationality by conceiving remaining single as the outside option. This conception implicitly assumes that there are always some empty rooms to be shared. However, there are many instances when this is not the case. We introduce roommate problems with a limited number of rooms, where the outside option is having no room. In this general framework, we show that the core equals the set of Pareto optimal and stable matchings.
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    Characterization of the core in full domain marriage problems
    (Elsevier Science Bv, 2014) Nizamogullari, Duygu; Ozkal-Sanver, Ipek
    In this paper, we study the core of two-sided, one-to-one matching problems. First, in a model in which agents have strict preferences over their potential mates and are allowed to remain single, we characterize the core as the unique solution that satisfies individual rationality, Pareto optimality, gender fairness, consistency, and converse consistency. Next, in a model that relaxes the constraint that agents have strict preferences over their potential mates, we show that no solution exists that satisfies Pareto optimality, anonymity, and converse consistency. In this full domain, we characterize the core by individual rationality, weak Pareto optimality, monotonicity, gender fairness, consistency, and converse consistency. (C) 2014 Elsevier B.V. All rights reserved.
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    Coalitional stability and efficiency of partitions in matching problems
    (Springer, 2011) Nizamogullari, Duygu; Ozkal-Sanver, Ipek
    A-zkal-Sanver (Theory Decis 59:193-205, 2005) studies stability and efficiency of partitions of agents in two-sided matching markets in which agents can form partitions by individual moves only, and a matching rule determines the matching in each coalition in a partition. In this study, we present the relationship between stability and efficiency of partitions that is analyzed for several matching rules and under various membership property rights codes, now allowing coalitional moves.
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    Consistent enlargements of the core in roommate problems
    (Springer, 2015) Nizamogullari, Duygu; Ozkal-Sanver, Ipek
    In this paper, we study consistent enlargement of a solution. By computing it, one actually evaluates the extent to which the solution would have to be expanded in order to be well-defined and consistent. We show that the union of stable matchings and the matching recommended by a single-valued, well-defined, individually rational, and consistent solution is a minimal consistent enlargement of the core. Although individual rationality is sufficient it is not a necessity. Next, we show that for any fixed order on the set of agents in the society, the union of stable matchings and the serial dictatorship matching is a minimal consistent enlargement of the core.