1. The idea is standard: there is no subset of initial owners who could exchange their houses and be matched with other agents such that all of them are better-off. In a housing market setting, Roth and Postlewaite (1977) defined two different core notions: strict and weak. The former imposes that the preference relation in condition (3) of the above definition is strict for every member of the coalition. The weak version is similar to ours, allowing indifferences for some members of the coalition. Our next proposition shows that even for a I-initial ownership this (weak) core notion may be empty;School Choice: A Mechanism Design Approach,2003
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