A note on the direct proof for ex-post stability implies well-ordered ex-post stability



We provide a novel and direct proof of the following result: each ex-post stable probabilistic assignment can be decomposed into a collection of deterministic stable assignments, which can be ordered in such a way that each man’s welfare is non-increasing and each woman’s welfare is non-decreasing as we follow the assignments from the first to the last.


Marriage problem, pr obabilistic assignments, ex-post stability

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