In this paper we study the lattice structure of the random matching set , that is, all lotteries of stable matchings. We define the l.u.b. ( least upper bound ) and theg.l.b. ( greatest lower bound ) for both sides of the matching market, and we prove the that with these binary operations the set of random matchings has two dual lattices.
For a many-to-many matching market, we study the lattice structure of the set of random stable matchings. We define the least upper bound and the greatest lower bound for both sides of the matching market, and we prove the that with these binary operations the set of random stable matchings forms two dual lattices.
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In this paper
For a many-to-many matching market,
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random matching set , that is, all lotteries of
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