For any matching market where the set of stable matchings has a lattice structure, if the binary operations ( l.u.b. and g.l.b. ) are computed via a "pointing function", then the set of random matchings (lotteries of stable matchings) has a lattice structure .
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 the g.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 .
R
For any matching market where the set
In this paper we study the lattice structure of the random matching set, that is, all lotteries
R
has a lattice structure, if the binary operations (
. We define the
R
and
(least upper bound) and the
R
) are computed via a "pointing function", then the
(greatest lower bound) for both sides of the matching market, and we prove the that with these binary operations the
R
(lotteries of stable matchings) has a lattice structure
has two dual lattices