We show that, given two matchings of which say the second is stable, if (a) no firm prefers the first matching to the second, and (b) no firm and the worker it is paired with under the second matching prefer each other to their respective assignments in the first matching, then no worker prefers...

We show that a simple generalisation of the Deferred Acceptance Procedure with men proposing due to Gale and Shapley (1962) yields outcomes for a generalised marriage problem, which are necessarily stable. We also show that any outcome of this procedure is Weakly Pareto Optimal for Men, i.e....

We show that, given two matchings for a room-mates problem of which say the second is stable, and given a non-empty subset of agents S if (a) no agent in S prefers the first matching to the second, and (b) no agent in S and his room-mate in S under the second matching prefer each other to their...