The paper considers a one-to-one matching with contracts model in the presence of price controls. This set-up contains two important streams in the matching literature, those with and those without monetary transfers, as special cases and allows for intermediate cases with some restrictions on...

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...

It is known that in two-sided many-to-many matching markets, pair-wise stability is not logically related with the (weak) core, unlike in many-to-one matching markets (Blair, 1988). In this paper, we seek a theoretical foundation for pairwise stability when group deviations are allowed. Group...

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...

In a matching problem between students and schools, a mechanism is said to be robustly stable if it is stable, strategy-proof, and immune to a combined manipulation, where a student first misreports her preferences and then blocks the matching that is produced by the mechanism. We find that even...

A new mechanism was introduced in New York City and Boston to assign students to public schools. This mechanism was advocated for its superior fairness property, besides others. We introduce a new framework for school-choice problems and two notions of fairness in lottery design based on ex-ante...

Ostrovsky [10] develops a theory of stability for a model of matching in exogenously given networks. For this model a generalization of pairwise stability, chain stability, can always be satisfied as long as agents’ preferences satisfy same side substitutability and cross side complementarity....

We adopt the notion of von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a von...

Suppose that the agents of a matching market contact each other randomly and form new pairs if is in their interest. Does such a process always converge to a stable matching if one exists? If so, how quickly? Are some stable matchings more likely to be obtained by this process than others? In...