A Measure to Compare Matchings in Marriage Markets

A Measure of Instability for Matchings in Marriage Markets

In marriage markets (two-sided one-to-one matching problems) the number of blocking pairs which exist against a matching is often used as a measure of instability. We argue that in many cases this measure is economically implausible. To fix the problem, we state two principles which should be fulfilled by sets of blocking pairs whose cardinalities are taken as measures of instability. We offer ...

Coalitional Exchange Stable Matchings in Marriage and Roommate Markets

We consider the stable roommates problem with respect to the stability based on exchange of agents. We present three natural variants of coalitional exchange stability and identify the relations between them. We also present a number of impossibility results. In particular, we show that even a (standard) exchange stable matching may not exist for dichotomous preferences. We prove that exchange ...

Stable Matchings for A Generalized Marriage Problem

We show, that a simple generalization of the Deferred Acceptance Procedure with men proposing due to Gale and Shapley (1962), yields outcomes for a generalized marriage problem, which are necessarily stable. We also show, that any outcome of this procedure is Weakly Pareto Optimal for Men, i.e. there is no other outcome which all men prefer to an outcome of this procedure. In a final concluding...

Popular Matchings in the Stable Marriage Problem

The input is a bipartite graph G = (A ∪B ,E) where each vertex u ∈ A ∪B ranks its neighbors in a strict order of preference. This is the same as an instance of the stable marriage problem with incomplete lists. A matching M∗ is said to be popular if there is no matching M such that more vertices are better off in M than in M∗. Any stable matching of G is popular, however such a matching is a mi...

Marriage Markets and Bargaining Marriage Markets and Bargaining Between Spouses