Stable Marriage Problem Mapped to Lotka-volterra Model: Stable Equilibria Mapped from Stable Matchings

Characterization of Dynamics of Stable Matchings: Attractors Mapped from Stable Matchings

This note characterizes the dynamic structure of stable matchings of the stable marriage problem (SMP). The characterization focuses on the dynamic process of how the stable matching will be attained. To this end, the discrete problem of the SMP will be mapped to nonlinear dynamical models whose attractors include the counterparts of the stable matchings in the original SMP. A simple measure of...

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...

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...

Part C project : Stable matchings Supervisor : James Martin Stable marriage

The “stable marriage” problem is often described as follows. There are n men and n women; each of the men has an order of preference on the women, and each of the women has an order of preference on the men. A “matching” of the people into n man-woman pairs is said to be unstable if there exist some man and some woman who both prefer each other to their partner in the matching. If there is no s...

The Stable Marriage Problem