On random exchange-stable matchings

Random stable matchings

The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent vertices in a graph such that no unpaired vertices prefer each other to their partners under the matching. The problem of finding stable matchings is known as the s...

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 ...

A Survey on Simulating Stable Random Variables

In general case, Chambers et al. (1976) introduced the following algorithm for simulating any stable random variables $ X/sim(alpha, beta, gamma, delta) $ with four parameters. They use a nonlinear transformation of two independent uniform random variables for simulating an stable random variable... (to continue, click here)

On Stable Matchings and Flows

We describe a flow model related to ordinary network flows the same way as stable matchings are related to maximum matchings in bipartite graphs. We prove that there always exists a stable flow and generalize the lattice structure of stable marriages to stable flows. Our main tool is a straightforward reduction of the stable flow problem to stable allocations. For the sake of completeness, we p...

Stable Matchings