β Scribed by Alejandro Lage-Castellanos; Roberto Mulet
No coin nor oath required. For personal study only.
We study the stable marriage problem from different points of view. We proposed a microscopic dynamic that led the system to a stationary state that we are able to characterize analytically. Then, we derive a thermodynamical description of the Nash equilibrium states of the system that agree very well with the results of Monte Carlo simulations. Finally, through large-scale numerical simulations we compare the global optimum of the society with the stable marriage of lower energy. We showed that both states are strongly correlated and that the selfish attitude results in a benefit for most of the practitioners belonging to blocking pairs in the global optimum of the society.
π SIMILAR VOLUMES
A stable matching for an instance of the stable marriages problem or the stable roommates problem is bistable if it is also a stable matching when the ordering of the input preference lists is reversed. For the stable marriages problem, it is shown that the bistable matchings are a sublattice of the