The marriage problem: from the bar of appointments to the agency

Details The marriage problem: from the bar of appointments to the agency The marriage problem: from the bar of appointments to the agency

2005-08-11

arxiv.org/abs/physics/0508073v1

Physics

Physics and Society

15 pages, 9 figures. To be published in Physica A (2005)

Scientific paper

10.1016/j.physa.2005.08.042

We study the stable marriage problem from different points of view. We proposed a microscopic dynamic that lead 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 selffish attitude results in a benefit for most of the practitioners belonging to blocking pairs in the Global Optimum of the society.

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