On graphs and marriages
This thesis presents and verifies the works of Balinski and Ratier on Graphs and Marriages published in the The American Mathematical Monthly (1998). It centers on a marriage game where there are two distinct, finite sets of players M (the 'men) and W (the women ), each player has strict prefer...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
1999
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16556 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | This thesis presents and verifies the works of Balinski and Ratier on Graphs and Marriages published in the The American Mathematical Monthly (1998). It centers on a marriage game where there are two distinct, finite sets of players M (the 'men) and W (the women ), each player has strict preference order over those players of the opposite set whom he/she considers acceptable. A matching in a marriage game is a set of marriages among consenting players and some players who may be celibate.
The fundamental idea in the analysis of a marriage game is that each player is a rational soul who seeks to optimize his/her preferences. It aims to verify the stability of matchings in marriage graphs and to present proofs of some of the theorems in the article Graphs and Marriages. One important result shows that the set of all stable matchings in a marriage graph forms a distributive lattice. |
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