The Perron-Frobenius theorem and its application to the Games of the Generals

• Main Authors: Esguerra, Jose Eduardo T., Manlapig, Mary Micah C.
• Format: text
• Language: English
• Published: Animo Repository 2007
• Subjects: Algebras, Linear; Board games
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/17465
• Institution: De La Salle University

This thesis is an exposition of a beautiful, but often neglected, theorem in Linear Algebra called The Perro-Frobenius Theorem. It was Appendix D of the Lecture Notes of Peter J. Cameron on Linear Algebra (2006) which called the attention of the writers of this thesis to the theorem of Perron and Frobenius. Appendix D of Cameron's lecture notes, entitled Who's on top of the league? , discusses the application of the Perron-Frobenius Theorem to the ranking of football teams. The writers of this thesis found that the Perron-Frobenius Theorem can be used to find the ranking of the officials in the Games of the Generals (GG), a board game that was invented in the Philippines by Sofronio H. Pasola, Jr. in 1972. It was found that, contrary to perception, the Private is not the lowest ranking official in GG. In fact, the Private ranks higher than six other officials!