Problems Related to the Zermelo and Extended Zermelo Model

In this thesis we consider a few results related to the Zermelo and Extended Zermelo Model as well as outline some partial results and open problems related thereto. First we will analyze a discrete dynamical system considering under what conditions the convergence of this dynamical system predicts the outcome of the Extended Zermelo Model. In the following chapter we will focus on the Zermelo Model by giving a method for simplifying the derivation of Zermelo ratings for tournaments in terms of specific types of strongly connected components. Following this, the idea of stability of a tournament will be discussed and an upper bound will be obtained on the stability of three-team tournaments. Finally, we will conclude with some partial results related to the topics presented in the previous chapters.

Name thesis:degree_name

MS

Grantor dc:publisher

Brigham Young University - Provo

Author dc:creator

• Webb, Benjamin Zachary

• Zermelo
• ranking
• dynamical system
• tournament
• Mathematics

Language dc:language

English

Repository record dc:identifier

https://scholarsarchive.byu.edu/etd/124

OAI identifier oai:identifier

oai:scholarsarchive.byu.edu:etd-1123