The transition probabilities on wheel graphs: An application of evolutionary games on graphs

• Main Authors: Gaerlan, Carlos Jesus M., Tan, Michelle Denise S.
• Format: text
• Language: English
• Published: Animo Repository 2018
• Subjects: Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/18573
• Institution: De La Salle University

Evolutionary Graph Theory is the study of how population structures a ect evolutionary dynam- ics. Its main applications involve computing for xation probabilities and applying Evolutionary Game Theory by playing evolutionary games on di erent graphs. This paper focuses on an expo- sition and application of Broom, Hadjichrysanthou, and Rychtar's Evolutionary games on graphs and the speed of the evolutionary process published in 2009 by the journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. The main reference explores the evo- lutionary dynamics of the Hawk-Dove game on cycles, star graphs, and complete graphs. The main application in this paper will be obtaining transition probabilities for wheel graphs of order 5, 6, 7, and 8. Transition diagrams will also be introduced to demonstrate how a population may update itself on these wheel graphs.