Dissertation

Evolutionary Game Theory: Infinite and Finite Dynamics

King, Harry G

2019

Overview

In this dissertation, I describe the philosophy of and techniques employed by evolutionary game theorists. I have considered various models used by evolutionary game theorists, and the dynamics of each model. I have compared the similarities and differences of each one, which are more viable in certain contexts, which fall apart under certain conditions and so on. Solution concepts for evolutionary games and their dynamical implications are discussed. The continuous replicator equation for two strategies is analysed rigorously using an argument based on bifurcations. The geometric point of view regarding ordinary differential equations is given a extensive coverage, including fixed points, periodic orbits, heteroclinic orbits, Lyapunov functions, manifolds, linearisation techniques and so on. Phase portraits and cobweb-staircase diagrams are produced using Matlab, the code for some of which are provided in an appendix at the end of this dissertation. There were some directions I wished to consider, but did not have the time nor scope: stochastic models, such as the Moran process [23] and Wright-Fisher model [15]; extensive form games, as covered in [6].

• Publisher: ProQuest Dissertations & Theses
• Subject: Games / Mathematics / Ordinary differential equations