I’m Daniel Cownden a PhD student here at Queen’s doing my thesis on evolutionary game theory. This is the math 339 coursepage, if you’re looking for my website it’s here. I’m glad you are taking this course. Hopefully through it you will come to know a collection of beautiful ideas commonly referred to as evolutionary game theory. I have plans centered around the assignments and final project which I hope will make this course not just about mathematical theory but also about how to see that theory embedded in the world. Also some of the assignments are just going to be straight up fun.
Each number is roughly a week of lectures
1 Introduction to game theory, what is a game, how do you write a game down, and what is a Nash Equilibrium
2 Equivalent and Dominated Strategies
3 Pareto optimality, continuous strategies, and games where nature moves
4 Mixed Strategies
5 Sub-games and bargaining games
6 Evolutionary games and evolutionary stable strategies (ESS)
7 Crash course in dynamical system
8 Replicator dynamics relating ESS to dynamical systems
Story the Topics Tell
Games are useful models!
The Nash equilibrium predicts behaviour!
but only sometimes…
under potentially unreasonable assumptions.
We can make different possibly more reasonable assumptions in an evolutionary setting.
Evolution and Game Theory a match made in heaven!
Currently most game theory texts are deeply embedded in an economic framework. While many of these texts are good I don’t find them suitable for an undergraduate math course. To that end we will be working with some notes that the previous instructors of the course and I have developed over the past few years. They will be available for free download from this website. So in short you don’t need to worry about a text book.