Games as Graphs - A New Approach to Game Theory

Explore the foundations of game theory through a graph-based approach in this 46-minute seminar by Iman Shames from The Australian National University. Examine a new model of games defined by players' preference orders, introducing the concept of 'response graphs'. Discover how this innovative perspective offers fresh insights into game theory and its evolutionary aspects. Delve into topics such as utility foundations, pure and mixed Nash equilibria, and the application to Evolutionary Game Theory. Learn about the Replicator Dynamic, chain components, and attractors of the Replicator. Gain a deeper understanding of long-run outcomes in game theory and explore when content becomes a sink chain component.

Intro
Overview
Modelling: a Goldilocks problem
A (very) brief history of game theory
Two simple games
Utilities
Pure and mixed Nash equilibria
Another piece of history...and an inspiration
A new way of thinking
Special cases of two-player game
Check point: Summary
Application to Evolutionary Game Theory
Replicator Dynamic
What does a long-run outcome look like?
The main concepts
Chain Components
Attractors of the Replicator
When is the content a sink chain component?