Game Theory – Mathematical Analysis and Engineering Applications
Introduction to game theory, mathematical tools including convex optimisation and fixed point theory relevant for analyzing games, zero sum games, pure and mixed strategies, minimax theorem, nonzero sum games, Nash and Stackelberg equilibria, potential games, convex games, Bayesian games, analytic and numerical computation of equilibrium strategies. The focus of the course is on mathematical formulations and analysis of games. The theory will be motivated through real-world examples of multi-agent decision making in engineering problems.
The students passing the course will master formulating mathematically multi-agent decision-making problems arising in engineering applications as games, analyze using mathematical theory the equilibria of the games and compute them using optimization theory, analyze mathematically the outcome of the game.
Online lectures open to registered UBC students (through Canvas Collaborate Ultra or Zoom – I will finalize as I am in coordination with CTLT on use of canvas with ipad)
In-class quizzes, take-home exam/project.
The slides of the lecture notes will be available online. Furthermore, the following freely available books can be used as additional resources:
An Introductory Course in Noncooperative Game Theory (Joao P. Hespanha)
Dynamic Noncooperative Game Theory: Second Edition (Tamer Basar and Geert Jan Olsder)
Convex optimization (Stephen Boyd and Lieven Vandenberghe)