Prerequisite: While I have put effort into making the lectures more accessible to students with diverse backgrounds, mathematical knowledge in the following subjects is deemed necessary:
Set Theory: familiar with notations like \(a\in A\), \(A \subset B\), \(A\cup B\), \(A\cap B\), "for all", "there exists"
Linear Algebra: arithmetics of vectors and matrices like computing \(\vec{y}^\textsf{T} \mathbf{A} \vec{x} \), solving linear systems \(\mathbf{A} \vec{x} = \vec{b}\)
Calculus: partial derivatives \(\frac{\partial f}{\partial x_i}\), integration \(\int_a^b f(x)\,\mathsf{d}x\), first & second order conditions for unconstrained optimization, method of Lagrange multipliers
Probability: expected values of discrete and continuous probability distribution
Analysis and \(\mathbb{R}^n\) topology: limit of sequence \(\lim_{n\rightarrow\infty} a_n\), limit/accumulation points, convex/open/closed/compact sets, continuous/convex/concave functions
You will benefit more from this course if you have further completed courses in algorithm design & analysis, optimization, dynamical systems, machine learning or microeconomics.
Warning: I deliberately insert simple math notations/formulae above. If you do not know their meanings or you are uncomfortable with them, do not take this course.
Origin: Shortly after joining ANU, I had the opportunity to teach a summer course "Algorithmic Game Theory and Economics" at the AMSI Summer School 2024.
The summer school was four weeks long, so we could cover only a limited range of topics. The materials provided here are intended to be an expanded version of the summer course.
Format: Eventually, I will put some exercise problems by the end of each lecture note.
The problems are either "simple" or "challenging".
You should solve all "simple" problems before moving to the next lecture. However, for faster dissemination, I may not include exercise problems in the lecture notes initially.