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.
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 learnt algorithm design & analysis, optimization, dynamical systems, machine learning or microeconomics.