Game Theory
Lecture Notes — A Study Companion
Preface
\[ \newcommand{\E}{\mathbb{E}} \newcommand{\R}{\mathbb{R}} \newcommand{\Prob}{\mathbb{P}} \newcommand{\BR}{\operatorname{BR}} \newcommand{\eps}{\varepsilon} \newcommand{\given}{\,\vert\,} \newcommand{\argmax}{\operatorname*{arg\,max}} \newcommand{\argmin}{\operatorname*{arg\,min}} \newcommand{\sm}{\setminus} \newcommand{\defeq}{\equiv} \]
These are comprehensive study notes for an undergraduate course in game theory. They follow the structure and content of the five lecture handouts by Ju Hu (National School of Development, Peking University, Fall 2024), reorganised into continuous prose with full definitions, the central proofs, and worked examples.
The slides are terse by design; these notes aim to be self-contained reading material. Where the slides state a result and leave the argument implicit, the notes supply the reasoning. Where the slides show a payoff matrix or a game tree, the notes redraw it and walk through how it is solved.
How the book is organised
The five chapters mirror the four-way classification that organises the whole subject — whether information is complete or incomplete, and whether moves are static (simultaneous) or dynamic (sequential) — preceded by an introduction.
| Chapter | Topic | Central solution concept |
|---|---|---|
| 1 Introduction | Introduction: strategic interaction & expected utility | — |
| 2 Static Games with Complete Information | Static games, complete information | Nash equilibrium |
| 3 Dynamic Games with Complete Information | Dynamic games, complete information | Subgame-perfect equilibrium |
| 4 Static Games with Incomplete Information | Static games, incomplete information | Bayesian Nash equilibrium |
| 5 Dynamic Games with Incomplete Information | Dynamic games, incomplete information | Perfect Bayesian equilibrium |
Each new solution concept is a refinement prompted by a weakness of the previous one: Nash equilibrium permits non-credible threats in dynamic games, which subgame perfection removes; incomplete information forces beliefs into the model, which Bayesian equilibrium and then perfect Bayesian equilibrium handle.
Conventions
- Numbering. Definitions, theorems, propositions and lemmas are numbered by chapter, matching the lecture handouts (e.g. Definition 2.8 is “Definition 2.8”).
- Players. We write \(i\) for a generic player and \(-i\) for “everyone except \(i\)”. A strategy profile is \(s=(s_i, s_{-i})\).
- Payoffs in matrices. In a bimatrix, the row player is player 1 and the column player is player 2; a cell reads \((\text{payoff to 1}, \text{payoff to 2})\).
- Game trees are drawn with player labels at decision nodes, actions on the branches, and payoff vectors at the terminal nodes.
These notes are a derivative study aid. All credit for the course material and its exposition belongs to the original lecturer; any errors introduced in re-expressing it are the note-taker’s.