- Content map: SMU H3 Game Theory Map
Chapter 1: Introduction
What is Game Theory?
Definition:
Game theory studies strategic decision-making: each player’s outcome depends on their own action and on the actions of others.
- A situation is strategic when the best action depends on how other players behave.
- The aim is to model these interdependencies and predict the resulting behaviour.
- Applications appear in economics and in everyday coordination, competition, and bargaining problems.
Insight:
Most strategic problems are forecasting problems: players must guess what others are trying to guess.
Ingredients of a Game
- Players: the decision-makers.
- Strategies: the available actions or complete plans of action.
- Information: what each player knows, including the sequence of moves.
- Payoffs: how outcomes are ranked from each player’s perspective.
Insight:
Changing any ingredient changes the strategic problem, so modelling comes before solving.
Classification of Games
- Timing: simultaneous-move games (players do not observe others’ choices when acting) versus sequential games (players move in turn).
- Payoff structure: zero-sum games (one player’s gain is the other’s loss) versus non-zero-sum games (players may jointly do better).
- Information: complete-information games (players know the ingredients of the game) versus incomplete-information games (some ingredients are unknown).
Insight:
Classification matters because it determines both the representation of the game and the right solution method.
Rationality
Definition:
Players are rational if they aim to get the best outcome available to them, as defined by their payoff function, and can work out how to do so.
- Rationality means payoff maximisation within the model.
- It does not require selfishness: altruistic motives can be part of payoffs.
- Different players may have different payoff functions.
- In complex games, experience and learning help players identify good plans of action.
Common Knowledge
Definition:
A fact is common knowledge if everyone knows it, everyone knows that everyone knows it, and so on indefinitely.
- Strategic analysis often assumes common knowledge of the game’s ingredients.
- It also often assumes common knowledge of players’ rationality.
- This is stronger than “everyone knows” because higher-order reasoning matters.
Insight:
Coordination can fail even when players share the same information if that information is not common knowledge.
Equilibrium
Definition:
An equilibrium is a strategy profile in which each player is doing the best they can given what the others are doing.
- Games with rational players and common knowledge are analysed through an equilibrium concept.
- In equilibrium, no player can improve by changing strategy alone.
- Equilibrium is therefore stable and self-enforcing.
Result:
Equilibrium captures strategic stability: no player wants to deviate unilaterally.
Backward Induction
Definition:
Backward induction solves a finite sequential game by solving the last decision first and then working back to the initial move.
- Start from the final decision and identify the optimal action there.
- Replace that continuation by its implied outcome.
- Repeat until the first move is solved.
- In sequential games, later incentives shape earlier choices.
Insight:
Backward induction turns a dynamic problem into a chain of optimal continuation choices.