• Content map: SMU H3 Game Theory Map

Chapter 2: General Principles

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.