06/06/2026, 16:19 Game Theory — ECON2291 Revision Guide
ECON2291 — ECONOMIC THEORY
Game Theory
Strategic games · extensive form · SPNE · mixed strategies · zero-sum games
Lectures 16–19 Normal Form Extensive Form SPNE Mixed Strategies Zero-Sum
IESDS Commitment
Contents
I What is a Game? II Normal-Form Games
III Dominant Strategies & Nash IV Classic Games
Equilibrium
V Maximin & Minimax Strategies VI Zero-Sum Games & Saddle Points
VII IESDS VIII Mixed Strategy Nash Equilibrium
IX Extensive Form Games X Subgame Perfect Nash Equilibrium
XI Commitment & Credibility XII Information Sets
XIII Past Paper Questions XIV Practice Questions
PART I
What is a Game?
Game theory is the formal study of strategic interaction — situations where the
outcome for any agent depends not only on their own choices but on the choices of
others. Unlike standard consumer or firm theory, where an individual optimises
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against prices taken as given, game theory requires each player to reason about the
rational behaviour of every other player at the same time. This mutual dependence
is what makes the subject both more demanding and more powerful.
The theory was formalised by von Neumann and Morgenstern (1944) and extended
by Nash (1950), whose equilibrium concept remains the central solution concept in
the field. Nash's contribution was to move beyond zero-sum games and establish
that a stable, self-enforcing outcome — one from which no player wishes to deviate
— always exists in finite games.
FORMAL DEFINITION — A STRATEGIC GAME
A strategic game G consists of three elements:
▸ Players: A finite set N = {1, 2, …, n} .
▸ Strategy sets: For each player i ∈ N , a set Si of available strategies. A
strategy profile is s = (s1, …, sn) where si ∈ Si .
▸ Payoff functions: For each player i , a function ui : S1 × … × Sn → ℝ .
The notation s-i refers to all players' strategies except player i 's, so
payoffs are written ui(si, s-i) .
STRATEGIC / NORMAL FORM EXTENSIVE FORM
Players choose strategies Players move sequentially,
simultaneously (or without potentially observing prior
observing others' choices). actions. Represented as a game
Represented as a payoff matrix. tree with nodes, branches, and
Time plays no role. Examples: information sets. Examples: Entry
Prisoner's Dilemma, Battle of the Game, Centipede Game, Battle of
Sexes. Sexes (sequential).
PART II
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Normal-Form Games
The normal form represents a two-player game as a matrix: rows correspond to
Player 1's strategies, columns to Player 2's, and each cell contains the payoff pair
(u1, u2) — row player first. Players are assumed to have ordinal utility: action A
is preferred to B if and only if the numerical payoff of A exceeds that of B.
Left Right
Top 1, 2 0, 0
Player 1
Bottom 0, 0 2, 1
In cell (Top, Left), Player 1 receives 1 and Player 2 receives 2. The assumption of
common knowledge of rationality is critical: each player knows the other is
rational, knows the other knows this, and so on. Payoffs can encode any motivation
— profit, altruism, spite — but players maximise whatever those payoffs represent.
PART III
Dominant Strategies and Nash Equilibrium
DEFINITION — STRICTLY DOMINANT STRATEGY
Strategy si* is strictly dominant for player i if:
ui(si*, s-i) > ui(si, s-i) for all si ≠ si*, all s-i
A strictly dominant strategy is the unique best response regardless of what
opponents do. A rational player always plays it if one exists.
DEFINITION — STRICTLY DOMINATED STRATEGY
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ECON2291 — ECONOMIC THEORY
Game Theory
Strategic games · extensive form · SPNE · mixed strategies · zero-sum games
Lectures 16–19 Normal Form Extensive Form SPNE Mixed Strategies Zero-Sum
IESDS Commitment
Contents
I What is a Game? II Normal-Form Games
III Dominant Strategies & Nash IV Classic Games
Equilibrium
V Maximin & Minimax Strategies VI Zero-Sum Games & Saddle Points
VII IESDS VIII Mixed Strategy Nash Equilibrium
IX Extensive Form Games X Subgame Perfect Nash Equilibrium
XI Commitment & Credibility XII Information Sets
XIII Past Paper Questions XIV Practice Questions
PART I
What is a Game?
Game theory is the formal study of strategic interaction — situations where the
outcome for any agent depends not only on their own choices but on the choices of
others. Unlike standard consumer or firm theory, where an individual optimises
file:///C:/Users/tyala/Downloads/game_theory_revision_guide (2).html#p14 1/30
,06/06/2026, 16:19 Game Theory — ECON2291 Revision Guide
against prices taken as given, game theory requires each player to reason about the
rational behaviour of every other player at the same time. This mutual dependence
is what makes the subject both more demanding and more powerful.
The theory was formalised by von Neumann and Morgenstern (1944) and extended
by Nash (1950), whose equilibrium concept remains the central solution concept in
the field. Nash's contribution was to move beyond zero-sum games and establish
that a stable, self-enforcing outcome — one from which no player wishes to deviate
— always exists in finite games.
FORMAL DEFINITION — A STRATEGIC GAME
A strategic game G consists of three elements:
▸ Players: A finite set N = {1, 2, …, n} .
▸ Strategy sets: For each player i ∈ N , a set Si of available strategies. A
strategy profile is s = (s1, …, sn) where si ∈ Si .
▸ Payoff functions: For each player i , a function ui : S1 × … × Sn → ℝ .
The notation s-i refers to all players' strategies except player i 's, so
payoffs are written ui(si, s-i) .
STRATEGIC / NORMAL FORM EXTENSIVE FORM
Players choose strategies Players move sequentially,
simultaneously (or without potentially observing prior
observing others' choices). actions. Represented as a game
Represented as a payoff matrix. tree with nodes, branches, and
Time plays no role. Examples: information sets. Examples: Entry
Prisoner's Dilemma, Battle of the Game, Centipede Game, Battle of
Sexes. Sexes (sequential).
PART II
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, 06/06/2026, 16:19 Game Theory — ECON2291 Revision Guide
Normal-Form Games
The normal form represents a two-player game as a matrix: rows correspond to
Player 1's strategies, columns to Player 2's, and each cell contains the payoff pair
(u1, u2) — row player first. Players are assumed to have ordinal utility: action A
is preferred to B if and only if the numerical payoff of A exceeds that of B.
Left Right
Top 1, 2 0, 0
Player 1
Bottom 0, 0 2, 1
In cell (Top, Left), Player 1 receives 1 and Player 2 receives 2. The assumption of
common knowledge of rationality is critical: each player knows the other is
rational, knows the other knows this, and so on. Payoffs can encode any motivation
— profit, altruism, spite — but players maximise whatever those payoffs represent.
PART III
Dominant Strategies and Nash Equilibrium
DEFINITION — STRICTLY DOMINANT STRATEGY
Strategy si* is strictly dominant for player i if:
ui(si*, s-i) > ui(si, s-i) for all si ≠ si*, all s-i
A strictly dominant strategy is the unique best response regardless of what
opponents do. A rational player always plays it if one exists.
DEFINITION — STRICTLY DOMINATED STRATEGY
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