Managerial economics
Kobe Van Den Ouweland
March 2026
1 Game Theory and competition
1.1 Game theory in managerial economics
= mathematical tool used to represent strategic interactions → study interactions
Strategic interactions: players keep other player’s decisions in mind
→ predict outcomes when players have conflicting goals
Outcomes: dependent on the interactions of the decision-makers
Represent by payoff: ranking of outcomes by most to least preferred
→ strategies: actions to achieve a goal
→ outcome
Assumptions:
• Individual rationality: rational preferences over the outcomes
= every player kan rank the possible outcomes based on preferences
• Payoff-maximizing: players choose strategies to achieve their highest possible payoff
(̸= selfish: preferences can be in favour for someone else)
(companies often choose to maximize profits)
1.1.1 3 main categories of games:
2 axes:
• Horizontal: information = all players know the actions and consequences of every other player
(̸= certainty)
• Vertical: static:
– One-shot game
– Simultaneous choice: no certainty about the other’s choice
1
, Complete / perfect information Asymmetric information
Static Strategic games Bayesian games
Dynamic Extensive games Sequential (Bayesian) games
1. Strategic games:
• Set of players
• Set of actions for each player
• Payoff function (for every combination of actions for each player)
To structure: payoff-matrix (if only 2 players)
• Row-player: payoff is the first number in each cell
• Column-player: payoff is the second number in each cell
Each cell is an action profile → payoff in the cell Same payoff? → indifference
Findig an equilibrium: considering every posible action of the other player
→ what would you react?
→ eliminate dominated strategies (= strategies you never choose)
(a strategy is strictly dominant if you would always choose that strategie)
Repeat for the other play
⇒ Equilibrium in dominant strategies
• Pros: only possible outcome = reliable prediction
• Cons: too restrictive
⇒ Nash Equilibrium: more general
= an action profile so that none of the players strictly increase their payoff by choosing a different strategy,
taking the other player’s strategies for given
(no player can benefit by unilaterally deviating)
= best response on the choice of other players
(resting point, nothing optimal about an NE)
2. Extensive games:
Several decisions are made in the same game
→ reactions
2
, • Set of players
• Set of histories: ”states” of the game
– Terminal: game ends if they are reached
– Non-terminal
• Play function: what player acts in each non-terminal history
• Players payoffs: for each terminal function
To structure: extensive form
• Nodes: histories
• Terminal branches: terminal histories
Strategies: for each node a choice of one action
(e.g. Burger King is active in 1 history → strategies: Enter, NotEnter)
(e.g. McD is active after 2 histories → 4 strategies: Enter-NotEnter, Enter-Enter, NotEnter-Enter,
NotEnter-NotEnter)
Finding an equilibrium: backward induction
(a) Last decision node in each brand: best option for the acting players
(b) Taking the resulting outcome as given, go up a node
(c) Repeat
→ always an equilibrium: subgame-perfect Nash Equilibrium (SPNE)
• Always exists (in finite games)
• Unique (under weak conditions)
Nash equilibria that are not subgame perfect exist
→ ignore them: unlikely in reality
3
, 1.2 Demand and competition
Demand: for a given price → demand
→ Normal good: p↑ → q↓
→ Price elasticity: decrease of units sold for an increment in the price
→ Negative
∆q/q ∂q(p) p
ε= = ×
∆p/p ∂p q(p)
• |ε| < 1 : inelastisch → p↑ ⇒ revenues ↑
• |ε| > 1 : elastisch → p↑ ⇒ revenues ↓
Lineair demand: slope is constant
⇔ elasticity is not constant
Inverse market demand: price on y-axis: intersection = max willingness to pay
Perfect competition
Price elasticity = −∞: consumers can compare evere price → choose the lowest
= Single-agent problem: individual firm is too small to affect demand (→ no strategic interaction)
At a given (exogenous) market price → determine quantity (for profitmaximization)
max π(q) = p̄ · q − C(q)
∂C(q)
=⇒ 0 = p̄ −
∂q
⇐⇒ p̄ = C ′ (q)
Monopolie
Monopolist can set the price
= Single-agent problem
4
Kobe Van Den Ouweland
March 2026
1 Game Theory and competition
1.1 Game theory in managerial economics
= mathematical tool used to represent strategic interactions → study interactions
Strategic interactions: players keep other player’s decisions in mind
→ predict outcomes when players have conflicting goals
Outcomes: dependent on the interactions of the decision-makers
Represent by payoff: ranking of outcomes by most to least preferred
→ strategies: actions to achieve a goal
→ outcome
Assumptions:
• Individual rationality: rational preferences over the outcomes
= every player kan rank the possible outcomes based on preferences
• Payoff-maximizing: players choose strategies to achieve their highest possible payoff
(̸= selfish: preferences can be in favour for someone else)
(companies often choose to maximize profits)
1.1.1 3 main categories of games:
2 axes:
• Horizontal: information = all players know the actions and consequences of every other player
(̸= certainty)
• Vertical: static:
– One-shot game
– Simultaneous choice: no certainty about the other’s choice
1
, Complete / perfect information Asymmetric information
Static Strategic games Bayesian games
Dynamic Extensive games Sequential (Bayesian) games
1. Strategic games:
• Set of players
• Set of actions for each player
• Payoff function (for every combination of actions for each player)
To structure: payoff-matrix (if only 2 players)
• Row-player: payoff is the first number in each cell
• Column-player: payoff is the second number in each cell
Each cell is an action profile → payoff in the cell Same payoff? → indifference
Findig an equilibrium: considering every posible action of the other player
→ what would you react?
→ eliminate dominated strategies (= strategies you never choose)
(a strategy is strictly dominant if you would always choose that strategie)
Repeat for the other play
⇒ Equilibrium in dominant strategies
• Pros: only possible outcome = reliable prediction
• Cons: too restrictive
⇒ Nash Equilibrium: more general
= an action profile so that none of the players strictly increase their payoff by choosing a different strategy,
taking the other player’s strategies for given
(no player can benefit by unilaterally deviating)
= best response on the choice of other players
(resting point, nothing optimal about an NE)
2. Extensive games:
Several decisions are made in the same game
→ reactions
2
, • Set of players
• Set of histories: ”states” of the game
– Terminal: game ends if they are reached
– Non-terminal
• Play function: what player acts in each non-terminal history
• Players payoffs: for each terminal function
To structure: extensive form
• Nodes: histories
• Terminal branches: terminal histories
Strategies: for each node a choice of one action
(e.g. Burger King is active in 1 history → strategies: Enter, NotEnter)
(e.g. McD is active after 2 histories → 4 strategies: Enter-NotEnter, Enter-Enter, NotEnter-Enter,
NotEnter-NotEnter)
Finding an equilibrium: backward induction
(a) Last decision node in each brand: best option for the acting players
(b) Taking the resulting outcome as given, go up a node
(c) Repeat
→ always an equilibrium: subgame-perfect Nash Equilibrium (SPNE)
• Always exists (in finite games)
• Unique (under weak conditions)
Nash equilibria that are not subgame perfect exist
→ ignore them: unlikely in reality
3
, 1.2 Demand and competition
Demand: for a given price → demand
→ Normal good: p↑ → q↓
→ Price elasticity: decrease of units sold for an increment in the price
→ Negative
∆q/q ∂q(p) p
ε= = ×
∆p/p ∂p q(p)
• |ε| < 1 : inelastisch → p↑ ⇒ revenues ↑
• |ε| > 1 : elastisch → p↑ ⇒ revenues ↓
Lineair demand: slope is constant
⇔ elasticity is not constant
Inverse market demand: price on y-axis: intersection = max willingness to pay
Perfect competition
Price elasticity = −∞: consumers can compare evere price → choose the lowest
= Single-agent problem: individual firm is too small to affect demand (→ no strategic interaction)
At a given (exogenous) market price → determine quantity (for profitmaximization)
max π(q) = p̄ · q − C(q)
∂C(q)
=⇒ 0 = p̄ −
∂q
⇐⇒ p̄ = C ′ (q)
Monopolie
Monopolist can set the price
= Single-agent problem
4
