DOT96a
Managerial Economics
By Leonard Treuren
Bachelor of TEW & ERB – Second Year
2024 – 2025
,Lecture 1: Game theory and competition
Game Theory: Fundamentals
= mathematical tool used to represent strategic interactions in a treatable way
“Games” → stylized representation of agents’ goals, information and capabilities
- Predict outcomes (players with conflicting goals)
- Understand factors that gives some players an advantage
- Identify problems that hinder good outcomes (and avoid them)
Real life:
Decision-makers have goals/preferences about outcomes of their interactions
Preferences like revenues, market value give a certain payoff
In a game:
Preferences can be ranked (have a numerical value = payroll) → high numerical value = outcome more
preferred
Strategies = actions that agents can chose to achieve their goals
- Action: setting different prices, time you study for a course
- Strategy: studying a lot/ almost nothing for a course
Outcome of a game = result of all player’s strategies
Agents (players) are individually rational:
1. They have rational preferences (over the outcomes)
Preference between options, liking one more than the other (all else equal)
2. They are payoff-maximizing (=/= selfish)
Goal in the long run: maximizing profits → “you want to get things that you like more”
e.g. if you have a love for charity, when maximalizing you don’t get the money
or for some companies is maximalizing the goals: largen the consumer basis
• Not always about the making “the most” money
3 main categories of games:
➢ Strategic games
➢ Extensive games
➢ Sequential and Bayesian games
1
,Strategic games
- Static: one-shot (1 interaction) and simultaneous choice (players choose strategy without knowing
the strategy of the others)
o In reality: price setting – companies are looking at each other
- Complete or perfect information: all players know the actions/ consequences (not the decision of
other players)
Complete information ≠ certainty:
Games involve measurable risk → risk under uncertainty (e.g. you don’t know the exact price of stock
tomorrow)
Asymmetric information (some players know things others don’t) → auction off building of a bridge to
different companies
Complete/Perfect information Asymmetric information
Static Strategic games Bayesian games
Rock – Paper – Scissors Sealed-Bid Auction
Dynamic Extensive games, repeated Sequential (Bayesian) games e.g. best out of 5
games Poker
Chess, Monopoly
→ One company enters a market; the other waits to see
the outcome of the other one before entering himself
Strategic games: abstract form
- Set of players: P = {Player1, Player2}
- Set of actions: AP1 = {Defect, Cooperate}, AP2 = {Defect, Cooperate}
- Players’ payoff functions
Normal (payoff-matrix) form
- Rows = the row-player’s actions
- Columns = the column-player’s actions
- Each cel = action profile → within always the payoff
(preference for an outcome, action profiles = cause)
2
, Finding an equilibrium:
Elimination of dominated strategies
P2: X → P1: D
P2: Y → P1: D
P2: T → P1: C
o There is not one strategy that is always the best
o Regardless of what P2 does: if P1 plays D you will always have a better outcome than if you play H
o D strictly dominates H
o A rational player would never play H → We eliminate action H
P1: D → P2: X
P1: C → P2: X
o X strictly dominates (eliminate Y &T)
o P2 has a strategy that will always give you the best outcome
(one’s H is eliminated)
P2: X → P1: D
(D, X) = equilibrium in dominant strategies
+ Only possible outcome, very predictable
- Too restrictive (most games don’t have one)
More general equilibrium: Nash Equilibrium
= an action profile such that each player’s strategy maximizes that player’s payoff conditional on the other
players’ strategies.
- No players can benefit by unilaterally deviating (changing their decision alone)
- NE has a resting point and has nothing optimal about it
- When several players move at the same time → often better off
- Each player is playing their best response to the other players’ strategies (doing what’s optimal)
o In a NE, each player achieves the highest possible payoff False
o An equilibrium in dominant strategies is also always a NE True
o Players can never choose a strictly dominated strategy in a NE True
o In a NE, the sum of players’ payoffs is higher than in any other combination of strategies False (vb. 1)
o A strategic game with 2 players always has at least one NE in pure strategies False (vb.2)
o If a NE exists, then it is unique False (vb. 3)
3
Managerial Economics
By Leonard Treuren
Bachelor of TEW & ERB – Second Year
2024 – 2025
,Lecture 1: Game theory and competition
Game Theory: Fundamentals
= mathematical tool used to represent strategic interactions in a treatable way
“Games” → stylized representation of agents’ goals, information and capabilities
- Predict outcomes (players with conflicting goals)
- Understand factors that gives some players an advantage
- Identify problems that hinder good outcomes (and avoid them)
Real life:
Decision-makers have goals/preferences about outcomes of their interactions
Preferences like revenues, market value give a certain payoff
In a game:
Preferences can be ranked (have a numerical value = payroll) → high numerical value = outcome more
preferred
Strategies = actions that agents can chose to achieve their goals
- Action: setting different prices, time you study for a course
- Strategy: studying a lot/ almost nothing for a course
Outcome of a game = result of all player’s strategies
Agents (players) are individually rational:
1. They have rational preferences (over the outcomes)
Preference between options, liking one more than the other (all else equal)
2. They are payoff-maximizing (=/= selfish)
Goal in the long run: maximizing profits → “you want to get things that you like more”
e.g. if you have a love for charity, when maximalizing you don’t get the money
or for some companies is maximalizing the goals: largen the consumer basis
• Not always about the making “the most” money
3 main categories of games:
➢ Strategic games
➢ Extensive games
➢ Sequential and Bayesian games
1
,Strategic games
- Static: one-shot (1 interaction) and simultaneous choice (players choose strategy without knowing
the strategy of the others)
o In reality: price setting – companies are looking at each other
- Complete or perfect information: all players know the actions/ consequences (not the decision of
other players)
Complete information ≠ certainty:
Games involve measurable risk → risk under uncertainty (e.g. you don’t know the exact price of stock
tomorrow)
Asymmetric information (some players know things others don’t) → auction off building of a bridge to
different companies
Complete/Perfect information Asymmetric information
Static Strategic games Bayesian games
Rock – Paper – Scissors Sealed-Bid Auction
Dynamic Extensive games, repeated Sequential (Bayesian) games e.g. best out of 5
games Poker
Chess, Monopoly
→ One company enters a market; the other waits to see
the outcome of the other one before entering himself
Strategic games: abstract form
- Set of players: P = {Player1, Player2}
- Set of actions: AP1 = {Defect, Cooperate}, AP2 = {Defect, Cooperate}
- Players’ payoff functions
Normal (payoff-matrix) form
- Rows = the row-player’s actions
- Columns = the column-player’s actions
- Each cel = action profile → within always the payoff
(preference for an outcome, action profiles = cause)
2
, Finding an equilibrium:
Elimination of dominated strategies
P2: X → P1: D
P2: Y → P1: D
P2: T → P1: C
o There is not one strategy that is always the best
o Regardless of what P2 does: if P1 plays D you will always have a better outcome than if you play H
o D strictly dominates H
o A rational player would never play H → We eliminate action H
P1: D → P2: X
P1: C → P2: X
o X strictly dominates (eliminate Y &T)
o P2 has a strategy that will always give you the best outcome
(one’s H is eliminated)
P2: X → P1: D
(D, X) = equilibrium in dominant strategies
+ Only possible outcome, very predictable
- Too restrictive (most games don’t have one)
More general equilibrium: Nash Equilibrium
= an action profile such that each player’s strategy maximizes that player’s payoff conditional on the other
players’ strategies.
- No players can benefit by unilaterally deviating (changing their decision alone)
- NE has a resting point and has nothing optimal about it
- When several players move at the same time → often better off
- Each player is playing their best response to the other players’ strategies (doing what’s optimal)
o In a NE, each player achieves the highest possible payoff False
o An equilibrium in dominant strategies is also always a NE True
o Players can never choose a strictly dominated strategy in a NE True
o In a NE, the sum of players’ payoffs is higher than in any other combination of strategies False (vb. 1)
o A strategic game with 2 players always has at least one NE in pure strategies False (vb.2)
o If a NE exists, then it is unique False (vb. 3)
3
