Meri Delbroek
2023-2024
SAMENVATTING
MANAGERIAL
ECONOMICS
, 2023-2024: Meri Delbroek
Inhoud
Inhoud ................................................................................................................................................. 1
Summary: managerial economics ........................................................................................................... 6
Game theory: fundamentals ............................................................................................................... 6
Strategies and payoff ....................................................................................................................... 6
Individual rationality ........................................................................................................................ 6
Three main categories of games ..................................................................................................... 7
Strategic ........................................................................................................................................... 7
Demand, monopoly and competition ................................................................................................. 9
Market demand ............................................................................................................................... 9
Linear demand............................................................................................................................... 10
Perfect competition ....................................................................................................................... 10
Monopolist’s problem: price-setting ............................................................................................. 11
Imperfect competition: Bertrand duopoly .................................................................................... 11
Differentiated products ..................................................................................................................... 14
Price competition with differentiated products ............................................................................ 14
Demand for differentiated products.............................................................................................. 14
Cross price elastic of demand ........................................................................................................ 15
Bertrand Duopoly with differentiated goods................................................................................. 15
Key takeaway ................................................................................................................................. 16
Horizontal differentiation .................................................................................................................. 16
The Hotelling model ...................................................................................................................... 16
Extensive games ................................................................................................................................ 20
Illustrative example ....................................................................................................................... 20
Backwards induction and Equilibrium in extensive games............................................................ 21
Vertical differentiation ....................................................................................................................... 21
Model of vertical product differentiation ...................................................................................... 21
Vertical product differentiation: discussion................................................................................... 23
Horizontal and vertical product differentiation ............................................................................. 23
Multiproduct differentiation.............................................................................................................. 24
Hotelling monopolist ..................................................................................................................... 24
Monopolist with 1 product ............................................................................................................ 25
Monopolist with 2 products ......................................................................................................... 25
Multiproduct firm and location choice, n varieties ...................................................................... 26
How many products to produce .................................................................................................... 27
Product differentiation in general ..................................................................................................... 27
1
, 2023-2024: Meri Delbroek
Key takeaways................................................................................................................................ 27
Advertising......................................................................................................................................... 28
Introduction ................................................................................................................................... 28
Persuasive advertising ................................................................................................................... 28
Informative advertising ................................................................................................................. 28
Complementary advertising .......................................................................................................... 28
Informative advertising: example .................................................................................................. 29
Informative advertising: general ................................................................................................... 31
Persuasive advertising: models sketch .......................................................................................... 31
Complementary advertising: model sketch ................................................................................... 32
Entry deterrence................................................................................................................................ 33
Introduction ................................................................................................................................... 33
Predatory pricing ........................................................................................................................... 33
Game theory and the value of Commitment ................................................................................ 33
Predatory pricing: commitment to large production .................................................................... 33
Example ......................................................................................................................................... 34
Entry deterrence............................................................................................................................ 36
Product proliferation ..................................................................................................................... 36
Exclusionary practices: legality ...................................................................................................... 38
Exclusionary practices: landmark case .......................................................................................... 38
Repeated games ............................................................................................................................... 39
Categorization................................................................................................................................ 39
How to create a repeat game ........................................................................................................ 39
Present value and discounting....................................................................................................... 39
Compare investment projects ....................................................................................................... 40
Equilibrium in repeat games .......................................................................................................... 41
Collusion ............................................................................................................................................ 41
Finitely repeated Bertrand game................................................................................................... 41
Infinitely repeated Bertrand game ................................................................................................ 41
Critical discount rate ...................................................................................................................... 43
Bertrand duopoly example ............................................................................................................ 44
Other SPNE .................................................................................................................................... 44
The cartel prohibition in EU competition law, TFEU 101 ............................................................... 44
The Trucks cartel ............................................................................................................................ 44
Tacit collusion: price coordination absent explicit agreements .................................................... 45
Collusion: main idea ...................................................................................................................... 45
2
, 2023-2024: Meri Delbroek
Horizontal mergers ............................................................................................................................ 45
Examples of prolific mergers ......................................................................................................... 46
Mergers with homogeneous products .......................................................................................... 46
Mergers with differentiated products ........................................................................................... 47
Vertical mergers................................................................................................................................. 48
Vertical mergers............................................................................................................................. 48
Model of vertical mergers ............................................................................................................. 48
Vertical foreclosure........................................................................................................................ 51
Competition and innovation .............................................................................................................. 52
Incremental vs. drastic innovation ................................................................................................ 52
Two main innovative theories ....................................................................................................... 52
Innovation and competition: In the end, who was right? ............................................................. 54
Innovation and competition: Aghion et al. Inverted U .................................................................. 54
Investment spillovers ......................................................................................................................... 54
A model of process innovation ...................................................................................................... 54
Investment spillovers ..................................................................................................................... 56
A model of process innovation: the effects of R&D with spillovers .............................................. 57
A model of innovation: research joint ventures ............................................................................ 58
Intellectual property .......................................................................................................................... 59
Abridged history of the patent system .......................................................................................... 59
Patent requirements...................................................................................................................... 60
Simple model of patenting ............................................................................................................ 60
Static vs dynamic efficiency: each period’s payoff......................................................................... 60
Patents protection: the innovator problem................................................................................... 61
Patent protection: the regulator problem ..................................................................................... 61
Breadth and length of patents....................................................................................................... 61
How far are we from the optimum? .............................................................................................. 62
Cumulative innovation....................................................................................................................... 63
Patents, cumulative innovation and hold-up: a simple model ...................................................... 63
Patents and cumulative: empirical evidence ................................................................................. 64
Trends and current topics .................................................................................................................. 65
Patent paradox .............................................................................................................................. 65
Patent Litigation and “patent trolls” .............................................................................................. 65
Technological Standards and patent pools .................................................................................... 66
Key takeaways................................................................................................................................ 66
Bargaining theory .............................................................................................................................. 67
3
, 2023-2024: Meri Delbroek
Bargaining in general ..................................................................................................................... 67
Ultimatum game ............................................................................................................................ 67
Cooperative game theory: Nash Bargaining .................................................................................. 72
Bayesian Games................................................................................................................................. 74
Bayesian Games: categorization .................................................................................................... 74
Bayesian Games: abstract form (simplified) .................................................................................. 74
Bayesian Games: Simultaneous entry with Asymmetric Information ........................................... 75
Bayesian Nash equilibrium ............................................................................................................ 75
Auctions Theory................................................................................................................................. 75
Auctions in practice ....................................................................................................................... 75
Auctions: most common formats .................................................................................................. 76
Auctions: common rules ................................................................................................................ 76
Second price auction ..................................................................................................................... 76
Auctions: finding an equilibrium ................................................................................................... 77
Second price auction: Bidding under Asymmetric information .................................................... 77
Second price auction: Equilibrium ................................................................................................. 77
First price auction .......................................................................................................................... 78
First price auction: Solving the equilibrium ................................................................................... 78
All-Pay Auction............................................................................................................................... 79
Revenue Equivalence theorem ...................................................................................................... 79
Key takeaways................................................................................................................................ 79
Principal-Agent model ....................................................................................................................... 80
Principal-Agent models ................................................................................................................. 80
Principal-Agent taxonomy: Manager Decisions............................................................................. 80
Sequential Games .............................................................................................................................. 80
Sequential games: categorization .................................................................................................. 80
Sequential games – abstract form (simplified) .............................................................................. 81
Sequential Games: extensive form ................................................................................................ 81
Sequential Games: separating strategies ...................................................................................... 81
Sequential Games: extensive form ................................................................................................ 82
Bayesian perfect equilibrium (simplified)...................................................................................... 82
Signalling............................................................................................................................................ 82
Job-Market signalling (Spence, 1973)............................................................................................ 83
Spence signalling: costly signal for separation .............................................................................. 83
Spence signalling – Extensive form................................................................................................ 83
Spence signalling – Pooling equilibria D-D .................................................................................... 84
4
, 2023-2024: Meri Delbroek
Spence signalling – Pooling equilibria ND -ND .............................................................................. 84
Spence signalling – Separating equilibria ND-D............................................................................. 84
Spence signalling – Separating equilibria D-ND............................................................................. 85
Spence signalling – Separation: takeaways ................................................................................... 85
Adverse Selection .............................................................................................................................. 85
Principal-Agent: Adverse selection ................................................................................................ 85
Adverse selection: Credit rationing (Stiglitz and Weiss, 1981) ...................................................... 86
Credit rationing: risks and payoffs ................................................................................................. 86
Credit rationing: Adverse selection ............................................................................................... 86
Credit rationing: accounting for selection ..................................................................................... 87
Credit rationing: wrapping up........................................................................................................ 87
Adverse selection: “Market for lemons” (Akerlof, 1970)............................................................... 87
Moral hazard ..................................................................................................................................... 88
Principal-Agent: Moral hazard ....................................................................................................... 88
Moral hazard: Managerial compensation ..................................................................................... 89
Moral hazard: Remuneration schemes.......................................................................................... 89
Moral hazard: Risk neutral manager – Best response ................................................................... 90
Moral hazard: Concluding remarks................................................................................................ 91
Key takeaways................................................................................................................................ 91
Refresh Bayes rule ......................................................................................................................... 92
5
, 2023-2024: Meri Delbroek
Summary: managerial economics
Game theory: fundamentals
Game theory = mathematical tool to represent strategic interactions in a treatable way
- Games: a stylized representation of agents’ goals, information and capabilities
Goal:
- Predict the likely outcomes when multiple players have conflicting goals
- Understand what factors can give an edge to different players or affect the outcomes
(comparative static)
- Identify pitfalls that undermine desirable outcomes, and how to mitigate them (e.g.
opportunistic behaviour, asymmetric information)
Strategies and payoff
In real life: Decision-makers have goals/preferences about the outcome of their interactions.
- Example: “winning/losing elections”, “(not) getting a promotion", “quarterly revenues”
In a game: We represent these preferences assigning to outcomes a numerical value (payoff)
- We assign higher (lower) payoff, to outcomes that are more (less) preferred to them.
- Players might disagree on what outcome is the most desirable (gives them highest payoff)
- Strategies are actions or sequence of actions that agents can choose to achieve their goals.
- The outcome of a game is the result of all player’s strategies, and chance if the game involves
stochastic/random elements
Individual rationality
In game theory we assume that agents (players) are individually rational that is:
1. They have rational preferences (over the outcomes):
o Each player can rank outcomes from their most favourite to the least favourite.
(More precisely: we say that the “preference” relation defines a semi-order over
the set of possible outcomes.)
o This assumption is necessary in order to have a payoff representation.
2. They are payoff-maximizing:
o Players choose their strategies in order to achieve the highest payoff for
themselves.
o Note: this does not (necessarily) mean that players are selfish. A player might have
preferences(attribute high payoff) to a very equitable outcome.
6
, 2023-2024: Meri Delbroek
Three main categories of games
Strategic
1. Static
o
One-shot game: Players interact only once.
o
Simultaneous choice: Players choose their strategy without knowledge of the other
players’ choices
o Note: multiple choices might occur, but the outcome is observed only at the end.
2. Complete information
o All players know the capabilities (strategies available) of every other player.
o All players know the consequences (payoffs) of every combination of strategies
o Does NOT mean certainty
Games (and business) often involve quantifiable risk. If all the possible outcomes are known, and occur
with a known probability distribution we call this risk “uncertainty”.
Example: “If I buy a stock of Meta today, I don’t know the price it will have tomorrow, but I can
form expectations and quantify the likelihood of different price swings.”
However, sometimes agents a player might know something that other don’t. Then we say that players
have asymmetric information
Example: “Mark Zuckerberg secretly sets on fire the Meta headquarters and now he is short
selling Meta stocks. I know that he knows more than me, but I don’t know what he knows.”
Strategic games allow for uncertainty, but not asymmetric information.
Broad taxonomy of games
7
, 2023-2024: Meri Delbroek
Abstract form
A strategic game is fully described by:
1. Set of players
For example: P = {Player1, Player2}
2. Set of actions available for each player
For example: AP1 = {Defect, Cooperate}, AP2 = {Defect, Cooperate}
Remark: in strategic games “actions” and “strategies” coincide, since a strategy consists in a
single action.
3. Players’ payoff functions: a description of each player’s payoff for each combination of
actions
For example:
Very inconvenient! However, 2-players games, are usually represented in a much simpler and
parsimonious way through a payoff-matrix also known as their “normal form”.
Normal (payoff-matrix)
- Rows correspond to the row-player’s actions
In this case: AP1 = {D, C, H}
- Columns correspond to the column-player’s actions
In this case: AP2 = {X, Y , T}
- Each cell is an action profile i.e. a tuple of 1 action
per player
For example < C, X > is the action profile where P1
plays C and P2 plays X
- Within each cell, we find the payoffs associated with
each action profile
For example in < C, X > P1 receives -5 and P2 receives
+5
- Payoffs represent player’s preferences for a outcome,
while action profiles are its cause. Do not confuse them!
For example, < C, Y > and < H, T > have the same payoffs (3, 3),
so players are indifferent between the two outcomes.
Oefening dia 32
General equilibrium
An equilibrium in dominant strategy is a very strong notion, only relies on player’s rationality.
- Pros: (If players are rational) it is the only possible outcome. Very reliable prediction!
- Cons: Too restrictive. Most games don’t have one.
8
, 2023-2024: Meri Delbroek
Nash equilibrium
Definition:
- “A Nash Equilibrium (NE) is an action profile such that none of the players can increase their
payoff by choosing a different strategy, taking the other player’s strategies for given.”
- “A Nash Equilibrium (NE) is an action profile such that each player’s strategy maximizes that
player’s payoff conditional on the other player’s strategies.”
- In other words: it is an action profile such that no player can benefit from independently
deviating from it.
- Notice: it is a resting point (whence “equilibrium”), there is nothing (necessarily) “optimal”
about it.
- each player is playing their best-response to the other players’ strategies
Oefening dia 52
Statements:
- An equilibrium in dominant strategies is also always a NE.
- Players can never choose a strictly dominated strategy in a NE.
Demand, monopoly and competition
Market demand
Demand (function) tells us how many units of a product are purchased by consumers depending on
its price
- At price p1 consumers buy quantity q1
- The slope of the demand dq/dp tells us the decrease
(increase) of units sold for a small increment
(reduction) in the price. For normal goods, it is always
negative
- Not very useful for decisions!
If dq/dp = -1, it’s a very different story if q are candies or
$100 mil battleships
- Economists use price elasticity of demand ε(p)
∆q/q is the percentage change in q, and ∆p/p is the percentage change in p
- Always negative (for normal goods). Describes the ability/willingness
of consumers to substitute consumption with another good (or not
spend).
- |ε|= 1: if price reduces (increases) by 5%, then quantity increases
(reduces) by the same percentage amount
- |ε|< 1: Demand is inelastic =>Increasing price increases revenues
- |ε|> 1: Demand is elastic => Increasing price reduces revenues
9
2023-2024
SAMENVATTING
MANAGERIAL
ECONOMICS
, 2023-2024: Meri Delbroek
Inhoud
Inhoud ................................................................................................................................................. 1
Summary: managerial economics ........................................................................................................... 6
Game theory: fundamentals ............................................................................................................... 6
Strategies and payoff ....................................................................................................................... 6
Individual rationality ........................................................................................................................ 6
Three main categories of games ..................................................................................................... 7
Strategic ........................................................................................................................................... 7
Demand, monopoly and competition ................................................................................................. 9
Market demand ............................................................................................................................... 9
Linear demand............................................................................................................................... 10
Perfect competition ....................................................................................................................... 10
Monopolist’s problem: price-setting ............................................................................................. 11
Imperfect competition: Bertrand duopoly .................................................................................... 11
Differentiated products ..................................................................................................................... 14
Price competition with differentiated products ............................................................................ 14
Demand for differentiated products.............................................................................................. 14
Cross price elastic of demand ........................................................................................................ 15
Bertrand Duopoly with differentiated goods................................................................................. 15
Key takeaway ................................................................................................................................. 16
Horizontal differentiation .................................................................................................................. 16
The Hotelling model ...................................................................................................................... 16
Extensive games ................................................................................................................................ 20
Illustrative example ....................................................................................................................... 20
Backwards induction and Equilibrium in extensive games............................................................ 21
Vertical differentiation ....................................................................................................................... 21
Model of vertical product differentiation ...................................................................................... 21
Vertical product differentiation: discussion................................................................................... 23
Horizontal and vertical product differentiation ............................................................................. 23
Multiproduct differentiation.............................................................................................................. 24
Hotelling monopolist ..................................................................................................................... 24
Monopolist with 1 product ............................................................................................................ 25
Monopolist with 2 products ......................................................................................................... 25
Multiproduct firm and location choice, n varieties ...................................................................... 26
How many products to produce .................................................................................................... 27
Product differentiation in general ..................................................................................................... 27
1
, 2023-2024: Meri Delbroek
Key takeaways................................................................................................................................ 27
Advertising......................................................................................................................................... 28
Introduction ................................................................................................................................... 28
Persuasive advertising ................................................................................................................... 28
Informative advertising ................................................................................................................. 28
Complementary advertising .......................................................................................................... 28
Informative advertising: example .................................................................................................. 29
Informative advertising: general ................................................................................................... 31
Persuasive advertising: models sketch .......................................................................................... 31
Complementary advertising: model sketch ................................................................................... 32
Entry deterrence................................................................................................................................ 33
Introduction ................................................................................................................................... 33
Predatory pricing ........................................................................................................................... 33
Game theory and the value of Commitment ................................................................................ 33
Predatory pricing: commitment to large production .................................................................... 33
Example ......................................................................................................................................... 34
Entry deterrence............................................................................................................................ 36
Product proliferation ..................................................................................................................... 36
Exclusionary practices: legality ...................................................................................................... 38
Exclusionary practices: landmark case .......................................................................................... 38
Repeated games ............................................................................................................................... 39
Categorization................................................................................................................................ 39
How to create a repeat game ........................................................................................................ 39
Present value and discounting....................................................................................................... 39
Compare investment projects ....................................................................................................... 40
Equilibrium in repeat games .......................................................................................................... 41
Collusion ............................................................................................................................................ 41
Finitely repeated Bertrand game................................................................................................... 41
Infinitely repeated Bertrand game ................................................................................................ 41
Critical discount rate ...................................................................................................................... 43
Bertrand duopoly example ............................................................................................................ 44
Other SPNE .................................................................................................................................... 44
The cartel prohibition in EU competition law, TFEU 101 ............................................................... 44
The Trucks cartel ............................................................................................................................ 44
Tacit collusion: price coordination absent explicit agreements .................................................... 45
Collusion: main idea ...................................................................................................................... 45
2
, 2023-2024: Meri Delbroek
Horizontal mergers ............................................................................................................................ 45
Examples of prolific mergers ......................................................................................................... 46
Mergers with homogeneous products .......................................................................................... 46
Mergers with differentiated products ........................................................................................... 47
Vertical mergers................................................................................................................................. 48
Vertical mergers............................................................................................................................. 48
Model of vertical mergers ............................................................................................................. 48
Vertical foreclosure........................................................................................................................ 51
Competition and innovation .............................................................................................................. 52
Incremental vs. drastic innovation ................................................................................................ 52
Two main innovative theories ....................................................................................................... 52
Innovation and competition: In the end, who was right? ............................................................. 54
Innovation and competition: Aghion et al. Inverted U .................................................................. 54
Investment spillovers ......................................................................................................................... 54
A model of process innovation ...................................................................................................... 54
Investment spillovers ..................................................................................................................... 56
A model of process innovation: the effects of R&D with spillovers .............................................. 57
A model of innovation: research joint ventures ............................................................................ 58
Intellectual property .......................................................................................................................... 59
Abridged history of the patent system .......................................................................................... 59
Patent requirements...................................................................................................................... 60
Simple model of patenting ............................................................................................................ 60
Static vs dynamic efficiency: each period’s payoff......................................................................... 60
Patents protection: the innovator problem................................................................................... 61
Patent protection: the regulator problem ..................................................................................... 61
Breadth and length of patents....................................................................................................... 61
How far are we from the optimum? .............................................................................................. 62
Cumulative innovation....................................................................................................................... 63
Patents, cumulative innovation and hold-up: a simple model ...................................................... 63
Patents and cumulative: empirical evidence ................................................................................. 64
Trends and current topics .................................................................................................................. 65
Patent paradox .............................................................................................................................. 65
Patent Litigation and “patent trolls” .............................................................................................. 65
Technological Standards and patent pools .................................................................................... 66
Key takeaways................................................................................................................................ 66
Bargaining theory .............................................................................................................................. 67
3
, 2023-2024: Meri Delbroek
Bargaining in general ..................................................................................................................... 67
Ultimatum game ............................................................................................................................ 67
Cooperative game theory: Nash Bargaining .................................................................................. 72
Bayesian Games................................................................................................................................. 74
Bayesian Games: categorization .................................................................................................... 74
Bayesian Games: abstract form (simplified) .................................................................................. 74
Bayesian Games: Simultaneous entry with Asymmetric Information ........................................... 75
Bayesian Nash equilibrium ............................................................................................................ 75
Auctions Theory................................................................................................................................. 75
Auctions in practice ....................................................................................................................... 75
Auctions: most common formats .................................................................................................. 76
Auctions: common rules ................................................................................................................ 76
Second price auction ..................................................................................................................... 76
Auctions: finding an equilibrium ................................................................................................... 77
Second price auction: Bidding under Asymmetric information .................................................... 77
Second price auction: Equilibrium ................................................................................................. 77
First price auction .......................................................................................................................... 78
First price auction: Solving the equilibrium ................................................................................... 78
All-Pay Auction............................................................................................................................... 79
Revenue Equivalence theorem ...................................................................................................... 79
Key takeaways................................................................................................................................ 79
Principal-Agent model ....................................................................................................................... 80
Principal-Agent models ................................................................................................................. 80
Principal-Agent taxonomy: Manager Decisions............................................................................. 80
Sequential Games .............................................................................................................................. 80
Sequential games: categorization .................................................................................................. 80
Sequential games – abstract form (simplified) .............................................................................. 81
Sequential Games: extensive form ................................................................................................ 81
Sequential Games: separating strategies ...................................................................................... 81
Sequential Games: extensive form ................................................................................................ 82
Bayesian perfect equilibrium (simplified)...................................................................................... 82
Signalling............................................................................................................................................ 82
Job-Market signalling (Spence, 1973)............................................................................................ 83
Spence signalling: costly signal for separation .............................................................................. 83
Spence signalling – Extensive form................................................................................................ 83
Spence signalling – Pooling equilibria D-D .................................................................................... 84
4
, 2023-2024: Meri Delbroek
Spence signalling – Pooling equilibria ND -ND .............................................................................. 84
Spence signalling – Separating equilibria ND-D............................................................................. 84
Spence signalling – Separating equilibria D-ND............................................................................. 85
Spence signalling – Separation: takeaways ................................................................................... 85
Adverse Selection .............................................................................................................................. 85
Principal-Agent: Adverse selection ................................................................................................ 85
Adverse selection: Credit rationing (Stiglitz and Weiss, 1981) ...................................................... 86
Credit rationing: risks and payoffs ................................................................................................. 86
Credit rationing: Adverse selection ............................................................................................... 86
Credit rationing: accounting for selection ..................................................................................... 87
Credit rationing: wrapping up........................................................................................................ 87
Adverse selection: “Market for lemons” (Akerlof, 1970)............................................................... 87
Moral hazard ..................................................................................................................................... 88
Principal-Agent: Moral hazard ....................................................................................................... 88
Moral hazard: Managerial compensation ..................................................................................... 89
Moral hazard: Remuneration schemes.......................................................................................... 89
Moral hazard: Risk neutral manager – Best response ................................................................... 90
Moral hazard: Concluding remarks................................................................................................ 91
Key takeaways................................................................................................................................ 91
Refresh Bayes rule ......................................................................................................................... 92
5
, 2023-2024: Meri Delbroek
Summary: managerial economics
Game theory: fundamentals
Game theory = mathematical tool to represent strategic interactions in a treatable way
- Games: a stylized representation of agents’ goals, information and capabilities
Goal:
- Predict the likely outcomes when multiple players have conflicting goals
- Understand what factors can give an edge to different players or affect the outcomes
(comparative static)
- Identify pitfalls that undermine desirable outcomes, and how to mitigate them (e.g.
opportunistic behaviour, asymmetric information)
Strategies and payoff
In real life: Decision-makers have goals/preferences about the outcome of their interactions.
- Example: “winning/losing elections”, “(not) getting a promotion", “quarterly revenues”
In a game: We represent these preferences assigning to outcomes a numerical value (payoff)
- We assign higher (lower) payoff, to outcomes that are more (less) preferred to them.
- Players might disagree on what outcome is the most desirable (gives them highest payoff)
- Strategies are actions or sequence of actions that agents can choose to achieve their goals.
- The outcome of a game is the result of all player’s strategies, and chance if the game involves
stochastic/random elements
Individual rationality
In game theory we assume that agents (players) are individually rational that is:
1. They have rational preferences (over the outcomes):
o Each player can rank outcomes from their most favourite to the least favourite.
(More precisely: we say that the “preference” relation defines a semi-order over
the set of possible outcomes.)
o This assumption is necessary in order to have a payoff representation.
2. They are payoff-maximizing:
o Players choose their strategies in order to achieve the highest payoff for
themselves.
o Note: this does not (necessarily) mean that players are selfish. A player might have
preferences(attribute high payoff) to a very equitable outcome.
6
, 2023-2024: Meri Delbroek
Three main categories of games
Strategic
1. Static
o
One-shot game: Players interact only once.
o
Simultaneous choice: Players choose their strategy without knowledge of the other
players’ choices
o Note: multiple choices might occur, but the outcome is observed only at the end.
2. Complete information
o All players know the capabilities (strategies available) of every other player.
o All players know the consequences (payoffs) of every combination of strategies
o Does NOT mean certainty
Games (and business) often involve quantifiable risk. If all the possible outcomes are known, and occur
with a known probability distribution we call this risk “uncertainty”.
Example: “If I buy a stock of Meta today, I don’t know the price it will have tomorrow, but I can
form expectations and quantify the likelihood of different price swings.”
However, sometimes agents a player might know something that other don’t. Then we say that players
have asymmetric information
Example: “Mark Zuckerberg secretly sets on fire the Meta headquarters and now he is short
selling Meta stocks. I know that he knows more than me, but I don’t know what he knows.”
Strategic games allow for uncertainty, but not asymmetric information.
Broad taxonomy of games
7
, 2023-2024: Meri Delbroek
Abstract form
A strategic game is fully described by:
1. Set of players
For example: P = {Player1, Player2}
2. Set of actions available for each player
For example: AP1 = {Defect, Cooperate}, AP2 = {Defect, Cooperate}
Remark: in strategic games “actions” and “strategies” coincide, since a strategy consists in a
single action.
3. Players’ payoff functions: a description of each player’s payoff for each combination of
actions
For example:
Very inconvenient! However, 2-players games, are usually represented in a much simpler and
parsimonious way through a payoff-matrix also known as their “normal form”.
Normal (payoff-matrix)
- Rows correspond to the row-player’s actions
In this case: AP1 = {D, C, H}
- Columns correspond to the column-player’s actions
In this case: AP2 = {X, Y , T}
- Each cell is an action profile i.e. a tuple of 1 action
per player
For example < C, X > is the action profile where P1
plays C and P2 plays X
- Within each cell, we find the payoffs associated with
each action profile
For example in < C, X > P1 receives -5 and P2 receives
+5
- Payoffs represent player’s preferences for a outcome,
while action profiles are its cause. Do not confuse them!
For example, < C, Y > and < H, T > have the same payoffs (3, 3),
so players are indifferent between the two outcomes.
Oefening dia 32
General equilibrium
An equilibrium in dominant strategy is a very strong notion, only relies on player’s rationality.
- Pros: (If players are rational) it is the only possible outcome. Very reliable prediction!
- Cons: Too restrictive. Most games don’t have one.
8
, 2023-2024: Meri Delbroek
Nash equilibrium
Definition:
- “A Nash Equilibrium (NE) is an action profile such that none of the players can increase their
payoff by choosing a different strategy, taking the other player’s strategies for given.”
- “A Nash Equilibrium (NE) is an action profile such that each player’s strategy maximizes that
player’s payoff conditional on the other player’s strategies.”
- In other words: it is an action profile such that no player can benefit from independently
deviating from it.
- Notice: it is a resting point (whence “equilibrium”), there is nothing (necessarily) “optimal”
about it.
- each player is playing their best-response to the other players’ strategies
Oefening dia 52
Statements:
- An equilibrium in dominant strategies is also always a NE.
- Players can never choose a strictly dominated strategy in a NE.
Demand, monopoly and competition
Market demand
Demand (function) tells us how many units of a product are purchased by consumers depending on
its price
- At price p1 consumers buy quantity q1
- The slope of the demand dq/dp tells us the decrease
(increase) of units sold for a small increment
(reduction) in the price. For normal goods, it is always
negative
- Not very useful for decisions!
If dq/dp = -1, it’s a very different story if q are candies or
$100 mil battleships
- Economists use price elasticity of demand ε(p)
∆q/q is the percentage change in q, and ∆p/p is the percentage change in p
- Always negative (for normal goods). Describes the ability/willingness
of consumers to substitute consumption with another good (or not
spend).
- |ε|= 1: if price reduces (increases) by 5%, then quantity increases
(reduces) by the same percentage amount
- |ε|< 1: Demand is inelastic =>Increasing price increases revenues
- |ε|> 1: Demand is elastic => Increasing price reduces revenues
9
