Digression 9

Question 1

A tale about the importance of common knowledge:
Why does the anouncement of the outsider make a difference?

Answer 1

Before his anouncement, each islander knew that there are blue-eyed persons on the island, but she did not know that the other islander knew it as well, knew that she knows it etc.
==> Thus, the knowledge that there are blue-eyed islanders was not common knowledge. This changed with the anouncement by the outsider. From that moment on, the existence of blue-eyed persons became common knowledge.

Question 2

A tale about the importance of common knowledge:
Why does the fact that they have this common knowledge now make a difference?

Answer 2

To see this, one can use an inductive argument. If there is exactly one person with blue eyes, that person knows that there is no other person with blue eyes on the island. Before the anouncement of the outsider, it was a possibility that there is no one with blue eyes on the island, so there was no need to leave. However, given the information by the outsider, the blue-eyed person learns that she must have blue eyes, so she leaves at night one.

Question 3

A tale about the importance of common knowledge:
What does this want to tell us?

Answer 3

induction states that no one will leave during the first n−1 nights. However, given that everyone is still around after night n−1, each blue-eyed person has to conclude that there are n persons with blue eyes in total, one of them being him- or herself.
Thus, the rather innocuous-sounding announcement by the outsider allows the islanders to eventually figure out the color of their eyes.

Question 4

Existence of a Nash Equilibrium:
What is a pure strategy?

Answer 4

A pure strategy is a specific, deterministic choice of action that a player makes in a game. Unlike a mixed strategy, which involves randomizing among actions, a pure strategy selects one particular action without any randomness.

For example, in Rock-Paper-Scissors, a pure strategy would be choosing “Rock” every time

Question 5

Existence of a Nash Equilibrium:
Can a game have no Nash equilibrium? Provide an example.

Answer 5

Yes, a game can have no Nash equilibrium in pure strategies. An example is Rock-Paper-Scissors (RPS).

Question 6

Existence of a Nash Equilibrium:
Why does RPS have no Nash equilibrium in pure strategies?

Answer 6

In RPS, whenever a player chooses a best response, the opponent’s payoff can be improved by switching strategies, so no stable strategy profile exists.

Question 7

Existence of a Nash Equilibrium:
What is a mixed strategy?

Answer 7

A mixed strategy is a probability distribution over pure strategies, where each strategy is chosen with a specific probability.

Question 8

Existence of a Nash Equilibrium:
How do mixed strategies solve the problem of non-existence of Nash equilibria in games like RPS?

Answer 8

By randomizing strategies, players make their opponents indifferent between choices, creating a stable equilibrium.

Question 9

Existence of a Nash Equilibrium:
What is the key condition for a mixed strategy Nash equilibrium in RPS?

Answer 9

Each player’s mixed strategy must make their opponent indifferent between all pure strategies.

Question 10

Existence of a Nash Equilibrium:
What does Nash’s theorem guarantee?

Answer 10

Every game with a finite number of players and pure strategies has at least one Nash equilibrium in mixed strategies.

Question 11

Existence of a Nash Equilibrium:
Why is Nash’s theorem significant?

Answer 11

It ensures that predictions about game outcomes can be made under very general conditions.

Question 12

Existence of a Nash Equilibrium:
What is an example of a real-world application of mixed strategy Nash equilibria?

Answer 12

Penalty kicks in soccer, where goalkeepers and kickers randomize their choices (left, middle, right) with probabilities of 1/3.

Question 13

Existence of a Nash Equilibrium:
How do goalkeepers and kickers in soccer align with Nash equilibrium predictions?

Answer 13

Studies show their observed behavior in penalty kicks is consistent with theoretical predictions of mixed strategies.

Question 14

Economies of social media:
Why might the QWERTY keyboard be considered an inefficient standard?

Answer 14

The QWERTY keyboard layout was originally designed in the 19th century for typewriters, where it helped prevent jamming by spreading out commonly used letter pairings.

Over time, it became the default standard, even though more efficient layouts like the Dvorak Simplified Keyboard have since been designed, which are faster and less tiring to use.

However, QWERTY persists due to network effects:
- Most people have learned to type on QWERTY.
- Software, devices, and training materials are built around QWERTY.
- Transitioning to a new layout would require significant effort for users, educators, and manufacturers.

This situation is an example of a coordination problem: Everyone sticks to the QWERTY layout because everyone else uses it, even though an alternative might be better.

Question 15

Economies of social media:
How is the QWERTY example relevant to the economy?

Answer 15

It illustrates how multiple equilibria and coordination problems can lead to the persistence of inefficient standards, which is also at the core of many digital technologies.

Question 16

Economies of social media:
What is a network externality?

Answer 16

A phenomenon where the value of a platform or service increases as the number of users grows, making it more attractive to others.

Question 17

Economies of social media:
How do network externalities affect platform success?

Answer 17

Platforms with more users are more attractive and can dominate the market, even if they offer lower quality than competitors.

Question 18

Economies of social media:
What role do network externalities play in industries like social media?

Answer 18

Network externalities often dominate quality differences, allowing platforms with more users to thrive regardless of factors like user-friendliness or privacy transparency.

Question 19

Economies of social media:
What is a typical pattern observed in industries with network externalities?

Answer 19

In the early stages, multiple platforms compete, and the platform with the fastest-growing user base typically dominates, creating a strong incumbent advantage.

Question 20

Economies of social media:
How does game theory explain competition among platforms?

Answer 20

The competition is a game with multiple equilibria, where users may coordinate on different platforms. The number of users, not quality, predicts which platform will succeed.

Question 21

Economies of social media:
Why is it difficult for new platforms to succeed against incumbents?

Answer 21

Once a platform dominates the market due to its large user base, it is protected against new entrants, even if the new platforms offer better quality.

Question 22

Cooperation Problems and externalities:
When do externalities exist?

Answer 22

Externalities exist, if the acts of an individual A have an impact on the well-being of another individual B, that A does not take into consideration:
It is a non-internalized interdependency.

Question 23

Cooperation Problems and externalities:
In what way does the prisoner’s dilemma display the link between cooperation problems and externalities?

Answer 23

Looking at cooperation problems, like the prisoner’s dilemma, one sees that it is exactly an externality that is at the heart of the problem:
The rational behavior of one individual makes the other individual worse off, but the individuals do not find a way to internalize the effect.
Hence, cooperation problems are metaphors for situations with mutual externalities, like anthropogenic climate change.

Question 24

What is deterrence in the context of the Cold War?

Answer 24

Deterrence is the art of producing in the mind of the enemy the fear to attack, often through threats of severe retaliation.

Question 25

Cold War:
What was Mutually Assured Destruction (MAD)?

Answer 25

MAD was a nuclear strategy where both the USA and the USSR threatened devastating counterstrikes if attacked, ensuring mutual destruction in the event of war.

Question 26

Cold War:
Why did game theorists question the rationality of MAD?

Answer 26

Game theorists argued that once attacked, a country would have no rational incentive to retaliate, as it couldn’t undo the destruction. This undermined the credibility of MAD, potentially encouraging preemptive strikes.

Question 27

Cold War:
What is second-strike capability?

Answer 27

Second-strike capability is the ability to retaliate after being attacked, ensuring that a counterstrike is always possible, thereby reinforcing MAD.

Question 28

Cold War:
How did leaders use perceived irrationality to strengthen MAD?

Answer 28

Leaders were portrayed as unpredictable or irrational (e.g., Nixon as insane or drunk, Brezhnev as senile) to make threats of retaliation seem more credible.

Question 29

Cold War:
What role did uncertainty play in reinforcing MAD?

Answer 29

Uncertainty was introduced by spreading nuclear weapons across various locations and increasing their number, making it harder to guarantee that all could be stopped in the event of a first strike.

Question 30

Cold War:
What is a doomsday machine in the context of MAD?

Answer 30

A doomsday machine is a technology that ensures an automatic counterstrike without human intervention if a nuclear attack is detected, making MAD more credible.

Question 31

Cold War:
What was the USSR’s Perimeter or “Dead Hand” system?

Answer 31

Perimeter was an automated system capable of launching intercontinental ballistic missiles if sensors detected signs of a nuclear attack, ensuring a counterstrike even if leadership was incapacitated.

Question 32

Cold War:
Why is the Cold War often compared to the Prisoner’s Dilemma?

Answer 32

The Cold War is likened to the Prisoner’s Dilemma because both sides had incentives to preemptively strike to avoid being struck first, but this analogy assumes specific payoffs that may not have applied to Cold War leaders.

Question 33

Cold War:
What strategies were recommended by RAND to make MAD credible?

Answer 33

RAND (Research and development) recommended ensuring second-strike capability, portraying leaders as irrational, creating uncertainty about stopping counterstrikes, and developing doomsday machines.

Question 34

Cold War:
Who was the RAND? What role did they play in the cold war?

Answer 34

RAND (Research and Development) Corporation is a prominent American think tank.
Initially created to provide research and analysis for the U.S. military.

RAND played a significant role during the Cold War, employing top game theorists, economists, and scientists to study strategic and defense issues, including nuclear deterrence and strategies like Mutually Assured Destruction (MAD).

Question 35

What does the Zermolo theory state?

Answer 35

1. There must be a perfect way to play.
2. One of these outcomes is guaranteed:
   (White can force a win, black can force a win, both players can force at least a draw)

Question 36

To which games does the theorem apply? Which characteristics must these games have?

Answer 36

• Two players
• Perfect information (no hidden elements)
• Finite number of possible positions
• Players take turns
• No chance involved

Question 37

What does the theorem prove and tell us?

Answer 37

While the theorem proves that a perfect strategy exist, it doesn’t tell us what the strategy is.
==> In chess the game is so complex that we can’t actually determine the perfect way to play, even though we know it exists.

We know that there’s a “solution” to the game, but it’s too complicated for us to figure out with our current capabilities.

Question 38

What implications does Zermolo’s theorem have for game theory?

Answer 38

It has broader implications for game theory, showing that in certain types of games, there’s always an optimal way to play, even if we can’t practically determine what it is.

Question 39

What is a chainstore game?

Answer 39

A chainstore game is a strategic game in game theory that models situations where a party (typically a firm) has to decide whether to challenge or avoid conflict with an opponent (often a competitor) in a sequence of moves. The game is named after the idea of a chain of stores, where a dominant firm has to decide whether to fight a new entrant into the market or allow them to enter without resistance.

In the chainstore game, the dominant firm has a reputation for reacting strongly to challenges, which deters new entrants. However, if the firm decides to punish the entrant in each round of competition (e.g., through aggressive pricing or other strategies), it could end up worse off because the cost of retaliation might outweigh the benefits. If the firm backs down and does not retaliate, it may send a signal to other potential entrants that the firm is weak, which could invite more challenges.

Question 40

What are the key elements of the chainstore game?

Answer 40

1. Multiple rounds of play
   ==> The game is repeated over time, with each decision impacting the future
2. Reputation and deterrence
   ==> The dominant firm’s ability to deter new entrants or competition depends on its past actions and its perceived willingness to fight
3. Cost-benefit analysis
   ==> The firm must decide whether the cost of fighting (e.g. aggressive competition or retaliation) is worth it or if its better to allow the competition to enter

Question 41

Why are military conflicts an example of a social phenomenon that resembles

Answer 41

Military conflicts can resemble the chainstore game, where one party threatens to attack the other, but both parties would be worse off if the threat escalates into an actual attack.

Question 42

What are bailouts in the financial system?

Answer 42

Bailouts in the financial system refer to government interventions in which public funds are used to rescue failing financial institutions, such as banks, insurance companies, or other key players in the economy. Bailouts typically occur when a financial institution faces bankruptcy or severe financial distress, and the failure of that institution could lead to widespread economic damage, such as a financial crisis or loss of public confidence in the financial system.

Question 43

How do bailouts in the financial system relate to game theory?

Answer 43

Banks anticipate that they will be bailed out in case of failure due to the severe economic consequences, which can encourage them to take on riskier strategies. The state’s challenge is to make a “no-bailout” policy credible.

Question 44

What is the connection between game theory and the legalization of illegal immigrants?

Answer 44

Governments often signal a tough stance on illegal immigration to prevent it, but the debate over legalization shows the tension between strict policies and the economic benefits of allowing immigrants, especially in industries like agriculture.

Question 45

How can “touchiness” in a partnership relate to game theory?

Answer 45

In a partnership, one partner may benefit from being touchy or jealous, as it influences the other partner’s behavior. The strategic structure is about managing reputation and expectations to gain a favorable outcome.

Question 46

What is the challenge faced by social scientists using game theory?

Answer 46

The challenge is to distill complex social phenomena into their essential strategic structures, avoiding over-simplification by forcing all situations into familiar game theory models like the prisoner’s dilemma.

Question 47

What is a potential issue with applying game theory universally?

Answer 47

Game theory can lead to oversimplification, where every situation is interpreted as a cooperation or conflict problem, like trying to fit everything into the prisoner’s dilemma framework.

Question 48

What was the situation that the EU faced with its member states during the financial crisis?

Answer 48

The EU faced the challenge of institutional reforms in some of its member states, especially regarding bailout strategies and financial stability, similar to the dynamics of moral hazard and the risk of encouraging reckless behavior.

Question 49

What was President Obama’s stance on illegal immigration in 2014?

Answer 49

President Obama supported providing a path to legalization for illegal immigrants, even though Congress was not acting on the issue, due to humanitarian and economic arguments in favor of legalization.

Question 50

What argument do opponents of the legalization of illegal immigrants use?

Answer 50

Opponents argue that legalization sends the wrong signal and may encourage more illegal immigration, undermining efforts to control immigration.