Class 4: Strategic Interactions + Game Theory

Question 1

Barriers to Cooperation

Answer 1

Individual interests may lead actors to defect

Question 2

Defecting

Answer 2

Defecting is adopting an uncooperative strategy that undermines the collective goal

Question 3

Incentives to defect magnied by:

Answer 3

1. lack of trust
2. perceptions of bad intent
3. lack of information.

Question 4

Best Response Strategy:

Answer 4

• A plan to do as well as possible given one’s expectations about the interests and actions of others.
  - Hence, actors are \purposive”

**A best response strategy does not always guarantee that an actor will obtain its preferred outcome.

Question 5

Prisoners Dilemma Scenario

Answer 5

• Two criminals robbed a bank and hid the money
• Both are caught by police but there is not enough evidence to convict them
  
• Separated and offered the same deal:
  1. rat the other guy out while he keeps quiet-> you go free and get the money, he goes to jail
  2. stay quiet while the other guy rats you out->you go to jail, he goes free and gets the money
  3. rat him out while he rats you out ->both go to jail and split money upon release
  4. Both stay quiet-> both go free + split money

Collectively the prisoners would do best by cooperating with each other and staying quiet.

Yet each has an incentive to rat out his accomplice
- Here, ratting the other out is “defection”
- If the accomplice is going to rat you out, your best response is to: rat him out
- If the accomplice is going to stay quiet, your best response is to: rat him out

Defection is the best response whether the accomplice stays quiet or defects.

Both playing best responses–>both ratting each other out.

Question 6

• If the accomplice is going to rat you out, your best response is to:
• If the accomplice is going to stay quiet, your best response is to:

Answer 6

Rat him out for both:
Defection is the best response whether the accomplice stays quiet or defects.

Both playing best responses–>both ratting each other out.

Question 7

Defection:

Answer 7

Individual incentive to defect undermines the collective interest to cooperate.

Defection is the best response whether the accomplice stays quiet or defects.

Example: during the Cold War, the best strategy for both the US and Soviet Union was to defect and keep building weapons because could not be sure the other was not.

Question 8

Game Theory Key Concepts:

Answer 8

Key concepts:
- Players
- Strategies
- Outcomes
- Utilities

Players choose strategies which lead to outcomes that give players utility.

Question 9

Nash Equilibrium

Answer 9

Nash equilibrium: Outcome where neither player has a positive incentive to change their strategy.

- The result of best responses.
- Stable– no one has an incentive to change their behavior given what everyone else is doing.

Question 10

Pareto efficient:

Answer 10

Outcome such that no other outcome would make
an actor better off without making another actor worse off.
- Desirable normative properties.
- No “goodies” left on the table.

Question 11

Equilibria DO NOT have to be Pareto efficient.

Answer 11

!

Question 12

How to test if a set of strategies results in a Nash Equilibrium:

Answer 12

1. Identify the cell that would result from both players playing these strategies
2. Ask: given what the column player is doing, could the row player do better by changing his strategy?
3. Ask: given what the row player is doing, could the column player do better by changing his strategy?

If NO and NO you’ve found a (pure strategy) Nash Equilibrium

Question 13

A Collaboration Problem:

Answer 13

Public goods are socially desirable products dened by two qualities:

1. Non-excludable
2. Nonrival In consumption

Some examples: national defense, the provision of roads, clean air and water, etc.

Question 14

Public goods are socially desirable products defined by two qualities:

Answer 14

1. Non-excludable

2. Nonrival In consumption

Question 15

Public Goods:

Answer 15

Efforts to produce goods are hindered by collective action problems
- Each actor aims to benefit from the good without bearing the costs for it

Each individual has an incentive to free ride:
- Failing to contribute while benefiting from the efforts of others

Question 16

collective action problems

Answer 16

Efforts to produce goods are hindered by collective action problems

Because each actor aims to benefit from the good without bearing the costs for it

Question 17

free ride

Answer 17

Each individual has an incentive to free ride:

- Failing to contribute while benefiting from the efforts of others

Question 18

Chicken vs. Stag Hunt vs. Coordination Games

Answer 18

Diagram ***

Question 19

Chicken game

Answer 19

(DC > CC > CD > DD)

The game of Chicken represents a second strategic dilemma.
Two drivers speed down the middle of the road toward one another. The fi rst to turn aside, the “ chicken,” earns the derision of his or her peers. The other driver wins. If both swerve simultaneously, neither is humiliated. If neither turns aside, both risk death in a serious wreck.
Turning aside= cooperation
continuing down the middle of the road= defection,

Lacking a dominant strategy, the key to one’s strategy in Chicken is to do the opposite of what you think the other driver is likely to do. If you think your opponent will stand tough ( D), you should turn aside ( C).

the actors’ interests are DC > CC > CD > DD,

Ex. cuban missile crisis

Question 20

Chicken As Metaphor for Coercive Bargaining:

Nuclear Crises= Chicken Game:

Answer 20

Chicken is often taken as a metaphor for coercive bargaining.

Nuclear crises are usually thought of as Chicken games. Both sides want to avoid nuclear disaster (DD), but each has incentives to stand tough and get the other to back down ( DC). The state willing to take the greatest risk of nuclear war is therefore likely to force the other to capitulate. The danger, of course, is that if both sides are willing to run high risks of nuclear war to win, small mistakes in judgment or calculation can have horrific consequences.

Question 21

The Stag hunt game Scenario

Answer 21

Stag-Hunt: (CC > DC > DD > CD)
- Setting international standards

often taken as a metaphor for problems of coordination in international relations

Only by working together can two hunters kill a stag and feed their families well. One must fl ush the deer from the forest, and the other must be ready to fi re his arrow as the animal emerges. In the midst of the hunt, a lone rabbit wanders by. Each hunter now faces a decision: he could capture the rabbit alone, but to do so he must abandon the stag, insuring that it will get away

In this game, both hunters are best off cooperating ( CC) and sharing the stag. The next best outcome is to get a rabbit while the other tries for the stag ( DC); however, if both go for the rabbit ( DD), they then split the rabbit. The worst outcome for each hunter is to spend time and energy hunting the stag while the other hunts the rabbit ( CD), leaving him and his family with nothing.

two equilibria ( CC and DD).

The Stag Hunt also captures situations in which the primary barrier to cooperation is not an individual incentive to defect (like Prisoners Dilemma) but a lack of trust.

Question 22

Coordination Game

Answer 22

((CC; DD) > (CD; DC))

Scientic standard/measurements

Question 23

What happens if we repeat the Prisoner’s Dilemma

Answer 23

Things like lack of trust lead to the security dilemma.

If both sides can commit to playing the PD indefinitely, then there are more cooperative equilibria available.

This arises because repetition leads to:
1. Opportunities for reciprocity
2. Opportunities for punishment

Example: retaliatory taris in trade policy

Question 24

*Example of the repeated Prisoner’s Dilemma in Fearon Reading

Answer 24

…

Question 25

*Factors that can make cooperation easier, and how international institutions could foster this.

Answer 25

1. Institutions (state know they need to do business in the UN)
   2. Information (needed for knowing when to reciprocate/punish)
   3. Valuing the future

Institutions can facilitate cooperation domestically on international issues as well as facilitate cooperation directly between countries

Question 26

*Institutions can foster easier cooperation:

Answer 26

Institutions can facilitate cooperation domestically on international issues as well as facilitate cooperation directly between countries

Question 27

A Sequential-Move Game

Question 28

Credibility-

How to credibly convey a willingness to go nuclear:

Answer 28

• Tell the Soviets that the US will use nuclear weapons
• Establish a reputation for irrationality
• Burn the conventional forces

Question 29

The Role of Unpredictability

Answer 29

(Odd/Even Payoff game)
(1; -1) (-1;1)
(-1;1) (1;-1)

If a rebellion can only attack some cities in a country, and if a ruling power can only fortify some cities in a country, uncertainty is key