Class 4: Strategic Interactions + Game Theory Flashcards
1. Test yourself: can you come up with examples of a Prisoner's Dilemma, Stag Hunt, and game of Chicken that are relevant to international politics? 2. Could you represent collective action and free rider problems in game form? 3. How does the fact that actors may repeatedly interact change their incentives? 4. How could states deal with the issue of credibility? 5. When is uncertainty an asset in international politics? 1. Intro to Game Theory 2. Prisoner's Dilemma 3. Chicken 4. S
Barriers to Cooperation
Individual interests may lead actors to defect
Defecting
Defecting is adopting an uncooperative strategy that undermines the collective goal
Incentives to defect magnied by:
- lack of trust
- perceptions of bad intent
- lack of information.
Best Response Strategy:
- 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.
Prisoners Dilemma Scenario
- 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.
- 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:
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.
Defection:
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.
Game Theory Key Concepts:
Key concepts: - Players - Strategies - Outcomes - Utilities
Players choose strategies which lead to outcomes that give players utility.
Nash Equilibrium
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.
Pareto efficient:
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.
Equilibria DO NOT have to be Pareto efficient.
!
How to test if a set of strategies results in a Nash Equilibrium:
- Identify the cell that would result from both players playing these strategies
- Ask: given what the column player is doing, could the row player do better by changing his strategy?
- 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
A Collaboration Problem:
Public goods are socially desirable products dened by two qualities:
- Non-excludable
- Nonrival In consumption
Some examples: national defense, the provision of roads, clean air and water, etc.
Public goods are socially desirable products defined by two qualities:
- Non-excludable
2. Nonrival In consumption
Public Goods:
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
collective action problems
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
free ride
Each individual has an incentive to free ride:
- Failing to contribute while benefiting from the efforts of others
Chicken vs. Stag Hunt vs. Coordination Games
Diagram ***
Chicken game
(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
Chicken As Metaphor for Coercive Bargaining:
Nuclear Crises= Chicken Game:
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.
The Stag hunt game Scenario
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.
Coordination Game
((CC; DD) > (CD; DC))
Scientic standard/measurements
What happens if we repeat the Prisoner’s Dilemma
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
*Example of the repeated Prisoner’s Dilemma in Fearon Reading
…
*Factors that can make cooperation easier, and how international institutions could foster this.
- 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
*Institutions can foster easier cooperation:
Institutions can facilitate cooperation domestically on international issues as well as facilitate cooperation directly between countries
A Sequential-Move Game
Credibility-
How to credibly convey a willingness to go nuclear:
- Tell the Soviets that the US will use nuclear weapons
- Establish a reputation for irrationality
- Burn the conventional forces
The Role of Unpredictability
(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
