Prisoners' dilemma: the problem and prevalence Week 3

Question 1

What is the dominant strategy equilibrium in this prisoners dilemma example

Answer 1

The dominant strategy equilibrium is (cheat, cheat)

Question 2

Cheating/defecting/confessing explained in prisoners’ dilemma

Answer 2

• Choosing a selfish option that benefits you but harms the group
• Breaks potential mutual cooperation (even if no formal agreement exists)
• Example: betraying someone or businesses undercutting each other instead of working together

Question 3

Cooperating explained in prisoners’ dilemma

Answer 3

• Working together for shared benefits, even without a formal agreement
• Leads to mutual gain and avoids conflict
• Example: companies colluding to keep prices high for mutual profit

Question 4

The generalised prisoners’ dilemma explained

Answer 4

c>a>d>b
The Nash equilibrium (also a dominant strategy equilibrium) is {Do not cooperate, Do not cooperate}
Yet, both are better off cooperating as a>d this is the prisoners’ dilemma

Any game with this basic payoff structure is a Prisoners’ Dilemma. The players do not have to be prisoners or oligopolists.

Question 5

Applications of prisoners’ dilemma

Answer 5

Oligopoly collusion, international trade and investment, environmental problems, prisoners, wage inflation, public goods, human capital investment (and more)

Question 6

Prisoners’ dilemma characteristics

Answer 6

• The moves of the game are hidden
• You do not know the others decision until after you’ve made you decision

(appropriate to model it as a simultaneous game)

Question 7

Prisoners’ dilemma explained essay question.

Answer 7

The moves of the game are therefore hidden and
it is appropriate to model the situation as a simultaneous move game (even if the
prisoners are not actually being interviewed exactly at the same time). An implicit
assumption of the game is that the prisoners did in fact commit
the crime that they are being questioned about. The suspects can
either confess to the crime or deny their involvement in it. If
neither prisoner confesses the police are not able to convict either
for the major crime but are able to secure a conviction against
both of them in relation to a lesser crime. However, if just one of
them confesses to the major crime they can both be convicted.
The dilemma for the prisoners is that if one of them confesses but
the other does not the one who confesses receives a much shorter
sentence than the other (his reward for acting as an informer or
‘grass’).
For both prisoners confess
is the best response to either deny or confess by the other implying that each player’s
dominant strategy is to confess. The dominant strategy equilibrium is therefore {confess,
confess} and the game theoretic prediction is that that faced with these strategy choices
and payoffs both prisoners will confess.
The dilemma for the players is that they could both have higher payoffs if they both
denied. Since the {confess, confess} equilibrium is Pareto dominated by {deny, deny} it
is not Pareto efficient. Both prisoners can work out that {confess, confess} is not an
efficient outcome (as can the police) but the rational, self-interested dominant strategy is
clearly to confess.

Question 8

Pareto efficiency

Answer 8

In a two person game an outcome is Pareto efficient if it is not possible to improve
one player’s payoff without at the same time lowering the payoff of the other

Question 9

Preferences of the players in generalised prisoners’ dilemma

Answer 9

c>a>d>b

(can’t avoid doing buttstuff)

Question 10

asymetric oligopoly collusion in Prisoners’ dilemma

Answer 10

This is also a form of prisoners’ dilemma

Question 11

How can you tell if a game is a Hawk-dove game or a Prisoners’ Dilemma?

Answer 11

Prisoners Dilemma:
Cooperation leads to the best mutual outcome, but defection (selfishness) is the dominant strategy for both players, leading to a worse outcome overall. It occurs when the cost of defection (C) is less than the benefit of cooperation (C) for individuals

Hawk-Dove game:
There is no dominant strategy. Players alternate between cooperation and aggression, as mutual aggression is too costly. This occurs when the cost of defection (C) exceeds the benefit of cooperation (V).

Question 12

What are economic public goods?

Answer 12

Economic public goods are non-rival and non-excludable
Outcome: under provision if let to the market
Examples of economic public goods are national defense, street lights, vaccinations, recycling, clean air, polite behaviour etc.

Positive externality effects on other once supplied (cause of free rider effects)

Question 13

Non-rival definition

Answer 13

One person’s consumption does not reduce the amount available to others = positive externality

Question 14

Non-excludable definition

Answer 14

No restrictions on access - available to one, available to all - cannot be provided profitably by markets = free riders

Question 15

Public goods implications

Answer 15

Public goods - non-rivalry, non-excludability -> free rider effects -> under-provision

Acting in self-interest not socially efficient - everyone worse off - all could be better off if acted cooperatively instead

Prisoners’ dilemma e.g., lower environmental quality, less people vaccinated, tax evasion

Question 16

Open access goods implications

Answer 16

Open access goods - non-excludability bu rivalry -> individual optimisation leads to over-use
- Depletion of reneweable resources, over grazing, over harvesting, excesss fishing -> erostion of habitats, extinction, non-sustainable shocks

Prisoners’ dilemma example = tragedy of the commons

Question 17

Application: Transport, roads and congestion

Answer 17

Transport issues are complicated because roads are an open access facility like public parks
- Leads to congestion and overuse
- Generally a local issue

Most transport causes pollution
- Negative externality in consumption
- Policy in this context is usually to tax e.g., via a tax on petrol

Question 18

Congestion on roads:

If the alternative route takes 18 minutes, which route will the individual in car 6 choose and why? What are the consequences of this individual’s decision for the other drivers?

Answer 18

• Direct route takes 14 minutes
• Indirect route takes 18 minutes
• So driver in car 6 will take the direct route (saves 4 minutes)
• But this ignores the costs imposed on other drivers
• Individual optimisation leads to a net social loss (selfish decisions worsen outcomes for everyone)

Question 19

Policy implications prisoners’ dilemma

Answer 19

Ways of resolving these prisoners’ dilemmas
- Governments/international invervention and regulation e.g., supply of public goods
- Establishing/restricting property rights to open access resources/facilities. E.g., establishing restricted rights to areas of forests and sea, charges for road use
- Social norms: confirming to or internalisation of social pressures e.g., not dropping rubbish
- Collective action through pressure groups