Prisoners’ Dilemmaand Its Implications

What is Prisoners’ Dilemma?Alternatives Consequences

Prisoner A Prisoner B A’s sentence B’s sentence

Keep quiet Keep quiet 1 year 1 yearKeep quiet Confess and

squeal10 years 0 year

Confess and squeal

Keep quiet 0 year 10 years

Confess and squeal

Confess and squeal

3 years 3 years

There is not communication between the two prisoners.What would each prisoner do?

A Problem of Game Theory

• The prisoners’ dilemma is a problem in Game theory.

• It is non-zero-sum game.

Penalty Table for PrisonersB

Quiet Squeal

AQuiet A: 1 B: 1 A: 10 B: 0

Squeal A: 0 B: 10 A: 3 B: 3

The numbers in table represent years of sentence.

Prisoners’ Strategy

• The strategy ‘keep quiet’ is called ‘cooperation’, while ‘confess and squeal’ is called ‘defection’.

A’s Contemplation (1)• “Squeal” would make me better off no

matter whatever B does, since– If B “quiet”, my possible penalty would be

1 year (if I “quiet”), or 0 year (if I “squeal);

– If B “squeals”, my possible penalty would be10 years (if I “quiet”), or3 year (if I “squeal”)

A’s Contemplation (2)• “Squeal” would make my penalty no worse

than B’s, while “quiet” would make my penalty no better than B’s:– If I keep “quiet”, our penalties would be

A:1/B:1 or A:10/B:0,– If I “squeal”, our penalties would be A:0/B:10

or A:3/B:3.

Rational Choice• A’s rational opportunistic choice is

“Squeal” (defection).• Similarly, B’s rational opportunistic choice

is also “Squeal” (defection).

Disappointing Outcome

• Since both A and B select “squeal”, they both get 3 years in jail.

• If both kept “quiet”, then each would get only 1 year.

• Each one pursues the best for his own. But they end up with failing to get their best.

Dilemma Around• Prisoner’s dilemma exists around us.• It reveals, tragically, the behavior pattern

of interacting people.– Natural choices of individuals lead to mutual

damage and mutual destruction.– Disparity between individual rationality and

group rationality

Arms RacePayoff Table (numbers show benefits in terms of security and expenditure)

Country B

Arm expansion Disarmament

Country A

Arm expansion A: 1 B: 1 A: 3 B: 0

Disarmament A: 0 B: 3 A: 2 B: 2

CorruptionCompany A and B are competing on a bid of a projectPayoffs: 3 = win the bid for sure; 3 2 = not sure to win, without bribing; 2 1 = not sure to win, even after bribing; 1 0 = lose the bid for sure. 0

Company BDo not bribe Bribe

Company A

Do not bribe A: 2 B: 2 A: 0 B: 3Bribe A: 3 B: 0 A: 1 B: 1

• Rational strategy for A and B: Bribe

Riding on Crowded BusesAlternatives Consequences

Individual X Others X’s waiting time

Other’s waiting time

stay in line stay in line 8 minutes 8 minutesstay in line not stay in line >360 minutes 30 minutes

not stay in line stay in line 0 minute 8.1 minutenot stay in line not stay in line 30 minutes 30 minutes

• Individual X’s rational strategy:Not stay in line.

PunctuationPeruvian government announced a campaign (Jan. 2007) to stamp out “Peruvian time” (one hour late). In a poll, 80% said they are punctual, while only 3% think others are too.Penalty: 0 = No waiting; 1 = May wait for some short time; 2 = Having to wait for a long time, definitely.

Person BBeing Punctual Being Late

Person ABeing Punctual A: 0 B: 0 A: 2 B: 0

Being Late A: 0 B: 2 A: 1 B: 1

• Rational strategy for A and B: Being late.

Equilibrium• Equilibrium is a status of balance in stable,

such that any deviation would be corrected automatically back to the original status.

A

C

B

XY Z

At Equilibrium: Disorder• Defection is at equilibrium

– If both take defection, then any attempt to give up ‘defection’ would be penalized.

• Therefore, unfortunately, disorder is at equilibrium, while order is not.

disorder disorder

order

What Prisoners’ Dilemma Implies?

• People would naturally give up “win-win” outcome associated with cooperation, and take defection which leads to mutual damage.

• Rational individual behaviors add up to irrational and self-destructive group effect.

• Social order can be stable, but not at equilibrium.

Vulnerable Social Order• It takes a long time to build up civilization

and order of a society, which looks stable. • Prisoners’ dilemma tells that it can

collapse in moment due to a natural disaster (Katrina, earthquake), war, terrorist attach, or even a big sale.

• Once order is broken, it cannot come back automatically without some external force.

Causes behind Prisoners’ Dilemma

• Lack of communication.• Distrust between people.• Egoism.

Law of Entropy• Entropy is a measure of randomness or

disorder in a system of thermodynamics.• The second law of thermodynamics says

“the total entropy (disorder) of an isolated system tends to increase over time, approaching a maximum value."

Is Disorder Our Destiny?

• Factor of penalty on cooperation– The larger the penalty on cooperation, the

more likely people would take defection.• So, reducing the penalty on cooperation is

an effective way to set up and maintain an ordered society.

To Strengthen Social Order• Reduce penalty of cooperation by e.g.

increasing social wealth;• Increasing penalty of defection by e.g. law

enforcement.• Enhancing communication between

individuals, people groups, and countries.