prisoners’ dilemma and its implications
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Prisoners’ Dilemma and Its Implications. What is Prisoners’ Dilemma?. A Problem of Game Theory. The prisoners’ dilemma is a problem in Game theory. It is non-zero-sum game. Penalty Table for Prisoners. Prisoners’ Strategy. - PowerPoint PPT PresentationTRANSCRIPT
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.