Transcript Prisoners’ Dilemma • Scenario: • You and an accomplice are arrested on suspicion of committing some nasty crime • The District Attorney and the police have been unable.

Prisoners’ Dilemma
• Scenario:
• You and an accomplice are
arrested on suspicion of
committing some nasty
crime
• The District Attorney and
the police have been
unable to produce enough
evidence to convict you of
that offense
Prisoners’ Dilemma
• We do have enough evidence to convict you of
some lesser charge
• The only way the DA can nail you for the more
serious offense is if one of you rats out the other
• Conversely, you and your partner can largely
elude prosecution if you both stay silent
• You and your partner are placed in separate
holding cells and are unable to communicate with
each other
• DA enters and offers you the following:
Rat
Hang Tough
Rat
Hang
Tough
Prisoners’ Dilemma
From your perspective, you and your accomplice are faced with the following:
Don’t Cooperate
with each other
(rat)
Cooperate with each
other
(hang tough)
Don’t Cooperate
with each other
(rat)
Cooperate
with each
other
(hang tough)
Prisoners’ Dilemma
Rat
Rat
Hang Tough
0, 10
Hang
Tough
Prisoners’ Dilemma
Rat
Hang Tough
0, 10
Rat
Hang
Tough
10, 0
Prisoners’ Dilemma
Column Player
Rat
Hang Tough
0 , 10
Rat
Row
Player
Hang
Tough
10 , 0
Prisoners’ Dilemma
Rat
Hang Tough
Rat
5, 5
0, 10
Hang
Tough
10, 0
Prisoners’ Dilemma
Rat
Hang Tough
Rat
5, 5
0, 10
Hang
Tough
10, 0
1, 1
Prisoners’ Dilemma
What to do? Which strategy should you select?
Rat
Hang Tough
Rat
5, 5
0, 10
Hang
Tough
10, 0
1, 1
Prisoners’ Dilemma
Dominant
Strategy
Rat
Hang Tough
Rat
5, 5
0, 10
Hang
Tough
10, 0
1, 1
Dominant
Strategy
Prisoners’ Dilemma
Dominant
Strategy
Rat
Hang Tough
Rat
5, 5
0, 10
Hang
Tough
10, 0
1, 1
Dominant
Strategy
Prisoners’ Dilemma
Neither player can improve his/her position,
Nash Equilibrium
Rat
Hang Tough
Rat
5, 5
0, 10
Hang
Tough
10, 0
1, 1
Prisoners’ Dilemma
Neither player can unilaterally
improve his/her position
Nash Equilibrium
Rat
Hang Tough
Rat
5, 5
0, 10
Hang
Tough
10, 0
1, 1
Prisoners’ Dilemma
Prisoners’ Dilemma
• Generalized Form:
• Rank Outcomes, from most preferred to
least preferred
–
–
–
–
1 = first choice
2 = second choice
3 = third choice
4 = fourth choice
• Choice is “cooperate” or “not cooperate”
Don’t
Cooperate
Don’t
Cooperate
Cooperate
3,3
1,4
4,1
2,2
Cooperate
Prisoners’ Dilemma
Prisoners’ Dilemma
• Symbolic Form:
• We’re in a Prisoner’s Dilemma situation
whenever:
T>R>P>S
Temptation to defect > Rewards of
Cooperation
Rewards > Punishment for Not Cooperating
Punishment > Sucker’s Payoff
Prisoners’ Dilemma
• Note that even if we start at the cooperative
outcome, that outcome is not stable
• Each player can improve his/her position by
adopting a different strategy
Don’t
Cooperate
Don’t
Cooperate
Cooperate
3,3
1,4
4,1
2,2
Cooperate
Prisoners’ Dilemma
Prisoners’ Dilemma
• But since both players have changed
strategy we end up at the non-cooperative
outcome, where both players are worse off
than if they had chosen to cooperate
Don’t
Cooperate
Don’t
Cooperate
Cooperate
3,3
1,4
4,1
2,2
Cooperate
Prisoners’ Dilemma
Prisoners’ Dilemma
• And, as we noted, this non-cooperative
outcome is also a Nash equilibrium
outcome;
• Neither player has any incentive to change
strategy since whoever changes will do
immediately worse by making the move
Don’t
Cooperate
Don’t
Cooperate
Cooperate
3,3
1,4
4,1
2,2
Cooperate
Prisoners’ Dilemma
PD & Interest Group
• If a “collective good” is involved,
individuals have little incentive to work
towards achieving that good.
• Makes sense for others to do the work and
sit back and reap the benefits of their labor
• But if that’s the case, then no one will do
the work and the collective benefit won’t be
delivered