Download - Prisoner Dilemma Edited
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Basic Slides
PRISONER'S DILEMMA
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Issue dealt
Two prisoners caught while trying to break in
Charged with trespass
To receive 1 month sentence if both keep quiet
Other-receives 12 month if one doesnt confess
Other let off
Will receive 8 months each -confess
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Assumptions and Definitions
Decision makers-rationale and Strategic(Players).
Aim-maximization of pay-outs.
Game-Indicates circumstances-decision is
dependent on Decision Makers(D.M)
Pay off or utility- Pay out received due to a
Decision.
Information Set- Info available at a particular point
of a Sequential Game
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Assumptions and Definitions
Equilibrium- both players decision made,
outcome reached.
Can also use positive utility function
Utility function- ranking
Negative used to indicate minimization
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Using No of months
Numerical-1
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Initial matrixPlayer-2
Player-1 Keep quiet Confes
s
Keep quiet -1,-1 -12,0
Confess 0,-12 -8,-8
Player -1- 1stelement in each -pay-offs for keeping quiet and confessing
Player-2- 2ndElement in eachpay offs for keeping quiet and confessing
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Analysis
Looking into each move in isolation
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Condition-1
Player 1 analysis- what if player 2 kept quiet
Decision- Confess else will spend 1 month in jail
Player 1 considers his pay off only.
Player-1 Keep quiet
Keep quiet -1,?
Confess 0,?
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Condition-2
Player 1 analysis- what if player 2 confesses
Decision- Confession-8 months in jail , else will
spend 12 months in jail
Player 1 considers his pay off only again.
Player-1 Confess
Keep quiet -12,?
Confess -8,?
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CONFESS
Player-1 is better off confessing regardless of the decision of
Player-2
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Condition-3
Player 2 analysis- what if player 2 kept quiet
Decision-Player 2 should confess- let off
Player 2 considers his pay off only.
Player-2
Keep
quiet
Confess
KeepQuiet
?,-1 ?,0
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Condition-4
Player 2 analysis- what if player 2 confessed
Decision-Player 2 should confess- receives 8
months as compared to the 12 months
Player 2 considers his pay off only again.
Player-2
Keep
quiet
Confess
KeepQuiet
?,-12 ?,8
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SOLUTION
BOTH MUST CONFESS
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CONCLUSION- Part-1
Law has triumphed
Case successfully investigated by the inspector
Both the prisoners acquitted for 8 months
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Using preference ranking
Numerical-2
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Initial matrixPlayer-2
Player-1 Keep quiet Confes
s
Keep quiet 3,3 1,4
Confess 4,1 2,2
Player -1- 1stelement in each -pay-offs for keeping quiet and confessing
Player-2- 2ndElement in eachpay offs for keeping quiet and confessing
Utility in terms of preferred outcome
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Condition-1
Player 1 analysis- what if player 2 kept quiet
Decision- Confess has better ranking
Player 1 considers his pay off only.
Player-1 Keep quiet
Keep quiet 3,?
Confess 4,?
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Condition-2
Player 1 analysis- what if player 2 confesses
Decision- Confession-better
Player 1 considers his pay off only again.
Player-1 Confess
Keep quiet 1,?
Confess 2,?
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Condition-3
Player 2 analysis- what if player 2 keeps quiet
Decision-Player 2 should confess- let off
Player 2 considers his pay off only.
Player-2
Keep
quiet
Confess
KeepQuiet ?,3 ?,4
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Condition-4
Player 2 analysis- what if player 2 confesses
Decision-Player 2 should confess
Player 2 considers his pay off only again.
Player-2
Keep
quiet
Confess
KeepQuiet ?,1 ?,2
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CONCLUSION- Part-2
Case successfully investigated by the inspector
on the basis of preferential ranking also
The result is found to be the same as in Months In reality however results change based on
constraints considered say friendship or feeling of
sacrifice or nature of human being
Also we see one set of utility strictly dominate
other