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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