1 2 (2-person cooperative Game)

1.

2/22

1. -

1 2(2-person cooperative games) .

2 (coalition) , .

2 (transferable utility) .

2 (n-person) .

3 (n-person nontransferable utility games) .

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(Prisoners Dilemma) .

, .

.

.

Prisoners Dilemma ( ) version

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... . 1 ... 1 25 ... 3 . 2 10 . ? .

2 . .

Prisoners Dilemma ( ) version ()

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(); .

10, 10 1, 25

25, 1 3, 3

Prisoners Dilemma ( ) version()

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;

(25 10 ).

1 3 .

, . . .

. ?

Prisoners Dilemma ( ) version()

() ()

10, 10 1, 25

25, 1 3, 3

7/22

1. -

: 1) 2) (binding agreement) .

: , ? ... ? . , ?

1) () 2) . , , .

() ()

()

() 10, 10 , 25

25, 3, 3

9-5-12

8/22

1. -

()

.

( ) : (strategic standpoint) ; . , . )

( ): - . , (axiomatic bargaining theory) .

* (, axiom): , . ' ' .

9/22

1. -

, .

Nash(1950, 1953) , Harsanyi Selten (1988; A general Theory of Equilibrium Selection in Games, MIT Press) : .

Shapley (1953), Rubinstein (1982), Binmore and Dasgupta (1987) .

10/22

1. -

.

1. (fairness)

2. (naturalness)

3.

4.

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1. -

(Fairness)

Nash ( ) . ( ? =? NO. .)

(:embody) . .

: . -> Shapley Value; (Utilitarianism) . ? (Egalitarianism) : .

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I: (Utilitarianism) Sidgwick, Henry (1907) The Methods of Ethics, 7th ed., London

, (just). (fair).

(net satisfaction) .

: , ( ) , , .-> . . (positive economics; )

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II: (Egalitarianism) Rawls, John (1971) A Theory of Justice, Harvard University Press, Cambridge Mass.

.

(Normative economics; , (Karl Marx) Chicago .

, .

? Q: MP3 . . ? Which type are you?

(Social Welfare Function) .

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U1

U2

=(Linear)

( )

Egalitarianism vs. Utilitarianism Social Welfare Function(SWF)

Utilitarianism

A B ? UtilitarianismA A

B

15/22

U1

U2

Egalitarianism vs. Utilitarianism Social Welfare Function(SWF)

=0

(45)

Egalitarianism

*SWF , 1 2 . 2 SWF .

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U1

U2

Senian SWF

Egalitarianism vs. Utilitarianism Social Welfare Function(SWF)

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(Posner, 1994, The Economics of Justice, Havard University Press, 5th printing, Cambridge, Massachusetts and London, England)

?(Uncertain domain)

?(Peril of instrumentalism)

A , B , A . , ?

[] [totalitarianism] [] .

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(Maximin Rule) (Posner, 1994, The Economics of Justice, Havard University Press, 5th printing, Cambridge, Massachusetts and London, England)

The basic idea is Rawls maximin rule forces us to worry too much about what has very slim chance to occur and then forces us not to choose to take risk at all.

Harsanyis counter-example: Bad job in NY, good job offer from Chicago. Go or stay? Maximin rule-> worst scenario -> choose a better one, i.e. stay.

But Bayesian Rule says; if prob. of accident is small, take the job in Chicago.

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NY-Chicago plane accident

No NY-Chicago plane accident

Choose NY job (stay)

Poor job But stay alive

Poor job Stay alive

Choose Chicago job(leave)

Die Good job Stay alive

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1. - (naturalness) :

.

.

, , core . , core . core , (empty). core .

Core , . ( ) ? What should happen will happen. (Sen, Armartya 1970, Collective Choice and Social Welfare Holden-Day, San Francisco)

20/22

1. -

(naturalness) : .()

, .

, (fairness) .

(: ) , .

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1. -

(naturalness) : .()

, ( , agreement) , (Pareto Optimal) , .

, (ex ante). , (arbitration scheme) .

ex ante: from(out of) + before from what is done before

ex post: from + after from what is done afterwards

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1. -

. .

, (Nash Bargaining Model) , . , (Fixed Threat Game) , . (Shapley Value) .

(Nash Variable Threat Solution) (Bargaining Set) .

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1. 1.1

Pareto(1848~1923, ) Optimal:

Status Quo

Pareto Improvement

Pareto Optimal

U1

U2

Pareto superior? NO.