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Θεωρία Παιγνίων

Transcript of Σημειώσεις Παραδόσεων Θεωρία Παιγνίων Για Πολιτικούς...

  • : 2008

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    .

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    .

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    70%

    30%.

    ,

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  • , . (2004), :

    , : [1990] ()

    .

  • Dixit and Skeath (1999), Games of Strategy, US:Norton (DandS)

    Dixit and Nalebuff (2001), - , , : [1991] (DandN)

    Shepsle and Bonchek (1997), Analyzing Politics,NY: Norton (S)

  • ()

    () (2002), John Nash: , : ()

    , (2000), ,: [1984] (A)

    Morrow (1994), Game theory for politicalscientists, NJ: Princeton Univ. Press (M)

  • 2008

    : (sequential moves):

    (backwards induction)(DandN) .2 (DandS) .3

    12/03

    . (, )() . 2,3 (DandN) .1, (DandS) .1,2

    05/03

    : ( )(DandN) .1, (DandS) .1,2, () .:21-61

    27/02

  • . - (sub-games) (sub-game perfectquilibrium)

    (DandN) .7, (DandS) . 6, () . 3

    02/04

    (simultaneous movegames with mixed strategies): (mixed strategy equilibrium)

    () .3, (DandN) .7, (DandS) .5

    26/03

    (simultaneous movegames with pure strategies): (dominant and dominated strategies), (dominant strategy equilibrium), Nash.

    () .3, (DandN) .3, (DandS) .4

    19/03

    2008

  • : .

    ,

    () . 3, (DandN) .4, (DandS) .8, () .1,2

    16/04

    09/04

    : , , . ,

    (DandN) .5, 6, (DandS) .9, () . 5

    07/05

    2008

  • - (incentives andenforceable contracts, principal-agent control models).(S) .: 358-404 , () . 5,7

    28/05

    (uncertainty, incomplete and asymmetric information) (moral hazardand adverse selection):

    (signaling and screening)(DandN) .12, (DandS) .12, SandN, . 11

    21/05

    : () . 4, (DandS) .11, (S) . 8, 11

    14/05

    2008

  • . 60: Theory of Games and Economic Behavior Johnvon Neumann and Oskar Morgenstern (Princeton UP:1943) . 50-60. John Nash Thomas Schelling.

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    ,

  • o -

    o

    o

  • -

    200

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  • ; ; ; ; -;

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    .

  • ;

    ( )

  • : :

    - (output) - (payoff):

  • ()

    : - ( status quo, ,

    )

  • ()

    (expected payoff):

    -

  • ()

    : 0 75%

    25% 100 0.75*0 +0.25*100=25( )

  • ( ):

  • : : . . . .

    .

  • : : . . . .

    .

  • .

    )

    ;

  • (game tree).

    () (extensive form ofthe game)

  • ()

    : (initial node) (decision nodes) (terminal node) (branches)

  • : ()(Gray) (Green)

  • :

    . (Green) ,

    ( )

  • :

    . (Green) ,

    ( )

  • GRAY, GREEN

    1, 1

    3, 3

    2, 4

    4, 2

    GREEN

    b

    GREEN

    c

    No Ads

    Ads

    GRAY

    a

    FIGURE 3.1 Tree for Senate Race Game Copyright 2000 by W.W. Norton & Company

  • ;

    1: (pure strategies) .

  • ;

    , . O

    .

    (contingent pure strategies).

  • ;

    Gray ads no ads .

    Green , .

    Gray.

    (IN) (OUT ).

  • ;

    Green :1) Gray Ads , IN, No Ads IN

    2) Gray Ads, OUT, No Ads IN

    3) Gray Ads, IN, No Ads OUT

  • ;

    4) Gray Ads, OUT No Ads OUT

    Green, . Green b, c:

    1) , 2) OUT, IN 3) IN, OUT 4) OUT, OUT

  • ;

    2: .

  • ;

    ( ).

  • ;

    rollback ( ).

  • ;

    .

  • ;

    Green 2) Gray Ads, OUT, NoAds IN.

    Gray Green Ads.

    - : (Ads; Out,In)

  • 1, 1

    3, 3

    2, 4

    4, 2

    (a) Pruning at terminal nodes

    GREEN

    b

    GREEN

    c

    No Ads

    Ads

    GRAY

    a

    GRAY, GREEN

    FIGURE 3.2 A Using Rollback Copyright 2000 by W.W. Norton & Company

  • 1, 1

    3, 3

    2, 4

    4, 2

    (b) Fully pruned tree

    GREEN

    b

    GREEN

    c

    No Ads

    Ads

    GRAY

    a

    GRAY, GREEN

    FIGURE 3.2 B Using Rollback Copyright 2000 by W.W. Norton & Company

  • $100,000/yr

    $250,000/yr on average

    $0$5m/yr

    politics

    $50,000/yr

    $600,000/yr

    management

    family practice

    $50,000/yr

    $150,000/yr

    $500,000/yr

    $35,000 $200,000/yr

    FUTURESELF

    CURRENTSELF

    lawschool

    businessschool

    medicalschool

    FIGURE 3.3 One-Player Game Copyright 2000 by W.W. Norton & Company

  • 1, 1

    4, 2

    3, 3

    2, 4

    GRAY

    GRAYOut

    In

    GREEN

    GREEN, GRAY

    FIGURE 3.4 Change of Move Order in the Senate Race Game Copyright 2000 by W.W. Norton & Company

  • U 1, 5, 5

    5, 5, 2

    5, 2, 5

    3, 4, 4

    2, 5, 5

    4, 3, 4

    4, 4, 3

    4, 4, 4

    TITAN

    Rd

    UTITAN

    Re

    UTITAN

    Rf

    UTITAN

    Rg

    BIGGIANT

    b

    U

    R

    BIGGIANT

    c

    U

    R

    FRIEDASa

    U

    R

    PAYOFFS

    FIGURE 3.5 Three-Player Game Tree Copyright 2000 by W.W. Norton & Company

  • bottomleft

    Player OPlayer X Player X

    X wins

    X wins

    topleft

    bottomright

    Player X

    X wins

    X wins

    bottomleft

    bottomright

    Player X

    X wins

    X wins

    topleft

    bottomleft

    topright

    bottomleft

    topright

    Player OPlayer X

    Player X

    Player X

    topleft

    bottomright

    topleft

    bottomright

    X wins

    X wins

    topleft

    bottomright

    X wins

    X wins

    topright

    bottomright

    X wins

    X wins

    topleft

    topright

    Player O

    Player X Player XPlayer X

    X wins X winsbottom

    rightbottom

    left

    X wins X winsbottom

    righttop

    right

    Player X

    X wins X winsbottom

    lefttop

    right

    bottomleft

    bottomright

    topright

    topleft

    Player XPlayer X Player X

    X wins X wins

    bottomleft

    X wins X wins

    topright

    topleftX wins X wins

    bottomleft

    topright

    bottomright

    topright

    bottomleft

    topleft

    Player O

    topleft

    FIGURE 3.6 A More Complex Tree Copyright 2000 by W.W. Norton & Company

  • TakeDimes

    TakeDimes

    TakeDimes

    TakeDimes

    TakeDime

    Pass Pass Pass PassA B A B B

    0, 1000, 4030, 00, 2010, 0

    Payoffs all shown as A, B

    0, 0Pass

    FIGURE 3.7 The Centipede Game Copyright 2000 by W.W. Norton & Company

  • PLAYER1

    R P

    PLAYER 2

    T, T L, WR

    P

    S

    W, L T, T

    L, W W, L

    S

    W, L

    L, W

    T, T

    (a) All payoffs shown

    PLAYER1

    R P

    PLAYER 2

    T LR

    P

    S

    W T

    L W

    S

    W

    L

    T

    (b) Zero-sum shorthand

    FIGURE 4.1 Rock-Paper-Scissors Game Copyright 2000 by W.W. Norton & Company

  • :

    .

    ----

  • ..

    :

    . .

    : Nash

  • Nash

    . Nash

  • : --

  • .

    (--)

    1/3 9

  • A,B,C a,b,c C :

    P(C,a) P(A,a) P(C,a) P(B,a) P(C,b) P(A,b).

  • ;

    :

    Times, News

  • ..

    . .. Bismark

    . minmax,maxmin (cell by cell inspection)

  • HUSBAND

    Confess(Defect)

    Deny(Cooperate)

    10 yr, 10 yr

    25 yr, 1 yr

    1 yr, 25 yr

    3 yr, 3 yr

    Confess(Defect)

    Deny(Cooperate)

    WIFE

    FIGURE 4.2 Prisoners Dilemma Copyright 2000 by W.W. Norton & Company

  • U.S.AIR FORCES

    North South

    JAPANESE NAVY

    2 2

    1 3

    North

    South

    FIGURE 4.3 Battle of the Bismarck Sea Copyright 2000 by W.W. Norton & Company

  • DONNASDEEP DISH

    High Medium

    PIERCES PIZZA PIES

    60, 60High

    Medium

    Low

    Low

    70, 36

    35, 36

    36, 70

    50, 50

    35, 30

    36, 35

    30, 35

    25, 25

    FIGURE 4.4 Successive Elimination of Dominated Strategies ($'000) Copyright 2000 by W.W. Norton & Company

  • OFFENSE

    Run Pass

    DEFENSE

    2Run

    Short Pass

    Medium Pass

    Blitz

    6

    6

    5

    5.6

    4.5

    13

    10.5

    1

    Long Pass 10 3 2

    min = 2

    min = 5.6

    min = 1

    min = 2

    max = 10 max = 5.6 max = 13

    FIGURE 4.5 The Minimax Method Copyright 2000 by W.W. Norton & Company

  • DONNASDEEP DISH

    High Medium

    PIERCES PIZZA PIES

    60, 60High

    Medium

    Low

    Low

    70, 36

    35, 36

    36, 70

    50, 50

    35, 30

    36, 35

    30, 35

    25, 25

    FIGURE 4.6 Cell-by-Cell Inspection Copyright 2000 by W.W. Norton & Company

  • PiercesPrice,

    PPierceDonnas

    best response

    Piercesbest response

    Joint profitmaximized

    Nashequilibrium

    10

    Donnas Price, PDonna

    13.5

    7.5 10 13.5

    7.5

    FIGURE 4.7 Best-Response Curves and Equilibrium in thePizza Pricing Game Copyright 2000 by W.W. Norton & Company

  • (assurance game):

    (Chicken game):

    (The battle of the Sexes):

  • (preemptivemoves)

    x ante (focalpoints)

  • U.S.

    Refrain Build

    U.S.S.R.

    4, 4 1, 3

    3, 1 2, 2

    Refrain

    Build

    FIGURE 4.10 The Arms Race as an Assurance Game Copyright 2000 by W.W. Norton & Company

  • JAMES

    Swerve(Chicken)

    DEAN

    0, 0 1, 1

    1, 1 2, 2

    Straight(Tough)

    Swerve(Chicken)

    Straight(Tough)

    FIGURE 4.11 Chicken Copyright 2000 by W.W. Norton & Company

  • SCIENCEFACULTY

    Lab Theater

    HUMANITIES FACULTY

    2, 1 0, 0

    0, 0 1, 2

    Lab

    Theater

    FIGURE 4.12 Battle of the Two Cultures Copyright 2000 by W.W. Norton & Company

  • A0 1

    B

    0, 0

    2

    0, 5 0, 0

    5, 0 0, 0 5, 0

    0, 0 0, 5 5, 5

    0

    1

    2

    FIGURE 4.13 Lottery Copyright 2000 by W.W. Norton & Company

  • SELES

    DL CC

    HINGIS

    50 80

    90 20

    DL

    CC

    FIGURE 4.14 No Equilibrium in Pure Strategies Copyright 2000 by W.W. Norton & Company

  • ROW

    Left Right

    COLUMN

    1 4

    2 3

    Up

    Down

    (a)

    EXERCISE 4.1 a Copyright 2000 by W.W. Norton & Company

  • ROW

    Left Right

    COLUMN

    1 2

    4 3

    Up

    Down

    (b)

    EXERCISE 4.1 b Copyright 2000 by W.W. Norton & Company

  • ROW

    Left Middle

    COLUMN

    5Up

    Straight

    Down

    Right

    6

    1

    3

    2

    0

    1

    1

    0

    (c)

    EXERCISE 4.1 c Copyright 2000 by W.W. Norton & Company

  • ROW

    Left Middle

    COLUMN

    5Up

    Straight

    Down

    Right

    6

    1

    3

    4

    6

    2

    3

    0

    (d)

    EXERCISE 4.1 d Copyright 2000 by W.W. Norton & Company

  • ROW

    Left Right

    COLUMN

    2, 4 1, 0

    6, 5 4, 2

    Up

    Down

    (a)

    EXERCISE 4.2 a Copyright 2000 by W.W. Norton & Company

  • ROW

    Left Right

    COLUMN

    1, 1 0, 1

    1, 0 1, 1

    Up

    Down

    (b)

    EXERCISE 4.2 b Copyright 2000 by W.W. Norton & Company

  • ROW

    Left Middle

    COLUMN

    0, 1

    Right

    9, 0 2, 3

    5, 9 7, 3 1, 7

    7, 5 10, 10 3, 5

    Up

    Straight

    Down

    (c)

    EXERCISE 4.2 c Copyright 2000 by W.W. Norton & Company

  • ROW

    Left Center

    COLUMN

    1, 2

    Right

    2, 1 1, 0

    0, 5 1, 2 7, 4

    1, 1 3, 0 5, 2

    Up

    Level

    Down

    EXERCISE 4.4 Copyright 2000 by W.W. Norton & Company

  • ROW

    Left Middle

    COLUMN

    4, 3

    Right

    2, 7 0, 4

    5, 5 5, 1 4, 2

    Up

    Down

    EXERCISE 4.5 Copyright 2000 by W.W. Norton & Company

  • ROW

    Left Middle

    COLUMN

    3, 1

    Right

    2, 3 10, 2

    4, 5 3, 0 6, 4

    2, 2 5, 4 12, 3

    Top

    High

    Low

    5, 6 4, 5 9, 7Bottom

    EXERCISE 4.7 Copyright 2000 by W.W. Norton & Company

  • ROW

    A B

    COLUMN

    1, 1 0, 0

    0, 0 1, 1

    A

    B

    EXERCISE 4.8 Copyright 2000 by W.W. Norton & Company

  • A1 2

    B

    10, 10

    3

    0, 0 0, 0

    0, 0 15, 15 0, 0

    0, 0 0, 0 15, 15

    1

    2

    3

    EXERCISE 4.9 Copyright 2000 by W.W. Norton & Company

  • : ( ;)

    ,

    (leadership)

  • HUSBAND

    Confess Deny

    WIFE

    10 yr, 10 yr

    25 yr, 1 yr

    Confess

    Deny

    1 yr, 25 yr

    3 yr, 3 yr

    FIGURE 8.1 Payoffs for the Standard Prisoners Dilemma Copyright 2000 by W.W. Norton & Company

  • DONNA'SDEEP DISH

    High Medium

    PIERCE'S PIZZA PIES

    60, 60

    70, 36

    High

    Medium

    36, 70

    50, 50

    FIGURE 8.2 Pizza Stores in a Prisoners Dilemma ($000) Copyright 2000 by W.W. Norton & Company

  • ROW

    Defect Cooperate

    COLUMN

    D, D

    L, H

    Defect

    Cooperate

    H, L

    C, C

    FIGURE 8.3 General Version of the Prisoners Dilemma Copyright 2000 by W.W. Norton & Company

  • HUSBAND

    Confess Deny

    WIFE

    10 yr, 10 yrConfess

    Deny 25 yr, 21 yr

    21 yr, 25 yr

    3 yr, 3 yr

    FIGURE 8.4 Prisoners Dilemma with Penalty for the Lone Cheater Copyright 2000 by W.W. Norton & Company

  • HUSBAND

    Confess Deny

    WIFE

    30 yr, 30 yrConfess

    Deny 25 yr, 21 yr

    21 yr, 25 yr

    3 yr, 3 yr

    FIGURE 8.5 Prisoners Dilemma with Penalty for Any Cheating Copyright 2000 by W.W. Norton & Company

  • DONNA'SDEEP DISH

    High Medium

    PIERCE'S PIZZA PIES

    156, 60

    150, 36

    High

    Medium

    132, 70

    130, 50

    FIGURE 8.6 Donnas as Leader in the Pizza-Store Prisoners Dilemma Copyright 2000 by W.W. Norton & Company

  • (credibility) (commitment)

    (threats, promises)

  • JAMES

    Swerve Straight

    DEAN

    Swerve

    Straight

    1, 10, 0

    2, 21, 1

    JAMES

    Swerve Straight

    DEAN

    Straight 2, 21, 1

    Uncommitted

    JAMES

    Committed

    FIGURE 9.1 Chicken: Commitment by Restricting Freedom to Act Copyright 2000 by W.W. Norton & Company

  • JAMES

    Swerve Straight

    DEAN

    Swerve

    Straight

    1, 10, 0

    2, 21, 1

    JAMES

    Swerve Straight

    DEAN

    Swerve

    Straight

    4, 13, 0

    2, 21, 1

    Uncommitted

    JAMES

    Committed

    FIGURE 9.2 Chicken: Commitment by Changing Payoffs Copyright 2000 by W.W. Norton & Company

  • TEACHER

    Punctual Late

    STUDENT

    4, 3Weak

    Tough 3, 2

    2, 4

    1, 1

    FIGURE 9.3 Payoff Table for Class Deadline Game Copyright 2000 by W.W. Norton & Company

  • UNITEDSTATES

    Open Closed

    JAPAN

    4, 3Open

    Closed 2, 1

    3, 4

    1, 2

    FIGURE 9.4 Payoff Table for the United States-Japan Trade Game Copyright 2000 by W.W. Norton & Company

  • UNITEDSTATES

    Open Closed

    JAPAN

    Open

    Closed

    3, 44, 3

    1, 22, 1

    No Threat

    UNITEDSTATES

    ThreatJAPAN

    Closed

    Open

    (U.S., J)

    (1, 2)

    (4, 3)

    FIGURE 9.5 Tree for the United States-Japan Trade Game with Threat Copyright 2000 by W.W. Norton & Company

  • DONNA'SDEEP DISH

    High Medium

    PIERCE'S PIZZA PIES

    60, 60

    70, 36

    High

    Medium

    36, 70

    50, 50

    FIGURE 9.6 Payoff Table for the Pizza Sellers Prisoners Dilemma Copyright 2000 by W.W. Norton & Company

  • EUROPE

    Yes No

    UNITED STATES

    3, 3Yes

    No 4, 1

    2, 4

    1, 2

    FIGURE 9.7 Payoff table for the Military Intervention Problem Copyright 2000 by W.W. Norton & Company