Σημειώσεις Παραδόσεων Θεωρία Παιγνίων Για Πολιτικούς...
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Transcript of Σημειώσεις Παραδόσεων Θεωρία Παιγνίων Για Πολιτικούς...
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: 2008
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70%
30%.
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, . (2004), :
, : [1990] ()
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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)
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()
() (2002), John Nash: , : ()
, (2000), ,: [1984] (A)
Morrow (1994), Game theory for politicalscientists, NJ: Princeton Univ. Press (M)
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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
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. - (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
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: .
,
() . 3, (DandN) .4, (DandS) .8, () .1,2
16/04
09/04
: , , . ,
(DandN) .5, 6, (DandS) .9, () . 5
07/05
2008
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- (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
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. 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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- (output) - (payoff):
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(expected payoff):
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: 0 75%
25% 100 0.75*0 +0.25*100=25( )
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( ):
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: : . . . .
.
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: : . . . .
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)
;
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(game tree).
() (extensive form ofthe game)
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()
: (initial node) (decision nodes) (terminal node) (branches)
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: ()(Gray) (Green)
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:
. (Green) ,
( )
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:
. (Green) ,
( )
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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
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;
1: (pure strategies) .
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;
, . O
.
(contingent pure strategies).
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;
Gray ads no ads .
Green , .
Gray.
(IN) (OUT ).
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;
Green :1) Gray Ads , IN, No Ads IN
2) Gray Ads, OUT, No Ads IN
3) Gray Ads, IN, No Ads OUT
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;
4) Gray Ads, OUT No Ads OUT
Green, . Green b, c:
1) , 2) OUT, IN 3) IN, OUT 4) OUT, OUT
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;
2: .
-
;
( ).
-
;
rollback ( ).
-
;
.
-
;
Green 2) Gray Ads, OUT, NoAds IN.
Gray Green Ads.
- : (Ads; Out,In)
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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
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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
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$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
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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
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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
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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
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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
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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
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:
.
----
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..
:
. .
: Nash
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Nash
. Nash
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: --
-
.
(--)
1/3 9
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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).
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;
:
Times, News
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..
. .. Bismark
. minmax,maxmin (cell by cell inspection)
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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
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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
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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
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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
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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
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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
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(assurance game):
(Chicken game):
(The battle of the Sexes):
-
(preemptivemoves)
x ante (focalpoints)
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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
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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
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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
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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
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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
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ROW
Left Right
COLUMN
1 4
2 3
Up
Down
(a)
EXERCISE 4.1 a Copyright 2000 by W.W. Norton & Company
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ROW
Left Right
COLUMN
1 2
4 3
Up
Down
(b)
EXERCISE 4.1 b Copyright 2000 by W.W. Norton & Company
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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
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: ( ;)
,
(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
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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
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(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
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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
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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