14.12 Economic Applications of Game Theory Professor: Muhamet - - PDF document

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14.12 Economic Applications of Game Theory Professor: Muhamet - - PDF document

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14.12 Economic Applications of Game Theory Professor: Muhamet Yildiz 1 Merthyr Banbury Prime Meridian Luton WALES Oxford Tydfil Swindon Chelmsford London Swansea Gillingham Cardiff Bristol Newbury Barnstaple Maidstone UNITED

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SLIDE 1

14.12 Economic Applications of Game Theory

  • Professor: Muhamet Yildiz

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SLIDE 2

Truro Falmouth Plymouth Torquay Exeter Bodmin Celtic Sea Tiverton Cardiff Bristol Newbury London Prime Meridian Swindon Oxford Luton Banbury Merthyr Tydfil Swansea WALES UNITED KINGDOM Barnstaple Havant Bournemouth Brighton Eu Dieppe Yuetot Rouen Lisieux Caen Evreux La Ferte-Mace FRANCE BASSE-NORMANDIE Coutances St.-Lo 136 m 104 m Perros-Guirec 90 m English Channel Carentan Fecamp 50o 49o 1o 1o 2o 3o 2o Berck-sur-Mer Hastings Maidstone Chelmsford Gillingham Le Havre Cherbourg

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Image by MIT OpenCourseWare.

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SLIDE 3

Name of the game

Game Theory = Multi-person decision theory

  • The outcome is determined by the actions

independently taken by multiple decision makers.

  • Strategic interaction.
  • Need to understand what the others will do

... what the others think that you will do

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SLIDE 4

A coordination game

Left Right

Top

(1,1)

(0,0)

Bottom

(0,0)

(1,1 )

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SLIDE 5

A game

2 1

L m R T (1,1) (0,2) (2,1) M (2,2) (1,1) (0,0) B (1 ,0) (0,0) (-1,1)

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SLIDE 6

A coordination game

Left Right

Top

(1,1)

(0,0)

Bottom

(0,0)

(1,1 )

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SLIDE 7

Battle of Sexes

Baseball Opera Baseball (2,1 )

(0,0)

Opera

(0,0)

(1,2)

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SLIDE 8

Battle of The Sexes with perfect information

1 B

  • 2,1

0,0 0,0 1,2 9

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SLIDE 9

Battle of Sexes with outside option

1 Exit

B

(2,1) (0,0) (3/2,3/2) B

  • (0,0)

(1,2)

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SLIDE 10

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Hawk-Dove game

(V V /2) (0,V ) (V ,0)

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − 2 , 2

V > c

/2,

c V c V

Image by MIT OpenCourseWare.

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SLIDE 11

Hawk-Dove game

(y,y]

V<c

(V,O)

~

(OJ') (V/2 )

Hawk-Dove game

(V V /2) (0,V ) (V ,0)

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − 2 , 2

V < c

/2,

c V c V

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Image by MIT OpenCourseWare.

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SLIDE 12

Chicken

(-1,-1) (1,0)

~

~ .:.:.~.

:-.. . y

;' '

(0,1)

(1/2,1/2)

'' ..

  • '=..,

Chicken

) (0,1) (1,0) (-1,-1) (1/2,1/2

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Image by MIT OpenCourseWare.

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SLIDE 13

Stag Hunt

~

(3,3) (3,0)

¥

(0,3) (5,5) zyxwvutsrponmlkjihgfedcbaZYWVUTSRQPONMLJHGFEDCBA

Stag Hunt

(5,5) (0,4) (4,0) (2,2)

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Image by MIT OpenCourseWare.

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SLIDE 14

MIT OpenCourseWare http://ocw.mit.edu

14.12 Economic Applications of Game Theory

Fall 2012 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.