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

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 KINGDOM Tiverton 2 o Hastings Celtic Sea Exeter Havant Brighton Bodmin Bournemouth Berck-sur-Mer Torquay Truro Plymouth Eu Falmouth 50 o English Channel Dieppe Fecamp Cherbourg Yuetot 90 m Le Havre Carentan Rouen 104 m Caen Lisieux St.-Lo 136 m 49 o FRANCE Coutances Evreux Perros-Guirec BASSE-NORMANDIE La Ferte-Mace 3 o 2 o 1 o 1 o Image by MIT OpenCourseWare. 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 4

A coordination game Left Right (0,0) (1,1) Top (0,0) (1,1 ) Bottom 5

A game 2 m R 1 L T (1,1) (0,2) (2,1) (2,2) (1,1) (0,0) M (1 ,0) (0,0) (-1,1) B 6

A coordination game Left Right (0,0) (1,1) Top (0,0) (1,1 ) Bottom 7

Battle of Sexes Baseball Opera (0,0) Baseball (2,1 ) (0,0) Opera (1,2) 8

The Sexes with perfect information Battle of 1 o B 2,1 0,0 0,0 1,2 9

Battle of Sexes with outside option 1 Exit B 0 (2,1) (0,0) (3/2,3/2) B o (0,0) (1,2) 10

Hawk-Dove game V > c − − ⎛ ⎞ ( V ,0) V c V c ⎜ , ⎟ ⎝ 2 2 ⎠ (0, V ) ( V V /2, /2) Image by MIT OpenCourseWare. 11

~ Hawk-Dove game Hawk-Dove game V<c (y,y] (V , O) V < c ⎛ − − ⎞ V c V c ( V ,0) ⎜ ⎟ , ⎝ 2 2 ⎠ (OJ') (V /2 ) (0, V ) ( V V /2, /2) Image by MIT OpenCourseWare. 12

' .:.:.~. ~ ~ Chicken Chicken (-1,-1) (1,0) (-1,-1) (1,0) (0,1) (1 /2,1/2) (0,1) (1/2,1/2 ) :-.. . y ;' '' .. -'=.., Image by MIT OpenCourseWare. 13

~ Stag Hunt Stag Hunt (5 ,5) zyxwvutsrponmlkjihgfedcbaZYWVUTSRQPONMLJHGFEDCBA (2,2) (4,0) (3 ,3) (3 ,0) (0,4) (5,5) ¥ (0,3) Image by MIT OpenCourseWare. 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.