payoff

Assignment4

erthefollowinggametree.

(1)Findthetofstrategiesofeachplayer

(2)dtoindicatearrows.

(3)Findthebackwardinductionequilibrium(strategyprofile),theequilibrium

outcome(equilibriumpath),andtheequilibriumpayoff.

gofCountry1mustdecidewhethertohavehisarmyattackthearmyofCountry2

ventofanattack,thearmy

ofCountry2mayeitherfightorretreatoverabridgetoCountry2’off

associatedwithoccupyingtheislandis100,thepayoffassociatedwithnotoccupyingthe

betweenthetwoarmiesgiveachofthecountriesapayoffof-100.

(1)Describethisgameusingagametree,andfindthebackwardinductionequilibrium.

(2)AssumethatthebridgeconnectingtheislandtoCountry2isdestroyed,thuliminating

theCountry2’sthischangeaffectthegametreeandthe

equilibrium?

1

2

3

3

4

1,4,6,8

7,3,1,2

2,4,6,8

0,-3,2,2

1000,2,8,41

12,35,7,9

7,1,3,2

U

D

U

D

U

D

L

R

u

m

d

erthefollowinggametree.

(1)Findthetofstrategiesforbothplayers.

(2)Translatethegametreeintothenormalformreprentation.

(3)FindthepurestrategyNEofthenormalformgame.

erthefollowingCoordinationgame.

(1)hequentialgameusingthebackward

inductionmethod(indicatetheoptimalactionswitharrows).Whatisthebackwardinduction

outcome(orpath)?

(2)Whohasadvantages:thefirstmover,thecondmover,orboth?Explainwhy.

Sally

Harry

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