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1、5.2Example(2)1e3,831.1x2.3f31-1,7<1><α>g30.5y12,600,0Figure4.10e1,030.51.2x2.3f23-2,7<1><1-α>g3y2-1,90,0e3f3g3x1x22,4-1.5,70.5,7.5x1y21.5,4-0.5,3.51,3y1x20.5,0-1,3.5-0.5,4.5y1y20,00,00,02e3,831.1x2.3f31-1,7<1><α>g30.5y12,600,0Figure4.10e1,030.51.2x2.3
2、f23-2,7<1><1-α>g3y2-1,90,0Player2’sconditionallyexpectedpayoff(sequentialvalue)wouldbe8α+−=0(1αα)8ifshechose,e37αα+−=7(1)7ifshechosef,or36ααα+−=−9(1)93ifshechose.g33e3,831.1x2.3f31-1,7<1><α>g30.5y12,60,00Figure4.10e1,030.51.2x2.3f23-2,7<1><1-α>g3y2-1,
3、90,0Somovee3wouldbeoptimalforplayer2atstate3whenboth8α≥7and8α≥9-3α.Thatis,whenα≥7/8.4e3,831.1x2.3f31-1,7<1><α>g30.5y12,600,0Figure4.10e1,030.51.2x2.3f23-2,7<1><1-α>g3y2-1,90,0Somovef3wouldbeoptimalforplayer2atstate3whenboth78≥ααand7≥−93.Thatis,when.2/
4、3≤≤α78/5e3,831.1x2.3f31-1,7<1><α>g30.5y12,600,0Figure4.10e1,030.51.2x2.3f23-2,7<1><1-α>g3y2-1,90,0Somoveg3wouldbeoptimalforplayer2atstate3whenboth793≤−αααand.893≤−Thatis,whneα≤2/3.6e3,831.1x2.3f31-1,7<1><α>g30.5y12,60,00Figure4.10e1,030.51.2x2.3f23-2,
5、7<1><1-α>g3y2-1,90,0Movee3wouldbeoptimalforplayer2atstate3whenα≥7/8.Moveg3wouldbeoptimalforplayer2atstate3whenα≤2/3.Thereforethereisnovalueofαforwhiche3andg3bothwouldbeoptimalforplayer2atstate3.7e3,831.1x2.3f31-1,7<1><α>g30.5y12,60,00Figure4.10e1,030.
6、51.2x2.3f23-2,7<1><1-α>g3y2-1,90,0Sotheonlypossiblesupportsatinformationstate3forasequentialequilibriumare{e3},{f3},{g3},{e3,f3},and{f3,g3}.Whynot{e3,g3},{e3,f3,g3}?8e3,831.1x2.3f31-1,7<1><α>g30.5y12,60,00Figure4.10e1,030.51.2x2.3f23-2,7<1><1-α>g3y2-1
7、,90,0Rememberthate3wouldbeoptimalforplayer2whenα≥7/8,andf3wouldbeoptimalforplayer2when2/3≤α≤7/8.Sothereisajointatα=7/8,andhence(e3,f3)couldbeasupport.9e3,831.1x2.3f31-1,7<1><α>g30.5y12,60,00Figure4.10e1,030.51.2x2.3f23-2,7<1><1-α>g3y2-1,90,0Rememberth
8、atf3wouldbeoptimalforplayer2when2/3≤α≤7/8,andg3wouldbeoptimalforplayer2whenα≤2/3.Sothereisajointatα=2/3,andhence(f3,g3)couldbeasupport.10e3,831.1x2.3f31-1,7<1><α>g30.5y12,60,00Figure4.10e1,030.51.2x2.3f23-2,7<1><1-α>g3y2-1,90,0Rememberthate3wo
