博弈论实例ABABAB课件.xlsx

Dividing 6 items the data input page Type the values of the items for Ann and Beth into the fields itemsDEFGHISum value for A25131422224100 value for B161724844100 In this Excel sheet you can simulate the games ABABAB ABBABA ABBAAB using the abbreviated method using S states as discussed in Section 9 3 It is not easy to actually see what items are chosen when To do so you have to start in row 74 on the sheets and see what item Ann chooses first It is the one where in cells D74 to I74 there is a bold 1 Then you have to choose the row where exactly this one is missing and look for bold 1s again This is Beth s item Proceeding in this way you obtain who chooses what The achieved satisfaction is shown in cells M6 and M7 on the three sheets Dividing 6 items the data input page Type the values of the items for Ann and Beth into the fields In this Excel sheet you can simulate the games ABABAB ABBABA ABBAAB using the abbreviated method using S states as discussed in Section 9 3 It is not easy to actually see what items are chosen when To do so you have to start in row 74 on the sheets and see what item Ann chooses first It is the one where in cells D74 to I74 there is a bold 1 Then you have to choose the row where exactly this one is missing and look for bold 1s again This is Beth s item Proceeding in this way you obtain who chooses what The achieved satisfaction is shown in cells M6 and M7 on the three sheets ABABAB when distributing 6 items items DEFGHISum value for A2513142222410062 Ann s satisfaction achieved value for B16172484410039 Beth s satisfaction achieved who moves gain forAnn DEFGHIrowAnnBethD Here all 64 S states are listed where an S state just lists all items that are still available A 1 indicates the item is still there 100 1Beth200 1Beth300 11Ann400 1Beth500 11Ann600 11Ann700 111Beth800 1Beth900 11Ann1000 11Ann1100 111Beth1200 11Ann1300 111Beth1400 111Beth1500 1111Ann1600 1Beth1700 11Ann1800 11Ann1900 111Beth2000 11Ann2100 111Beth2200 111Beth2300 1111Ann2400 11Ann2500 111Beth2600 111Beth2700 1111Ann2800 111Beth2900 1111Ann3000 1111Ann3100 11111Beth3200 1Beth33000 11Ann34000 11Ann35000 111Beth36000 11Ann37000 111Beth38000 111Beth39000 1111Ann40000 11Ann41000 111Beth42000 111Beth43000 1111Ann44000 111Beth45000 1111Ann46000 1111Ann47000 11111Beth48000 11Ann49000 111Beth50000 111Beth51000 1111Ann52000 111Beth53000 1111Ann54000 1111Ann55000 11111Beth56000 111Beth57000 1111Ann58000 1111Ann59000 11111Beth60000 1111Ann61000 11111Beth62000 11111Beth63000 111111Ann64000 A bold 1 indicates the items the player to move would take in the corresponding state when playing optimally These values show the gain for Ann and Beth if the player to move chooses the corresponding item in that S position The bold ones occur in perfect play 62 39 Here all 64 S states are listed where an S state just lists all items that are still available A 1 indicates the item is still there 62 Ann s sum of values obtained 39 Beth s sum of values obtained Beth EFGHIDEFGHI 00 00 0000 00 0000 0000 000000 00 0000 0000 000000 0000 000000 000000 00000000 00 0000 0000 000000 0000 000000 000000 00000000 0000 000000 000000 00000000 000000 00000000 00000000 0000000000 0 000 000 00000 000 00000 00000 0000000 000 00000 00000 0000000 00000 Ann s satisfaction achieved Beth s satisfaction achieved 0000000 0000000 000000000 000 00000 00000 0000000 00000 0000000 0000000 000000000 00000 0000000 0000000 000000000 0000000 000000000 000000000 00000000000 These values show the gain for Ann and Beth if the player to move chooses the corresponding item in that S position The bold ones occur in perfect play ABBABA when distributing 6 items items DEFGHISum value for A2513142222410052 Ann s satisfaction achieved value for B16172484410076 Beth s satisfaction achieved who moves gain forAnn DEFGHIrowAnnBethD Here all 64 S states are listed where an S state just lists all items that are still available A 1 indicates the item is still there 100 1Ann200 1Ann300 11Beth400 1Ann500 11Beth600 11Beth700 111Ann800 1Ann900 11Beth1000 11Beth1100 111Ann1200 11Beth1300 111Ann1400 111Ann1500 1111Beth1600 1Ann1700 11Beth1800 11Beth1900 111Ann2000 11Beth2100 111Ann2200 111Ann2300 1111Beth2400 11Beth2500 111Ann2600 111Ann2700 1111Beth2800 111Ann2900 1111Beth3000 1111Beth3100 11111Beth3200 1Ann33000 11Beth34000 11Beth35000 111Ann36000 11Beth37000 111Ann38000 111Ann39000 1111Beth40000 11Beth41000 111Ann42000 111Ann43000 1111Beth44000 111Ann45000 1111Beth46000 1111Beth47000 11111Beth48000 11Beth49000 111Ann50000 111Ann51000 1111Beth52000 111Ann53000 1111Beth54000 1111Beth55000 11111Beth56000 111Ann57000 1111Beth58000 1111Beth59000 11111Beth60000 1111Beth61000 11111Beth62000 11111Beth63000 111111Ann64000 A bold 1 indicates the items the player to move would take in the corresponding state when playing optimally These values show the gain for Ann and Beth if the player to move chooses the corresponding item in that S position The bold ones occur in perfect play 52 76 Here all 64 S states are listed where an S state just lists all items that are still available A 1 indicates the item is still there 52 Ann s sum of values obtained 76 Beth s sum of values obtained Beth EFGHIDEFGHI 00 00 0000 00 0000 0000 000000 00 0000 0000 000000 0000 000000 000000 00000000 00 0000 0000 000000 0000 000000 000000 00000000 0000 000000 000000 00000000 000000 00000000 00000000 0000000000 0 000 000 00000 000 00000 00000 0000000 000 00000 00000 0000000 00000 Ann s satisfaction achieved Beth s satisfaction achieved 0000000 0000000 000000000 000 00000 00000 0000000 00000 0000000 0000000 000000000 00000 0000000 0000000 000000000 0000000 000000000 000000000 00000000000 These values show the gain for Ann and Beth if the player to move chooses the corresponding item in that S position The bold ones occur in perfect play ABBAAB when distributing 6 items items DEFGHISum value for A2513142222410052 Ann s satisfaction achieved value for B16172484410076 Beth s satisfaction achieved who moves gain forAnn DEFGHIrowAnnBethD Here all 64 S states are listed where an S state just lists all items that are still available A 1 indicates the item is still there 100 1Beth200 1Beth300 11Ann400 1Beth500 11Ann600 11Ann700 111Ann800 1Beth900 11Ann1000 11Ann1100 111Ann1200 11Ann1300 111Ann1400 111Ann1500 1111Beth1600 1Beth1700 11Ann1800 11Ann1900 111Ann2000 11Ann2100 111Ann2200 111Ann2300 1111Beth2400 11Ann2500 111Ann2600 111Ann2700 1111Beth2800 111Ann2900 1111Beth3000 1111Beth3100 11111Beth3200 1Beth33000 11Ann34000 11Ann35000 111Ann36000 11Ann37000 111Ann38000 111Ann39000 1111Beth40000 11Ann41000 111Ann42000 111Ann43000 1111Beth44000 111Ann45000 1111Beth46000 1111Beth47000 11111Beth48000 11Ann49000 111Ann50000 111Ann51000 1111Beth52000 111Ann53000 1111Beth54000 1111Beth55000 11111Beth56000 111Ann57000 1111Beth58000 1111Beth59000 11111Beth60000 1111Beth61000 11111Beth62000 11111Beth63000 111111Ann64000 A bold 1 indicates the items the player to move would take in the corresponding state when playing optimally These values show the gain for Ann and Beth if the player to move chooses the corresponding item in that S position The bold ones occur in perfect play 52 76 Here all 64 S states are listed where