博弈论实例Dividing5课件.xlsx

Dividing 5 Items Worksheet In the different worksheets of this file you can create data used for all other sheets For this data you can calculate the optimal possible values apply C C apply ABABA apply ABABB apply ABBAB apply ABBAA for complete information and also apply C C apply ABABA apply ABABB apply ABBAB apply ABBAA for incomplete information Here you can input the values of the five items called D E F G and H for Ann and Beth It is the only input possible in the whole Excel file items DEFGHSum value for A0 7 0 122 0 188 0 732 0 3832 126 value for B0 329 0 639 0 186 0 594 0 7932 54 0 000 000 000 000 000 000 000 000 00 0 000 000 000 000 000 000 00 0 00 0 000 000 000 00 0 000 000 000 000 000 000 00 0 000 000 000 000 000 000 00 0 000 000 000 000 000 000 00 0 000 00 0 160 140 120 10 080 060 040 020 0 0 2 0 4 0 6 0 8 1 1 2 Inefficiency Inequity 0 160 140 120 10 080 060 040 020 0 0 2 0 4 0 6 0 8 1 1 2 Inefficiency Inequity Here the maximum possible sum of satisfaction the maximum possible minimum satisfaction and the inequity the minimum possible absolute value of the difference between the satisfactions are computed This is done by looking at all 32 possible distributions and by calculating the satisfactions for all these 32 cases itemsDEFGHSum value for A0 7 0 12248 0 1883023 0 73197 0 383332 13 value for B0 32853 0 63901 0 1856667 0 59391 0 792652 54 Max sum of sat There are 32 distributions of the 5 items The letters on the grey bars shows indicate which one belong to Ann in each case 132 6 satisfactionsatisfactionsum of satisfactions1 Ann gets00 0 Beth gets2 54 100 0 100 0 2 D 0 7032 9 2 2187 1 120 0 3E 0 125 8 1 9074 8 80 6 4F 0 198 9 2 3592 7 101 5 5G 0 7334 4 1 9576 6 111 0 6H 0 3818 0 1 7568 8 86 8 7 DE 0 8238 7 1 5761 9 100 6 8 DF 0 8941 8 2 0379 8 121 5 9 DG 1 4367 4 1 6263 7 131 0 10 DH 1 0851 0 1 4255 9 106 8 11EF 0 3114 6 1 7267 5 82 1 12EG 0 8540 2 1 3151 5 91 6 13EH 0 5123 8 1 1143 6 67 4 14FG 0 9243 3 1 7669 3 112 6 15FH 0 5726 9 1 5661 5 88 4 16GH 1 1252 5 1 1545 4 97 9 17 DEF 1 0147 5 1 3954 6 102 1 18 DEG 1 5573 1 0 9838 5 111 6 19 DEH 1 2156 7 0 7830 7 87 4 20 DFG 1 6276 2 1 4356 4 132 6 21 DFH 1 2759 8 1 2348 5 108 4 22 DGH 1 8285 4 0 8232 5 117 9 23EFG 1 0449 0 1 1244 1 93 2 24EFH 0 6932 6 0 9236 3 69 0 25EGH 1 2458 2 0 5120 2 78 5 26FGH 1 3061 3 0 9738 1 99 4 27 DEFG 1 7482 0 0 7931 2 113 2 28 DEFH 1 3965 6 0 5923 4 89 0 29 DEGH 1 9491 1 0 197 3 98 5 30 DFGH 2 0094 2 0 6425 2 119 4 31EFGH 1 4367 1 0 3312 9 80 0 32 DEFGH 2 13 100 0 0 000 0 100 0 Example of data giving less than 50 for Ann 0 28 0 307 1 712 2 091 2 056 0 259 1 295 2 465 3 086 2 143 55599 55599 Max min satinequity 63 7 4 minimum satisfaction difference of satisfactions 0 0 100 32 9 54 5 8 69 8 9 84 34 4 42 18 0 51 38 7 23 41 8 38 63 7 4 51 0 5 14 6 53 40 2 11 23 8 20 43 3 26 26 9 35 Here the maximum possible sum of satisfaction the maximum possible minimum satisfaction and the inequity the minimum possible absolute value of the difference between the satisfactions are computed This is done by looking at all 32 possible distributions and by calculating the satisfactions for all these 32 cases 45 4 7 47 5 7 38 5 35 30 7 26 56 4 20 48 5 11 32 5 53 44 1 5 32 6 4 20 2 38 38 1 23 31 2 51 23 4 42 7 3 84 25 2 69 12 9 54 0 0 100 0 31566157 4 518 10 96 5 928 15 18 9 9 Example of data giving less than 50 for Ann C C Cut and Choose complete information itemsDEFGHSum value for A0 70000 12250 18830 73200 3833 2 1260976 2 value for B0 32850 63900 18570 59390 7926 2 5397656 4 Ann has the choice between 32 proposals for a division which are shown below The letters on the gray line show what Ann proposes for herself Below on the left are payoffs and satisfactions for Ann and Beth Beth accepts if that means more than 50 satisfaction otherwise she flips The resulting satisfactions are shown to the right Then Ann checks these values and chooses the proposal maximizing her payoff there her choice and the corresponding satisfaction for Beth are shown in columns I and J 1 0 000 0 0 0 2 54100 0 B accepts100 0 2 D 0 7032 9 32 9 2 2187 1 B accepts87 1 3E 0 125 8 5 8 1 9074 8 B accepts74 8 4F 0 198 9 8 9 2 3592 7 B accepts92 7 5G 0 7334 4 34 4 1 9576 6 B accepts76 6 6H 0 3818 0 18 0 1 7568 8 B accepts68 8 7 DE 0 8238 7 38 7 1 5761 9 B accepts61 9 8 DF 0 8941 8 41 8 2 0379 8 B accepts79 8 9 DG 1 4367 4 67 4 1 6263 7 B accepts63 7 10 DH 1 0851 0 51 0 1 4255 9 B accepts55 9 11EF 0 3114 6 14 6 1 7267 5 B accepts67 5 12EG 0 8540 2 40 2 1 3151 5 B accepts51 5 13EH 0 5123 8 76 2 chosen by Ann 1 1143 6 Bflips56 4 56 4 14FG 0 9243 3 43 3 1 7669 3 B accepts69 3 15FH 0 5726 9 26 9 1 5661 5 B accepts61 5 16GH 1 1252 5 47 5 1 1545 4 Bflips54 6 17 DEF 1 0147 5 47 5 1 3954 6 B accepts54 6 18 DEG 1 5573 1 26 9 0 9838 5 Bflips61 5 19 DEH 1 2156 7 43 3 0 7830 7 Bflips69 3 20 DFG 1 6276 2 76 2 chosen by Ann 1 4356 4 B accepts56 4 56 4 21 DFH 1 2759 8 40 2 1 2348 5 Bflips51 5 22 DGH 1 8285 4 14 6 0 8232 5 Bflips67 5 23EFG 1 0449 0 51 0 1 1244 1 Bflips55 9 24EFH 0 6932 6 67 4 0 9236 3 Bflips63 7 25EGH 1 2458 2 41 8 0 5120 2 Bflips79 8 26FGH 1 3061 3 38 7 0 9738 1 Bflips61 9 27 DEFG 1 7482 0 18 0 0 7931 2 Bflips68 8 28 DEFH 1 3965 6 34 4 0 5923 4 Bflips76 6 29 DEGH 1 9491 1 8 9 0 197 3 Bflips92 7 30 DFGH 2 0094 2 5 8 0 6425 2 Bflips74 8 31EFGH 1 4367 1 32 9 0 3312 9 Bflips87 1 32 DEFGH 2 13100 0 0 0 0 000 0 Bflips100 0 DIV 0 achieved satisfaction ABABA complete information This sheet works only if the values are all smaller than 1000Ann chooses one then Beth then Ann then Beth then Ann Data itemsDEFGHSum value for A0 7 0 122 0 188 0 732 0 383 2 126176 2 achieved value for B0 329 0 639 0 186 0 594 0 7932 54056 4 satisfaction 1 Ann s 0 7 0 1221000 0 732 0 3830 1883Ann s last choice is Beth s lowest item 3 Choice0 186 0 329 0 6391000 0 594 0 793it is marked by 1000 here and below 1 Beth s0 1220 710001000 0 732 0 383Beth s last choice is Ann s lowest item among the remaining four 2 Choice0 32910001000 0 594 0 7930 639it is marked by 1000 here and below 1 Ann s 100010001000 0 732 0 3830 7and so on 2 Choice0 329100010001000 0 594 0 793 1 Beth s0 383100010001000 0 7321000 1 Choice100010001000 0 59410000 7926 1 Ann s 100010001000100010000 732 1 Choice0 59410001000100010001000 1 62 1 43 This sheet works only if the values are all smaller than 1000 Ann s last choice is Beth s lowest item it is marked by 1000 here and below Beth s last choice is Ann s lowest item among the remaining four it is marked by 1000 here and below ABABB complete information This sheet works only if the values are all smaller than 1000Ann chooses one then Beth then Ann then Beth chooses two Data itemsDEFGHSum value for A0 7 0 122 0 188 0 732 0 383 2 126167 4 achieved value for B0 329 0 639 0 186 0 594 0 7932 54063 7 satisfaction 1 Beth s0 1220 71000 0 188 0 732 0 383Beth s last choice is Ann s lowest item 3 Choice0 3291000 0 186 0 594 0 7930 639it is marked by 1000 here and below 1 Beth s0 1880 710001000 0 732 0 383Beth s second last choice is Ann s lowest item among the remaining four 2 Choice0 32910001000 0 594 0 7930 1857it is marked by 1000 here and below 1 Ann s 100010001000 0 732 0 3830 7and so on 2 Choice0 329100010001000 0 594 0 793 1 Beth s0 383100010001000 0 7321000 1 Choice100010001000 0 59410000 7926 1 Ann s 100010001000100010000 732 1 Choice0 59410001000100010001000 1 43 1 62 This sheet works only if the values are all smaller than 1000 Beth s last choice is Ann s lowest item it is marked by 1000 here and below Beth s second last choice is Ann s lowest item among the remaining four it is marked by 1000 here and below ABBAB complete information This sheet works only if the values are all smaller than 1000Ann chooses one then Beth chooses two then Ann then Beth Data itemsDEFGHSum value for A0 7 0 122 0 188 0 732 0 383 2 126143 3 achieved value for B0 329 0 639 0 186 0 594 0 7932 54069 3 satisfaction 1 Beth s0 1220 71000 0 188 0 732 0 383Beth s last choice is Ann s lowest item 3 Choice0 3291000 0 186 0 594 0 7930 639it is marked by 1000 here and below 1 Ann s 0 710001000 0 732 0 3830 1883Ann s last choice is Beth s lowest item among the remaining four 2 Choice0 186 0 32910001000 0 594 0 793it is marked by 1000 here and below 1 Beth s0 3830 710001000 0 7321000and so on 2 Choice0 32910001000 0 59410000 7926 1 Beth s0 7100010001000 0 7321000 1 Choice100010001000 0 59410000 3285 1 Ann s 100010001000100010000 732 1 Choice0 59410001000100010001000 0 92 1 76 This sheet works only if the values are all smaller than 1000 Beth s last choice is Ann s lowest item it is marked by 1000 here and below Ann s last choice is Beth s lowest item among the remaining four it is marked by 1000 here and below ABBAA complete information This sheet works only if the values are all smaller than 1000Ann chooses one then Beth twice then Ann twice Data itemsDEFGHSum value for A0 7 0 122 0 188 0 732 0 383 2 126176 2 achieved value for B0 329 0 639 0 186 0 594 0 7932 54056 4 satisfaction 1 Ann s 0 7 0 1221000 0 732 0 3830 1883Ann s last choice is Beth s lowest item 3 Choice0 186 0 329 0 6391000 0 594 0 793it is marked by 1000 here and below 1 Ann s 1000 0 1221000 0 732 0 3830 7Ann s second last choice is Beth s lowest item among the remaining four 2 Choice0 3291000 0 6391000 0 594 0 793it is marked by 1000 here and below 1 Beth s0 122100010001000 0 732 0 383and so on 2 Choice100010001000 0 594 0 7930 639 1 Beth s0 383100010001000 0 7321000 1 Choice100010001000 0 59410000 7926 1 Ann s 100010001000100010000 732 1 Choice0 59410001000100010001000 1 62 1 43 This sheet works only if the values are all smaller than 1000 Ann s last choice is Beth s lowest item it is marked by 1000 here and below Ann s second last choice is Beth s lowest item among the remaining four it is marked by 1000 here and below 1 42 3 C C incomplete information 0 008 0 225 these are the probabilities for a one item heap to be better than a four item heap or a two item heap to be better than a three item heap itemsDEFGHI value for A0 7 0 122 0 188 0 732 0 3830 2 12667 achieved value for B0 329 0 639 0 186 0 594 0 79302 5464 satisfaction 10 60 Expected value for A in percent 00 0 0 2 54 100 100 100 2 DExp 0 733 33 33 0 332 2 21187 87 87 3E 0 1226 6 6 0 065 1 90175 75 75 4F 0 1889 9 9 0 095 2 35493 93 93 5G 0 73234 34 34 0 347 1 94677 77 77 6H 0 38318 18 18 0 185 1 74769 69 69 7 DE 0 82239 39 39 0 438 1 57262 62 62 8 DF 0 88842 42 42 0 455 2 02680 80 80 9 DG 1 43267 67 67 chosen0 6740 595 1 61764 64 64 0 637 0 637 10 DH 1 08351 51 51 0 505 1 41956 56 56 11EF 0 31115 15 15 0 305 1 71568 68 68 12EG 0 85440 40 40 0 446 1 30751 51 51 13EH 0 50624 76 76 0 356 1 10844 56 56 14FG 0 9243 43 43 0 463 1 7669 69 69 15FH 0 57227 27 27 0 373 1 56161 61 61 16GH 1 11552 48 48 0 513 1 15345 55 55 17 DEF 1 01148 48 48 0 514 1 38755 55 55 18 DEG 1 55473 27 27 0 373 0 97839 61 61 19 DEH 1 20657 43 43 0 463 0 7831 69 69 20 DFG 1 6276 76 76 0 356 1 43256 56 56 21 DFH 1 27260 40 40 0 446 1 23349 51 51 22 DGH 1 81585 15 15 0 305 0 82532 68 68 23EFG 1 04349 51 51 0 505 1 12144 56 56 24EFH 0 69433 67 67 0 595 0 92236 64 64 25EGH 1 23858 42 42 0 455 0 51420 80 80 26FGH 1 30461 39 39 0 438 0 96838 62 62 27 DEFG 1 74382 18 18 0 185 0 79331 69 69 28 DEFH 1 39466 34 34 0 347 0 59423 77 77 29 DEGH 1 93891 9 9 0 095 0 1867 93 93 30 DFGH 2 00494 6 6 0 065 0 63925 75 75 31EFGH 1 42667 33 33 0 332 0 32913 87 87 32 DEFGH 2 126 100 0 0 0 00 100 100 0 555 these are the probabilities for a one item heap to be better than a four item heap or a two item heap to be better than a three item heap Expected value for A in percent ABABA incomplete information Ann chooses one then Beth then Ann then Beth then Ann Dataachieved distribution itemsDEFGHSumDEFG value for A0 7 0 122 0 188 0 732 0 383 2 1260 70 188 0 732 value for B0 329 0 639 0 186 0 594 0 793 2 5400 639 Ann s 0 7320 7 0 122 0 1880 0 383 1 ChoiceG0 329 0 639 0 1860 0 793 Beth s0 7 0 122 0 18800 1 ChoiceH0 793 0 329 0 639 0 18600 Ann s 0 70 0 122 0 18800 2 ChoiceD0 0 639 0 18600 Beth s00 0 18800 2 ChoiceE0 63900 0 18600 Ann s 0 18800000 3 ChoiceF00000 achieved HSumsatisfaction 1 62076 2 0 793 1 43256 4 ABABB incomplete information Ann chooses one then Beth then Ann then Beth takes two Dataachieved distribution itemsDEFGHSumDEFG value for A0 7 0 122 0 188 0 732 0 383 2 1260 70 732 value for B0 329 0 639 0 186 0 594 0 793 2 5400 639 0 186 Ann s 0 732