博弈论实例ShubikAuction课件.xlsx

Shubik Auction A B n p In these sheets you can input A B and p in the three yellow cells The maximum number n of rounds is fixed on every sheet After inputting the numbers backward induction analysis is performed automatically The grey cells behind the arrows indicate which moves are chosen the expected payoffs for each position are also updated The random moves are indicated in green 5 rounds 6 rounds 8 rounds 13 rounds 14 rounds 15 rounds 16 rounds 15 rounds and auctioneer 25 worth of the item for Ann 65 worth of the item for Beth Random version At each step the game will terminate with probability 0 2 AnnBethAnnBeth 10203040 Start Ann151515 6 5 5 5 26 25 Beth000 7 20 20 20 27 40 Sum15 passendpassendpassendpassend 01515 10 10 5 5 30 55004545 20 2025 Ann 50 25 40 pass 30 25 worth of the item for Ann worth of the item for Beth 45 worth of the item for Ann 35 worth of the item for Beth Random version At each step the game will terminate with probability 0 55 AnnBethAnnBeth 10203040 Start Ann353535 7 4 4 3 4 3 28 28 25 Beth000 0 3 19 19 18 18 33 Sum35 passendpassendpassendpassend 03535 10 101515 30 25001515 20 20 5 AnnBeth 5060 25 50 50 33 25 25 passendpass 30 5 5 5 40 40 worth of the item for Ann worth of the item for Beth 45 worth of the item for Ann 35 worth of the item for Beth Random version At each step the game will terminate with probability 0 01 AnnBethAnnBeth 10203040 Start Ann0 9 6 10 10 10 30 30 30 30 Beth2514 9151515 5 2 5 5 5 Sum25 passendpassendpassendpassend 03535 10 101515 30 25001515 20 20 5 AnnBethAnnBeth 50607080 50 50 50 50 70 70 70 25 25 25 25 45 45 45 passendpassendpassendpass 30 5 5 50 50 25 25 5 40 40 25 25 60 60 worth of the item for Ann worth of the item for Beth 30 worth of the item for Ann 70 worth of the item for Beth Random version At each step the game will terminate with probability 0 01 AnnBethAnnBeth 10203040 Start Ann202020 0 1000 20 20 Beth000 19 20 20 20 39 40 Sum20 passendpassendpassendpassend 02020 10 1000 30 60005050 20 2030 AnnBethAnnBethAnn 5060708090 20 20 40 40 40 40 60 60 60 40 40 59 60 60 60 79 80 80 passendpassendpassendpassendpass 30 20 20 50 50 40 40 70 70 30 40 401010 60 60 10 10 worth of the item for Ann worth of the item for Beth 0 7 BethAnnBethAnn 100110120130 60 80 80 80 80 100 100 100 80 99 100 100 100 119 120 120 endpassendpassendpassendpass 60 60 90 90 80 80 110 110 80 80 30 30 100 100 50 50 45 worth of the item for Ann 35 worth of the item for Beth Random version At each step the game will terminate with probability 0 45 AnnBethAnnBeth 10203040 Start Ann3535353 75151515 16 5 Beth000 4 3 20 20 20 24 40 Sum35 passendpassendpassendpassend 03535 10 101515 30 25001515 20 20 5 AnnBethAnnBethAnn 5060708090 5 5 36 25 25 25 56 45 45 40 40 44 60 60 60 64 80 80 passendpassendpassendpassendpass 30 5 5 50 50 25 25 70 70 5 40 40 25 25 60 60 45 45 worth of the item for Ann worth of the item for Beth BethAnnBethAnn 100110120130 45 90 90 90 110 110 110 110 130 80 83 98 98 97 97 106 106 95 endpassendpassendpassendpassend 45 45 90 90 65 65 110 110 85 80 80 65 65 100 100 85 85 120 Beth 140 130 95 pass 85 120 30 worth of the item for Ann 110 worth of the item for Beth Random version At each step the game will terminate with probability 0 3 AnnBethAnnBeth 10203040 Start Ann0 1 10 10 10 21 30 30 30 Beth1006390909043707070 Sum100 passendpassendpassendpassend 02020 10 1000 30 100009090 20 2070 AnnBethAnnBethAnn 5060708090 41 50 50 50 61 70 70 70 81 235050503303030 17 passendpassendpassendpassendpass 30 20 20 50 50 40 40 70 70 70 40 405050 60 603030 worth of the item for Ann worth of the item for Beth BethAnnBethAnn 100110120130 90 90 90 101 110 110 110 116 123 101010 37 10 10 10 111 107 endpassendpassendpassendpassend 60 60 90 90 80 80 110 110 100 80 801010 100 100 10 10 120 BethAnn 140150 123 120 120 107 140 140 passendpass 100 130 130 120 30 30 50 worth of the item for Ann 30 worth of the item for Beth Random version At each step the game will terminate with probability 0 7 AnnBethAnnBeth 10203040 Start Ann26 526 5 5 1 5 16 486 48 25 25 14 Beth0 330 331 11 1 20 20 19 19 40 Sum26 8 passendpassendpassendpassend 04040 10 102020 30 20001010 20 20 10 AnnBethAnnBethAnn 5060708090 14 45 45 34 34 65 65 54 54 40 39 39 60 60 59 59 80 80 passendpassendpassendpassendpass 3000 50 50 20 20 70 70 10 40 40 30 30 60 60 50 50 worth of the item for Ann worth of the item for Beth BethAnnBethAnn 100110120130 85 85 74 74 105 105 94 94 126 79 79 100 100 99 99 119 119 118 endpassendpassendpassendpassend 40 40 90 90 60 60 110 110 80 80 80 70 70 100 100 90 90 120 BethAnnBeth 140150160 126 115 115 150 150 118 137 137 130 130 passendpassendpass 80 130 130 100 100 120 110 110 140 140 30 worth of the item for Ann 50 worth of the item for Beth 10 worth of the item for the auctioneer Random version At each step the game will terminate with probability 0 5 AnnBethAnnBeth 10203040 Start Ann55 10 10 10 15 30 30 Beth1515303030 51010 Auctioneer10 pass10 end20 pass20 end20 pass50 end60 pass60 end 02020 10 1000 40003030 20 20 00020204040 AnnBethAnnBethAnn 5060708090 30 35 50 50 50 55 70 70 70 10 25 10 10 10 45 30 30 30 60 pass90 end100 pass100 end100 pass130 end140 pass140 end140 pass 30 30 20 20 50 50 40 40 70 1010 40 40 10 10 60 60 30 60608080100100120120140 worth of the item for Ann worth of the item for Beth worth of the item for the auctioneer BethAnnBethAnn 100110120130 75 90 90 90 95 110 110 110 113 65 50 50 50 8