博弈论实例ShubikAuction3课件.xlsx

3 players, maximal 17 rounds. Random version. At each step the game will terminate with probability 0.4 45 worth of the item for Ann You can input the values A, B, C of the item for the three players and the probability p that the game ends suddenly after each round p in the four cells to the right. The maximum number of rounds is 17. 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. 45 worth of the item for Beth 45 worth of the item for Cindy AnnBethCindyAnn 10203040 Payoffs for Start Ann88-10-10-10355 Beth1515252525-800 Cindy00000-12-30-30 passendpassendpassendpassend 035-10-10-1000 8002525-205 150250015-30 When one player passes, we enter a two-player Shubik auction, see the tree branches below. 45 worth of the item for Beth A1 45 worth of the item for Cindy BethCindyBethCindy 10203040 Start 88-10-10-10-12-30-30 1515252525-555 passendpassendpassendpassend 03535-10-101515 35002525-20-20 45 worth of the item for Ann B2 45 worth of the item for Cindy AnnCindyAnnCindy 10203040 Start 88-10-10-10-12-30-30 1515252525-555 passendpassendpassendpassend 03535-10-101515 45002525-20-20 45 worth of the item for Ann c3 45 worth of the item for Beth AnnBethAnnBeth 10203040 Start 88-10-10-10-12-30-30 1515252525-555 passendpassendpassendpassend 03535-10-101515 45002525-20-20 45 worth of the item for Cindya4 45 worth of the item for Beth CindyBethCindyBeth 10203040 Start 88-10-10-10-12-30-30 1515252525-555 passendpassendpassendpassend 03535-10-101515 45002525-20-20 45 worth of the item for Cindyb5 45 worth of the item for Ann CindyAnnCindyAnn 10203040 Start 88-10-10-10-12-30-30 1515252525-555 passendpassendpassendpassend 03535-10-101515 45002525-20-20 45 worth of the item for Beth c6 45 worth of the item for Ann BethAnnBethAnn 10203040 Start 88-10-10-10-12-30-30 1515252525-555 passendpassendpassendpassend 03535-10-101515 45002525-20-20 BethCindyAnnBethCindy 5060708090 5-25-1500-52-70-70-70 0-32-50-50-5000-35-35 -3000-15-15-45-3500 passendpassendpassendpassendpass 55-40-1500-25-70-70 00-5-50-50-5000-35 -30-3000-15-15-60-350 BethCindyBethCindyBeth 5060708090 -30-32-50-50-50-52-70-70-70 5-25-15-15-15-45-35-35-35 passendpassendpassendpassendpass -30-30-5-5-50-50-25-25-70 55-40-40-15-15-60-60-35 AnnCindyAnnCindyAnn 5060708090 -30-32-50-50-50-52-70-70-70 5-25-15-15-15-45-35-35-35 passendpassendpassendpassendpass -30-30-5-5-50-50-25-25-70 55-40-40-15-15-60-60-35 worth of the item for Ann worth of the item for Beth worth of the item for Cindy When one player passes, we enter a two-player Shubik auction, see the tree branches below. AnnBethAnnBethAnn 5060708090 -30-32-50-50-50-52-70-70-70 5-25-15-15-15-45-35-35-35 passendpassendpassendpassendpass -30-30-5-5-50-50-25-25-70 55-40-40-15-15-60-60-35 CindyBethCindyBethCindy 5060708090 -30-32-50-50-50-52-70-70-70 5-25-15-15-15-45-35-35-35 passendpassendpassendpassendpass -30-30-5-5-50-50-25-25-70 55-40-40-15-15-60-60-35 CindyAnnCindyAnnCindy 5060708090 -30-32-50-50-50-52-70-70-70 5-25-15-15-15-45-35-35-35 passendpassendpassendpassendpass -30-30-5-5-50-50-25-25-70 55-40-40-15-15-60-60-35 BethAnnBethAnnBeth 5060708090 -30-32-50-50-50-52-70-70-70 5-25-15-15-15-45-35-35-35 passendpassendpassendpassendpass -30-30-5-5-50-50-25-25-70 55-40-40-15-15-60-60-35 AnnBethCindyAnn 100110120130 00-55-55-85-7500-112 -65-5500-92-110-110-1100 -72-90-90-9000-75-75-105 endpassendpassendpassendpassend -7000-55-55-100-7500 -35-80-5500-65-110-110-110 0-45-90-90-9000-75-75 CindyBethCindyBeth 100110120130 -72-90-90-90-92-110-110-110-112 -65-55-55-55-85-75-75-75-105 endpassendpassendpassendpassend -70-45-45-90-90-65-65-110-110 -35-80-80-55-55-100-100-75-75 CindyAnnCindyAnn 100110120130 -72-90-90-90-92-110-110-110-112 -65-55-55-55-85-75-75-75-105 endpassendpassendpassendpassend -70-45-45-90-90-65-65-110-110 -35-80-80-55-55-100-100-75-75 Cindy BethAnnBethAnn 100110120130 -72-90-90-90-92-110-110-110-112 -65-55-55-55-85-75-75-75-105 endpassendpassendpassendpassend -70-45-45-90-90-65-65-110-110 -35-80-80-55-55-100-100-75-75 BethCindyBethCindy 100110120130 -72-90-90-90-92-110-110-110-112 -65-55-55-55-85-75-75-75-105 endpassendpassendpassendpassend -70-45-45-90-90-65-65-110-110 -35-80-80-55-55-100-100-75-75 AnnCindyAnnCindy 100110120130 -72-90-90-90-92-110-110-110-112 -65-55-55-55-85-75-75-75-105 endpassendpassendpassendpassend -70-45-45-90-90-65-65-110-110 -35-80-80-55-55-100-100-75-75 AnnBethAnnBeth 100110120130 -72-90-90-90-92-110-110-110-112 -65-55-55-55-85-75-75-75-105 endpassendpassendpassendpassend -70-45-45-90-90-65-65-110-110 -35-80-80-55-55-100-100-75-75 Cindy Cindy BethCindyAnnBeth 140150160170 -130-130-13000-115-115-160 0-95-95-125-11500-125 -9500-132-150-150-1500 passendpassendpassendpass -85-130-130-13000-115-115 00-95-95-140-11500 -120-9500-105-150-150-150 CindyBethCindy 140150160 -130-130-130-132-150-150 -95-95-95-125-115-115 passendpassendpass -85-85-130-130-105-105 -120-120-95-95-140-140 CindyAnnCindy 140150160 -130-130-130-132-150-150 -95-95-95-125-115-115 passendpassendpass -85-85-130-130-105-105 -120-120-95-95-140-140 BethAnnBeth 140150160 -130-130-130-132-150-150 -95-95-95-125-115-115 passendpassendpass -85-85-130-130-105-105 -120-120-95-95-140-140 BethCindyBeth 140150160 -130-130-130-132-150-150 -95-95-95-125-115-115 passendpassendpass -85-85-130-130-105-105 -120-120-95-95-140-140 AnnCindyAnn 140150160 -130-130-130-132-150-150 -95-95-95-125-115-115 passendpassendpass -85-85-130-130-105-105 -120-120-95-95-140-140 AnnBethAnn 140150160 -130-130-130-132-150-150 -95-95-95-125-115-115 passendpassendpass -85-85-130-130-105-105 -120-120-95-95-140-140 3 players, maximal 16 rounds Random version. At each step the game will terminate with probability 0.4 35 worth of the item for Ann You can input the values A, B, C of the item for the three players and the probability p that the game ends suddenly after each round p in the four cells to the right. The maximum number of rounds is 16. 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. 45 worth of the item for Beth 55 worth of the item for Cindy AnnBethCindyAnn 10203040 Payoffs forStart Ann44-10-1500-26 Beth000-2-20-20-200 Cindy21213515252525-9 passendpassendpassendpassend 025-10-10500 80025-20-20-20 21035002525 When one player passes, we enter a two-player Shubik auction, see the tree branches below. 45 worth of the item for Beth A1 55 worth of the item for Cindy BethCindyBethCindy 10203040 Start 88-10-10-10-12-30-30 212135353511515 passendpassendpassendpassend 03535-10-101515 45003535-20-20 35 worth of the item for Ann B2 55 worth of the item for Cindy AnnCindyAnnCindy 10203040 Start 44-10-10-10-16-30-30 212135353511515 passendpassendpassendpassend 02525-10-1055 55003535-20-20 35 worth of the item for Ann c3 45 worth of the item for Beth AnnBethAnnBeth 10203040 Start 252525-1555-21 000-2-20-20-20-22 passendpassendpassendpassend 02525-10-1055 45002525-20-20 55 worth of the item for Cindya4 45 worth of the item for Beth CindyBethCindyBeth 10203040 Start 45454511252525-9 000-2-20-20-20-22 passendpassendpassendpassend 04545-10-102525 45002525-20-20 55 worth of the item for Cindyb5 35 worth of the item for Ann CindyAnnCindyAnn 10203040 Start 45454511252525-9 000-6-20-20-20-26 passendpassendpassendpassend 04545-10-102525 35001515-20-20 45 worth of the item for Beth c6 35 worth of the item for Ann BethAnnBethAnn 10203040 Start 3535355151515-15 000-6-20-20-20-26 passendpassendpassendpassend 03535-10-101515 35001515-20-20 BethCindyAnnBethCindy 5060708090 -40-16000-56-70-280 0-5-5-50-5000-62-80 500-5-5-39-2500 passendpassendpassendpassendpass -5-40-40-4000-35-70-70 00-5-5-50-5000-35 -30500-5-5-60-250 BethCindyBethCindyBeth 5060708090 -30-32-50-50-50-52-70-70-70 15-19-5-5-5-39-25-25-25 passendpassendpassendpassendpass -30-30-5-5-50-50-25-25-70 1515-40-40-5-5-60-60-25 AnnCindyAnnCindyAnn 5060708090 -30-36-50-50-50-56-70-70-70 15-19-5-5-5-39-25-25-25 passendpassendpassendpassendpass -30-30-15-15-50-50-35-35-70 1515-40-40-5-5-60-60-25 worth of the item for Ann worth of the item for Beth worth of the item for Cindy When one player passes, we enter a two-player Shubik auction, see the tree branches below. AnnBethAnnBethAnn 5060708090 -15-15-15-41-35-35-35-61-55 -40-40-40-42-60-60-60-62-80 passendpassendpassendpassendpass -30-30-15-15-50-50-35-35-70 55-40-40-15-15-60-60-35 CindyBethCindyBethCindy 5060708090 555-29-15-15-15-49-35 -40-40-40-42-60-60-60-62-80 passendpassendpassendpassendpass -30-3055-50-50-15-15-70 55-40-40-15-15-60-60-35 CindyAnnCindyAnnCindy 5060708090 555-29-15-15-15-49-35 -40-40-40-46-60-60-60-66-80 passendpassendpassendpassendpass -30-3055-50-50-15-15-70 -5-5-40-40-25-25-60-60-45 BethAnnBethAnnBeth 5060708090 -5-5-5-35-25-25-25-55-45 -40-40-40-46-60-60-60-66-80 passendpassendpassendpassendpass -30-30-5-5-50-50-25-25-70 -5-5-40-40-25-25-60-60-45 AnnBethCindyAnn 100110120130 00-86-100-40000-111 -80-8000-65-65-108-1070 -35-35-69-5500-97-119-119 endpassendpassendpassendpassend -5500-65-100-100-10000 -80-80-8000-65-65-110-107 0-35-35-90-5500-65-119 CindyBethCindyBeth 100110120130 -72-90-90-90-91-108-108-107-107 -59-45-45-45-98-97-97-119-119 endpassendpassendpassendpassend -70-45-45-90-90-65-65-110-110 -25-80-80-45-45-100-100-65-65 CindyAnnCindyAnn 100110120130 -76-90-90-90-96-110-110-110-111 -59-45-45-45-79-65-65-65-119 endpassendpassendpassendpassend -70-55-55-90-90-75-75-110-110 -25-80-80-45-45-100-100-65-65 Cindy BethAnnBethAnn 100110120130 -55-55-81-75-75-75-101-95-95 -80-80-82-100-100-100-102-120-120 endpassendpassendpassendpassend -70-55-55-90-90-75-75-110-110 -35-80-80-55-55-100-100-75-75 BethCindyBethCindy 100110120130 -35-35-69-55-55-55-89-75-75 -80-80-82-100-100-100-102-120-120 endpassendpassendpassendpassend -70-35-35-90-90-55-55-110-