博弈论实例DMA3课件.xlsx

distribution in AnnDMABethDMA first third131221 goal advantage of Ann-2windrawloss 310 choose distribution for the second third: 1,3 2,1 2,2 2,3 3,1 0,40.2782.639 0.3892.483 0.255 2.664 0.271 2.625 0.289 2.5991 1,20.3382.559 0.4732.393 0.345 2.549 0.435 2.395 0.419 2.4362 1,30.3372.546 0.3952.465 0.292 2.593 0.369 2.471 0.322 2.5463 1,40.0502.912 0.0652.886 0.050 2.908 0.068 2.875 0.050 2.9074 2,20.2662.624 0.3122.560 0.234 2.662 0.255 2.619 0.251 2.6345 1234567890 after the second third, but before choosing the distribution for the last third goal dif-6 1,3 2,1 2,2 2,3 3,1 0,40303030303 1,20303030303 1,30303030303 1,40303030303 2,20303030303 goal dif-5 1,3 2,1 2,2 2,3 3,1 0,40303030303 1,20303030303 1,30303030303 1,40303030303 2,20303030303 goal dif-4 1,3 2,1 2,2 2,3 3,1 0,40303030303 1,20303030303 1,30303030303 1,40303030303 2,20303030303 goal dif-3 1,3 2,1 2,2 2,3 3,1 0,40.0233 2.9534 0.0272.946 0.016 2.969 0.014 2.972 0.014 2.972 1,20.0233 2.9534 0.0272.946 0.016 2.969 0.014 2.972 0.014 2.972 1,30.0133 2.9734 0.016 2.9688 0.008 2.984 0.008 2.984 0.008 2.984 1,40.0082.984 0.0082.984 0.005 2.991 0.003 2.993 0.003 2.993 2,20.0082.984 0.0082.984 0.005 2.991 0.003 2.993 0.003 2.993 goal dif-2 1,3 2,1 2,2 2,3 3,1mixed 0,40.1667 2.7778 0.1622.757 0.167 2.778 0.141 2.766 0.138 2.765 1,20.1667 2.7778 0.1622.757 0.167 2.778 0.141 2.766 0.138 2.765 1,30.1406 2.7656 0.141 2.76560.12 2.7840.12 2.7840.12 2.784 1,40.0962.832 0.0962.832 0.083 2.847 0.068 2.875 0.068 2.875 2,20.0962.832 0.0962.832 0.083 2.847 0.068 2.875 0.068 2.875 goal dif-1 1,3 2,1 2,2 2,3 3,1 0,40.5021 2.2923 0.5132.298 0.502 2.292 0.513 2.298 0.513 2.298 1,20.5505 2.2268 0.5132.2980.55 2.227 0.563 2.203 0.563 2.203 1,30.5505 2.2268 0.563 2.20310.55 2.227 0.563 2.203 0.563 2.203 1,40.482.280.482.280.482.280.482.280.482.28 2,20.482.280.482.280.482.280.482.280.482.28 goal dif0 1,3 2,1 2,2 2,3 3,1 0,41.3438 1.34381.321.32 1.344 1.3441.321.321.321.32 1,21.3438 1.34381.35 1.3359 1.344 1.344 1.344 1.344 1.344 1.344 1,31.3438 1.34381.35 1.3359 1.344 1.344 1.344 1.344 1.344 1.344 1,41.3438 1.34381.321.32 1.344 1.3441.321.321.321.32 2,21.3438 1.34381.321.32 1.344 1.3441.321.321.321.32 goal dif1 1,3 2,1 2,2 2,3 3,1 0,42.2031 0.5625 2.237 0.5484 2.203 0.5632.280.482.280.48 1,22.2031 0.5625 2.237 0.5484 2.203 0.5632.280.482.280.48 1,32.2268 0.5505 2.237 0.54842.280.48 2.347 0.417 2.347 0.417 1,42.2031 0.5625 2.237 0.5484 2.203 0.5632.280.482.280.48 2,22.2268 0.5505 2.237 0.54842.280.48 2.347 0.417 2.347 0.417 goal dif2 1,3 2,1 2,2 2,3 3,1 0,42.7582 0.1493 2.758 0.1493 2.766 0.141 2.832 0.096 2.832 0.096 1,22.7582 0.1493 2.758 0.1493 2.766 0.141 2.832 0.096 2.832 0.096 1,32.7656 0.1406 2.766 0.1406 2.832 0.096 2.875 0.069 2.875 0.069 1,42.7840.12 2.7840.12 2.847 0.0832.9 0.0532.9 0.053 2,22.7840.12 2.7840.12 2.847 0.0832.9 0.0532.9 0.053 goal dif3 1,3 2,1 2,2 2,3 3,1 0,42.9534 0.0233 2.9620.019 2.969 0.016 2.984 0.008 2.984 0.008 1,22.9548 0.0226 2.9620.019 2.969 0.016 2.984 0.008 2.984 0.008 1,32.9734 0.0133 2.9780.011 2.984 0.008 2.991 0.005 2.991 0.005 1,42.9840.008 2.9840.008 2.991 0.005 2.995 0.002 2.995 0.002 2,22.9840.008 2.9840.008 2.991 0.005 2.995 0.002 2.995 0.002 goal dif4 1,3 2,1 2,2 2,3 3,1 0,43030303030 1,23030303030 1,33030303030 1,43030303030 2,23030303030 goal dif5 1,3 2,1 2,2 2,3 3,1 0,43030303030 1,23030303030 1,33030303030 1,43030303030 2,23030303030 goal dif6 1,3 2,1 2,2 2,3 3,1 0,43030303030 1,23030303030 1,33030303030 1,43030303030 2,23030303030 PA in the second third: 12223 31231 12101 1,3 2,1 2,2 2,3 3,1 041 0,40.286 0.2857 0.267 0.267 0.222 0.2220.190.190.20.2 122 1,20.267 0.2667 0.333 0.3330.250.250.20.2 0.267 0.266667 131 1,30.250.250.250.250.20.2 0.167 0.167 0.1880.1875 140 1,40000000000 221 2,20.20.2 0.222 0.222 0.167 0.167 0.133 0.133 0.167 0.166667 PB in the second third: 12223 31231 12101 1,3 2,1 2,2 2,3 3,1 041 0,40.429 0.42860.20.2 0.333 0.333 0.214 0.2140.20.2 122 1,20.30.3 0.222 0.2220.250.2500 0.167 0.166667 131 1,30.250.25 0.167 0.1670.20.200 0.1250.125 140 1,40.214 0.2143 0.133 0.133 0.167 0.167000.10.1 221 2,20.20.2 0.167 0.167 0.167 0.16700 0.111 0.111111 AnnDMABethDMA 221311 goal advantage of Ann3windrawloss so far310 1122334455 2,2 3,0 3,1 3,2 4,0 1 1,32.984 0.008 3.000 0.000 2.996 0.002 3.000 0.000 3.000 0.000 2 2,12.978 0.011 3.000 0.000 2.991 0.005 3.000 0.000 3.000 0.000 3 2,22.991 0.005 3.000 0.000 2.997 0.001 3.000 0.000 3.000 0.000 4 2,32.995 0.002 3.000 0.000 2.999 0.001 3.000 0.000 3.000 0.000 5 3,12.991 0.005 3.000 0.000 2.996 0.002 3.000 0.000 3.000 0.000 so far:AnnDMA DMA SOCCER221 with 5 kickersstill3 roundsgoal advantage of Ann 3 the matrixso far Expected payoffD000000 for AnnM012345 A543210 DMA 0,0 0,1 0,2 0,3 0,4 0,5 005 0,02.75 0.125111111112.75 0.125 014 0,1302.75 0.125 2.407 0.296 2.156 0.422 1.976 0.512 2.855 0.072 023 0,230 2.926 0.0372.75 0.125 2.568 0.216 2.407 0.296 2.909 0.046 032 0,330 2.969 0.016 2.872 0.0642.75 0.125 2.627 0.187 2.939 0.031 041 0,430 2.984 0.008 2.926 0.037 2.843 0.0792.75 0.125 2.957 0.021 050 0,530 2.991 0.005 2.953 0.023 2.895 0.053 2.824 0.088 2.969 0.016 104 1,02.855 0.072 1.976 0.512 2.156 0.422 2.407 0.2962.75 0.12530 113 1,130 2.872 0.0642.75 0.1252.75 0.125 2.872 0.06430 122 1,230 2.962 0.019 2.895 0.053 2.872 0.064 2.926 0.03730 131 1,330 2.984 0.008 2.946 0.027 2.926 0.037 2.953 0.02330 140 1,430 2.992 0.004 2.969 0.016 2.953 0.023 2.969 0.01630 203 2,02.909 0.046 2.407 0.296 2.568 0.2162.75 0.125 2.926 0.03730 212 2,130 2.926 0.037 2.872 0.064 2.895 0.053 2.962 0.01930 221 2,230 2.978 0.011 2.946 0.027 2.946 0.027 2.978 0.01130 230 2,330 2.991 0.005 2.972 0.014 2.969 0.016 2.986 0.00730 302 3,02.939 0.031 2.627 0.1872.75 0.125 2.872 0.064 2.969 0.01630 311 3,130 2.953 0.023 2.926 0.037 2.946 0.027 2.984 0.00830 320 3,230 2.986 0.007 2.969 0.016 2.972 0.014 2.991 0.00530 401 4,02.957 0.0212.75 0.125 2.843 0.079 2.926 0.037 2.984 0.00830 410 4,130 2.969 0.016 2.953 0.023 2.969 0.016 2.992 0.00430 500 5,02.969 0.016 2.824 0.088 2.895 0.053 2.953 0.023 2.991 0.00530 000000 0000000 PA D000000 M012345 A543210 DMA0,00,10,20,30,40,5 005 0,00.500.000.000.000.000.00 014 0,11.000.500.330.250.200.17 023 0,21.000.670.500.400.330.29 032 0,31.000.750.600.500.430.38 041 0,41.000.800.670.570.500.44 050 0,50.500.420.360.310.280.25 104 1,00.500.000.000.000.000.00 113 1,11.000.500.330.250.200.17 122 1,21.000.670.500.400.330.29 131 1,31.000.750.600.500.430.38 140 1,40.500.400.330.290.250.22 203 2,00.500.000.000.000.000.00 212 2,11.000.500.330.250.200.17 221 2,21.000.670.500.400.330.29 230 2,30.500.380.300.250.210.19 302 3,00.500.000.000.000.000.00 311 3,11.000.500.330.250.200.17 320 3,20.500.330.250.200.170.14 401 4,00.500.000.000.000.000.00 410 4,10.500.250.170.130.100.08 500 5,00.250.000.000.000.000.00 PB D000000 M012345 A543210 DMA0,00,10,20,30,40,5 005 0,00.501.001.001.001.000.50 014 0,10.000.500.670.750.800.42 023 0,20.000.330.500.600.670.36 032 0,30.000.250.400.500.570.31 041 0,40.000.200.330.430.500.28 050 0,50.000.170.290.380.440.25 104 1,00.420.800.750.670.500.00 113 1,10.000.400.500.500.400.00 122 1,20.000.270.380.400.330.00 131 1,30.000.200.300.330.290.00 140 1,40.000.160.250.290.250.00 203 2,00.360.670.600.500.330.00 212 2,10.000.330.400.380.270.00 221 2,20.000.220.300.300.220.00 230 2,30.000.170.240.250.190.00 302 3,00.310.570.500.400.250.00 311 3,10.000.290.330.300.200.00 320 3,20.000.190.250.240.170.00 401 4,00.280.500.430.330.200.00 410 4,10.000.250.290.250.160.00 500 5,00.250.440.380.290.170.00 P0 D000000 M012345 A543210 DMA0,00,10,20,30,40,5 005 0,00.000.000.000.000.000.50 014 0,10.000.000.000.000.000.42 023 0,20.000.000.000.000.000.36 032 0,30.000.000.000.000.000.31 041 0,40.000.000.000.000.000.28 050 0,50.500.420.360.310.280.50 104 1,00.080.200.250.330.501.00 113 1,10.000.100.170.250.400.83 122 1,20.000.070.130.200.330.71 131 1,30.000.050.100.170.290.63 140 1,40.500.440.420.430.500.78 203 2,00.140.330.400.500.671.00 212 2,10.000.170.270.380.530.83 221 2,20.000.110.200.300.440.71 230 2,30.500.460.460.500.600.81 302 3,00.190.430.500.600.751.00 311 3,10.000.210.330.450.600.83 320 3,20.500.480.500.560.670.86 401 4,00.220.500.570.670.801.00 410 4,10.500.500.550.630.740.92 500 5,00.500.560.630.710.831.00 Beth DMA 001 payoff forwindraw lose 310 11111222 01234012 43210321 1,0 1,1 1,2 1,3 1,4 2,0 2,1 2,2 2.75 0.1251111112.75 0.1252.75 0.1251111 302.75 0.125 2.407 0.296 2.156 0.422 2.872 0.064302.75 0.125 2.407 0.296 30 2.926 0.0372.75 0.125 2.568 0.216 2.926 0.03730 2.926 0.0372.75 0.125 30 2.969 0.016 2.872 0.0642.75 0.125 2.953 0.02330 2.969 0.016 2.872 0.064 30 2.984 0.008 2.926 0.037 2.843 0.079 2.969 0.01630 2.984 0.008 2.926 0.037 30 2.991 0.005 2.953 0.023 2.895 0.053 2.978 0.01130 2.991 0.005 2.953 0.023 2.872 0.064 2.156 0.422 2.407 0.2962.75 0.12530 2.895 0.053 2.407 0.2962.75 0.125 30 2.895 0.053 2.824 0.088 2.895 0.0533030 2.926 0.037 2.926 0.037 30 2.969 0.016 2.926 0.037 2.946 0.0273030 2.978 0.011 2.969 0.016 30 2.987 0.007 2.962 0.019 2.969 0.0163030 2.991 0.005 2.984 0.008 30 2.993 0.003 2.978 0.0112.980.013030 2.995 0.002 2.991 0.005 2.926 0.037 2.568 0.2162.75 0.125 2.926 0.03730 2.946 0.0272.75 0.125 2.926 0.037 30 2.946 0.027 2.926 0.037 2.969 0.0163030 2.969 0.016 2.978 0.011 30 2.984 0.008 2.969 0.016 2.984 0.0083030 2.991 0.005 2.991 0.005 30 2.993 0.003 2.984 0.008 2.991 0.0053030 2.996 0.002 2.995 0.002 2.953 0.0232.75 0.125 2.872 0.064 2.969 0.01630 2.969 0.016 2.872 0.064 2.969 0.016 30 2.969 0.016 2.962 0.019 2.987 0.0073030 2.984 0.008 2.991 0.005 30 2.991 0.005 2.984 0.008 2.993 0.0033030 2.995 0.002 2.996 0.002 2.969 0.016 2.843 0.079 2.926 0.037 2.984 0.008302.980.01 2.926 0.037 2.984 0.008 302.980.01 2.978 0.011 2.993 0.0033030 2.991 0.005 2.995 0.002 2.978 0.011 2.895 0.053 2.953 0.023 2.991 0.00530 2.987 0.007 2.953 0.023 2.991 0.005 000000014 00000001 11111222 01234012 43210321 1,01,11,21,31,42,02,12,2 0.420.000.000.000.000.360.000.00 0.800.400.270.200.160.670.330.22 0.750.500.380.300.250.600.400.30 0.670.500.400.330.290.500.380.30 0.500.400.330.290.250.330.270.22 0.000.000.000.000.000.000.000.00 0.400.000.000.000.000.330.000.00 0.750.380.250.190.150.600.300.20 0.670.440.330.270.220.500.330.25 0.500.380.300.250.210.330.250.20 0.000.000.000.000.000.000.000.00 0.380.000.000.000.000.300.000.00 0.670.330.220.170.130.500.250.17 0.500.330.250.200.170.330.220.17 0.000.000.000.000.000.000.000.00 0.330.000.000.000.000.250.000.00 0.500.250.170.130.100.330.170.11 0.000.000.000.000.000.000.000.00 0.250.000.000.000.000.170.000.00 0.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.00 11111222 01234012 43210321 1,01,11,21,31,42,02,12,2 0.501.001.001.000.500.501.001.00 0.000.500.670.750.400.000.500.67 0.000.330.500.600.330.000.330.50 0.000.250.400.500.290.000.250.40 0.000.200.330.430.250.000.200.33 0.000.170.290.380.220.000.170.29 0.400.750.670.500.000.380.670.50 0.000.380.440.380.000.000.330.33 0.000.250.330.300.000.000.220.25 0.000.190.270.250.000.000.170.20 0.000.150.220.210.000.000.130.17 0.330.600.500.330.000.300.500.33 0.000.300.330.250.000.000.250.22 0.000.200.250.200.000.000.170.17 0.000.150.200.170.000.000.130.13 0.290.500.400.250.000.250.400.25 0.000.250.270.190.000.000.200.17 0.000.170.200.150.000.000.130.13 0.250.430.330.200.000.210.330.20 0.000.210.220.150.000.000.170.13 0.220.380.290.170.000.190.290.17 11111222 01234012 43210321 1,01,11,21,31,42,02,12,2 0.080.000.000.000.500.140.000.00 0.200.100.070.050.440.330.170.11 0.250.170.130.100.420.400.270.20 0.330.250.200.170.430.500.380.30 0.500.400.330.290.500.670.530.44 1.000.830.710.630.781.000.830.71 0.200.250.330.501.000.290.330.50 0.250.250.310.440.850.400.370.47 0.330.310.330.430.780.500.440.50 0.500.440.430.500.790.670.580.60 1.000.850.780.791.001.000.870.83 0.290.400.500.671.000.400.500.67 0.330.370.440.580.870.500.500.61 0.500.470.500.600.830.670.610.67 1.000.850.800.831.001.000.880.87 0.380.500.600.751.000.500.600.75 0.500.500.570.690.900.670.630.72 1.000.830.800.851.001.000.870.88 0.500.570.670.801.000.620.670.80 1.000.790.780.851.001.000.830.87 0.780.630.710.831.000.810.710.83 2333445 3012010 0210100 2,3 3,0 3,1 3,2 4,0 4,1 5,00 2.75 0.1252.75 0.125112.75 0.1252.75 0.1252.75 0.125 2.969 0.01600 2.895 0.053302.75 0.125 2.926 0.03730 2.969 0.0163000 2.946 0.02730 2.926 0.037 2.969 0.01630 2.991 0.0053000 2.969 0.01630 2.969 0.016 2.984 0.00830 2.996 0.0023000 2.980.0130 2.984 0.008 2.991 0.00530 2.998 0.0013000 2.987 0.00730 2.991 0.005 2.994 0.00330 2.9996E-043000 30 2.926 0.0372.75 0.12530 2.969 0.016303000 3030 2.969 0.0163030303000 3030 2.991 0.0053030303000 3030 2.996 0.00230303030101 3030 2.998 0.0013030303001 30 2.969 0.016 2.926 0.03730 2.991 0.005303001 3030 2.991 0.00530303030132 3030 2.997 0.00130303030143 3030 2.9996E-0430303030154 30 2.984 0.008 2.969 0.01630 2.996 0.002303004 3030 2.996 0.00230303030175 3030 2.9996E-043030303005 30 2.991 0.005 2.984 0.00830 2.998 0.001303005 3030 2.998 0.0013030303005 30 2.994 0.003 2.991 0.00530 2.9996E-04303005 01617181900 1234555 2333445 3012010 0210100 2,33,03,13,24,04,15,0 0.000.310.000.000.280.000.25 0.170.570.290.190.500.250.44 0.240.500.330.250.430.290.38 0.250.400.300.240.330.250.29 0.190.250.200.170.200.160.17 0.000.000.000.000.000.000.00 0.000.290.000.000.250.000.22 0.150.500.250.170.430.210.38 0.200.400.270.200.330.220.29 0.170.250.190.150.200.150.17 0.000.000.000.000.000.000.00 0.000.250.000.000.210.000.19 0.130.400.200.130.330.170.29 0.130.250.170.130.200.130.17 0.000.000.000.000.000.000.00 0.000.200.000.000.170.000.14 0.080.250.130.080.200.10