博弈论实例PascalFermat课件.xlsx

A number of rounds are played where Ann wins with probability p and Beth with probability q 1 p Who has first won six rounds wins an amount of 1 whereas the other loses 1 The sheet shows the expected payoff for all positions 6 0 1 21 5 0 p0 50 this number can be changed 1 20 97 q0 504 0 1 25 1 1 20 88 1 20 94 3 0 1 24 1 1 20 71 1 20 78 2 0 1 23 1 1 24 2 1 20 49 1 20 55 1 20 63 1 0 1 22 1 1 23 2 1 20 25 1 20 27 1 20 31 0 0 1 21 1 1 22 2 1 23 3 1 00 1 20 00 1 20 00 1 20 00 1 20 1 1 21 2 1 22 3 0 25 1 2 0 27 1 2 0 31 1 20 2 1 21 3 1 22 4 0 49 1 2 0 55 1 2 0 63 1 20 3 1 21 4 0 71 1 2 0 78 1 20 4 1 21 5 0 88 1 2 0 94 1 20 5 0 97 1 20 6 1 6 1 1 21 6 2 1 21 1 25 26 3 1 20 88 1 21 1 25 36 4 1 20 75 1 21 1 24 3 1 25 46 5 1 20 38 1 20 50 1 21 1 24 4 1 25 5 1 20 00 1 20 00 1 23 4 1 24 5 1 25 6 1 2 0 38 1 2 0 50 1 1 23 5 1 24 6 1 2 0 75 1 1 22 5 1 23 6 1 2 0 88 1 1 22 6 1 1 21 6 1 A number of rounds are played where Ann wins with probability p and Beth with probability q 1 p Who has first won six rounds wins an amount of 1 whereas the other wins nothing The sheet shows the expected payoff for all positions p 1 2 this number can be changed Put in a fraction 1 2 q 1 24 0 1 2 15 16 3 0 1 2 1 2 219 256 1 2 2 0 1 23 1 1 2 191 256 1 2 99 128 1 0 1 22 1 1 2 1 2 319 512 1 2 163 256 1 2 0 0 1 21 1 1 22 2 1 2 1 2 1 2 1 2 1 2 1 20 1 1 21 2 1 2 193 512 1 2 93 256 1 2 1 20 2 1 21 3 65 256 1 2 29 128 1 20 3 1 2 37 256 1 2 1 20 4 1 16 1 2 6 0 1 21 5 0 1 26 1 63 64 1 21 1 25 1 1 26 2 1 2 31 32 1 21 4 1 1 25 2 1 26 3 57 64 1 2 15 16 1 21 1 24 2 1 25 3 1 26 4 1 2 13 16 1 2 7 8 1 21 3 2 1 24 3 1 25 4 1 26 5 21 32 1 2 11 16 1 2 3 4 1 21 1 23 3 1 24 4 1 25 5 1 2 1 2 1 2 1 2 1 2 1 2 2 3 1 23 4 1 24 5 1 25 6 11 32 1 2 5 16 1 2 1 4 1 20 1 22 4 1 23 5 1 24 6 1 2 3 16 1 2 1 8 1 20 1