L25_Some more problems in game theory

# L25_Some more problems in game theory - Hillier and...

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Hillier and Lieberman Problem 14.4-2 Page 746 Consider the game having the following pay-off (to A) table: Player B Strategy 1 2 1 3 -2 Player A 2 -1 2

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Use the graphical procedure to determine the value of the game and the optimal strategy for each player according to the minimax criterion. When B plays strategy A’s Expected pay-off 1 3 x1-1(1-x1) = -1 + 4x1 2 -2 x1+2(1-x1) = 2 – 4x1
x 1 1 0 B 1 B 2 (3/8, 1/2)

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Thus A should play his strategies 1, 2 with probabilities 3/8, 5/8. And the value of the game = 1/2. Now if B’s optimal strategies are y 1 * and (1-y 1 *), then 3 y 1 * - 2(1- y 1 * ) = 1/2 Or 5 y 1 * = 5/2 , i.e., y 1 * = 1/2 = y 2 * Thus B should play his strategies 1, 2 with probabilities 1/2, 1/2.
Hillier and Lieberman Problem 14.4-3(a) Page 746 Consider the game having the following pay-off (to A) table: Player B Strategy 1 2 3 1 4 3 1 Player A 2 0 1 2

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Use the graphical procedure to determine the value of the game and the optimal strategy for each player according to the minimax criterion
Hillier and Lieberman Problem 14.4-3(b) Page 746 Player A Consider the game having the following pay-off (to A) table: Player B Strategy 1 2 3 1 1 -1 3 2 0 4 1 3 3 -2 5 4 -3 6 -2

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Use the graphical procedure to determine the value of the game and the optimal strategy for each player according to the minimax criterion. It is clear that the strategy 3 of player B is
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L25_Some more problems in game theory - Hillier and...

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