PartIIISec1_6

# PartIIISec1_6 - Game Theory Solutions to Exercises Bimatrix...

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Game Theory Solutions to Exercises: Bimatrix Games – Safety Levels Jan-Jaap Oosterwijk Fall 2007

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1 Bimatrix Games – Safety Levels 1.6.1 Convert the following extensive form game to strategic form. Solution: (See graphical appendix at the end of this document for the tree.) Player I has two pure strategies, X = { a,b } and Player II has two pure strategies as well, Y = { c,d } . The corresponding strategic form of this game is given by the 2 × 2 bimatrix, ± c d a 1 4 (1 , 3) + 3 4 (4 , 3) 1 4 (1 , 3) + 3 4 (7 , 0) b 1 4 (4 , 1) + 3 4 (4 , 3) 1 4 (0 , 8) + 3 4 (7 , 0) ² = ± c d a ( 13 4 , 3 ) ( 22 4 , 3 4 ) b ( 4 , 10 4 ) ( 21 4 , 2 ) ² = ± c d a ( 3 1 4 , 3 ) ( 5 1 2 , 3 4 ) b ( 4 , 2 1 2 ) ( 5 1 4 , 2 ) ² 1.6.2 Find the safety levels and maxmin strategies for the players in the bimatrix games, (a) ± (1 , 1) (5 , 0) (0 , 5) (4 , 4) ² Solution: The winnings of Player I and Player II are respectively given by A := ± 1 5 0 4 ² and B := ± 1 0 5 4 ² . Since
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PartIIISec1_6 - Game Theory Solutions to Exercises Bimatrix...

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