Game Theory 0-Sum Online games

 Essay on Game Theory 0-Sum Online games

MATH 4321 Spring 2013 Assignment Solution 0-Sum Game titles 2 1 . Reduce simply by dominance to 2x2 game titles and resolve. 5 some 4 three or more (a)   0 1   you 2 1 0 2 1   5 3  1 2

10 zero 7 you  (b)  a couple of 6 5 7     six 3 a few 5  

Solution: (a). Line 2 rules column 1; then line 3 rules row four; then line 4 rules column three or more; then row 1 rules row installment payments on your The producing submatrix contains row you and 3 vs . articles 2 and 4. Solving this two by a couple of game and moving returning to the original video game we find that value is definitely 3/2, I's optimal technique is s (1 a couple of, 0, 1 2, 0) and II's optimal technique is q  (0, 3 eight, 0, five 8). (b). Column two dominates line 4; then (1/2)row 1+ (1/2)row two dominates row 3; then (1/2)col 1+(1/2)col 2 rules col three or more. The resulting 2 by 2 game is easily fixed. Moving back in the original game we find the fact that value is usually 30/7, I's optimal approach is (2/7, 5/7, 0) and II's optimal approach is (3/7, 4/7, 0, 0).

2 . Reduce by dominance into a 3x2 matrix game and solve:

 0 almost eight 5    8 some 6. 12 4 a few   

Solution: Note that 5/8xCol2 + 3/8xCol1 uniformly rules Col3. Consequently , we can delete Col3 to get  0 almost eight *    8 4 * . Then, we use the graphic method inside the following. 12 4 *   

1/ 3 two / a few 0 5 / 12  0 8 your five    almost 8 /12  8 5 6  0 12 4 three or more   

Answer: The optimal technique for I can be (4/12, 8/12, 0) The optimal strategy for 2 is (1/3, 2/3, 0) Value sama dengan 16/3

three or more. Solve the subsequent magic sq . game.

16 3 a couple of 13   your five 10 eleven 8   .  9 6 7 12     four 15 16 1 

Solution: In an n  n magic square, A  aij , there exists a number s such that

i aij  s for all j, and  l aij  s for all i. In the event Player My spouse and i uses the mixed strategy (1 d, 1 in, , 1 n ) his common payoff isV  h n whatever Player II does. Precisely the same goes for gamer II, hence the value is s and and s is optimum for both equally players. Inside the example, n  4 and s i9000  thirty four, so the value of the game is 17/2 and the optimum strategies are

(1 5, 1 four, 1 4, 1 4).

4. Gamer II chooses a number j...

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