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MATCHING PENNIES

Minimize p = v+0x+0y subject to x-y-v <= 0, y-x-v <= 0, x+y <= 1, x+y >= 1,
x >= 0, y >= 0 

Optimal Solution: p = 0; v = 0, x = 0.5, y = 0.5

TRAFFIC GAME

Minimize p = 0w+0x+0y+0z subject to x-w >=0, y-z>=0, y-w >=0, x-z >=0, w+x+y+z >= 1, w+x+y+z <= 1, x >= 0, y >= 0, z >= 0, w >= 0 

Optimal Solution: p = 0; w = 0, x = 1, y = 0, z = 0

*** maximize player 1 payoff ***

Maximize p = 4w+x+5y+0z subject to x-w >=0, y-z>=0, y-w >=0, x-z >=0, w+x+y+z >= 1, w+x+y+z <= 1, x >= 0, y >= 0, z >= 0, w >= 0  

Optimal Solution: p = 5; w = 0, x = 0, y = 1, z = 0

*** maximize player 2 payoff ***

Maximize p = 4w+y+5x+0z subject to x-w >=0, y-z>=0, y-w >=0, x-z >=0, w+x+y+z >= 1, w+x+y+z <= 1, x >= 0, y >= 0, z >= 0, w >= 0 

Optimal Solution: p = 5; w = 0, y = 0, x = 1, z = 0

*** maximize sum of payoffs***

Maximize p = 8w+6x+6y+0z subject to x-w >=0, y-z>=0, y-w >=0, x-z >=0, w+x+y+z >= 1, w+x+y+z <= 1, x >= 0, y >= 0, z >= 0, w >= 0  

Optimal Solution: p = 6.66667; w = 0.333333, x = 0.333333, y = 0.333333, z = 0