Mathematics 483 (Game Theory)

Homework Assignment iii

prepared by:

Joseph Malkevitch
Mathematics Department
York College (CUNY)
Jamaica, NY 11451

email: joeyc@cunyvm.cuny.edu
web page: http://www.york.cuny.edu/~malk

1. For each of the games below:

a. Draw a movement diagram

b. Determine if there are dominating rows or columns from the point of view of Row and Column.

c. Determine if there is any equilibrium (equilibria) in pure strategies.

d. If the game is a 2 x 2 zero sum game, find the optimal strategies for each player, and the value of the game.

Game 1:

 Column I Column II Row 1 (3, 5) (2, 1) Row 2 (4, 2) (1, 5)

Game 2:

 Column I Column II Row 1 (2, 2) (3, 6) Row 2 (6, 3) (-2, -2)

Game 3:

 Column I Column II Row 1 (6, -6) (-3, 3) Row 2 (-2, 2) (1, -1)

Game 4:

 Column I Column II Row 1 (2, -2) (-4, 4) Row 2 (0, 0) (3, -3) Row 3 (-5, 5) (10, -10)

Game 5:

 Column I Column II Column III Row 1 (-1, 1) (1, -1) (5, -5) Row 2 (3, -3) (2, -2) (4, -4) Row 3 (4, -4) (0, 0) (-1, 1)

Game 6:

 Column I Column II Row 1 (14, -9) (-2, 3) Row 2 (-2, 5) (1, -7)

Game 7:

 Column I Column II Row 1 (1, 1) (-5, 5) Row 2 (5, -5) (-2, -2)