HOMEWORK ASSIGNMENT #3 [20 POINTS]. DUE IN CLASS ON WEDNESDAY, JAN. 21, 1998.

[ANSWERS ALONE ARE NOT SUFFICIENT--ALWAYS SHOW YOUR WORK]

1. [5 POINTS] Find all pure strategy Nash equilibrium combinations in the following matrix. What is the value of the game?
c1
c2
c3
c4

r1

1,-1

2,-2

1,-1

2,-2

r2

-4,4

-5,5

-3,3

3,-3

r3

1,-1

3,-3

1,-1

1,-1

r4

0,0

4,-4

-1,1

-3,3

2. [15 POINTS] Solve the following matrix by: (1) Find all pure strategy Nash equilibrium combinations of pure strategies, if any; (2) If there are none, sequentially eliminate all dominated strategies, if any; (3) Find the Nash equilibrium combination of mixed strategies, by calculating each player's equalizer mixed strategy. What is the value of the game?

c1
c2
c3

r1

3, -3

5, -5

-4, 4

r2

0, 0

2, -2

5, -5

r3

-2, 2

-3,3

4,-4