Self-test on dominant strategies, dominated strategies, and Nash equilibrium

For each game, click on the answer you think is right. That will take you to an explanation of why it is right or wrong. Since this is not a real test, also click on any answers you think might might be right, so you can understand why they are wrong.

In fact-- click on all of them. You should be able to understand why wrong answers are wrong as well as why right answers are right. A useful exercise, and possible test question, is to ask yourself how you would explain why a given answer is wrong.

After doing a few of these, you will find it easy to make up your own examples.

GAME 1

                                         Column
                                    Left         Right
                   Up              -1,-1        -10,0
 Row                                         
                   Down            0,-10         -8,-8

1_1 Which of the following is true?
A. Row has no dominant strategy.
B. Row's dominant strategy is Up.
C. Row's dominant strategy is Down.

1_2 Which of the following is true?
A. Column has no dominated strategies.
B. Column's strategy of Left is dominated.
C. Column's strategy of Right is dominated.

1_3 In the dominant-strategy equilibrium, the payoffs of the two players are:
A. -1,-1
B. -10,0
C. -8, -8
D. 0, -10

1_4 Do you recognize this game from your reading or the lecture? You can do a positive linear transformation on the payoffs of a game without changing its essential structure. In fact, you can even do more general positive monotonic transformations, though that will affect the probabilities in a mixed strategy equilibrium. Which game is disguised under the action names of Game 1? For the answer, click here

GAME 2

                                         Column
                                    Left         Right
                Up                -10,0         -1,-1
 Row                                         
                Down              -8,-8          0,-10

2_1 Which of the following is true?
A. Row has no dominant strategy.
B. Row's dominant strategy is Up.
C. Row's dominant strategy is Down.

2_2 Which of the following is true?
A. Column has no dominated strategies.
B. Column's strategy of Left is dominated.
C. Column's strategy of Right is dominated.

2_3 The dominant-strategy equilibrium is :
A. Up, Left
B. Up, Right
C. Down, Left
D. Down, Right

2_4 Do you recognize Game 2 from your reading or the lecture? You can do a positive linear transformation on the payoffs of a game without changing its essential structure. In fact, you can even do more general positive monotonic transformations, though that will affect the probabilities in a mixed strategy equilibrium. Which game is disguised under the action names of Game 2? For the answer, click here

GAME 3

                                         Column
                                    Left           Right
                Up                3,3             4,4
 Row                                         
                Down              4,2              3,10

3_1 Which of the following is true?
A. Row has no dominant strategy.
B. Row's dominant strategy is Up.
C. Row's dominant strategy is Down.

3_2 Which of the following is true?
A. Column has no dominated strategies.
B. Column's strategy of Left is dominated.
C. Column's strategy of Right is dominated.

3_3 The dominant strategy equilibrium is
A. Up, Left
B. Down, Right
C. Up, Right
D. None of the above

3_4 The Nash equilibrium is
A. Up, Left
B. Up, Right
C. Down, Left
D. Down, Right

GAME 4

                                           Column
                                     Left            Right
                   Up               10,3              1,1
 Row                                         
                   Down             2,2              3,10

4_1 Which of the following is true?
A. Row has no dominant strategy.
B. Row's dominant strategy is Up.
C. Row's dominant strategy is Down.

4_2 Which of the following is true?
A. Column has no dominated strategies.
B. Column's strategy of Left is dominated.
C. Column's strategy of Right is dominated.

4_3 Which of the following are Nash equilibria?
A. Up, Left
B. Up, Right
C. Down, Left
D. Down, Right

GAME 5

                                         Column
                                    Left           Right      Edge
                    Up             -10,0         -10,-1        -10,-1

Row                 Down           -8,-8         0,-10        2,-1           
                                                                                        
                    Bottom          4, 5         7,-10         1, 1

5_1 Which of the following is true?
A. Row has no dominant strategy.
B. Row's dominant strategy is Up.
C. Row's dominant strategy is Down.
D. Row's dominant strategy is Bottom.

5_2 Which of the following is true?
A. Column has no dominated strategies.
B. Column's strategy of Left is dominated.
C. Column's strategy of Right is dominated.
D. Column's strategy of Edge is dominated.

5_3 Select which of the following are Nash equilibria:
A. Up, Left
B. Up, Right
C. Down, Left
D. Down, Right
E. Bottom, Left
F. Bottom, Right
G. Down, Edge
H. Bottom, Edge
I. Up, Edge
J. None of the above

GAME 6

                                           Column
                                    Left           Right
                   Up               0,3             3,0
 Row                                         
                   Down             4,0             0,4

6_1 Which of the following is true?
A. Column has no dominated strategies.
B. Column's strategy of Left is dominated.
C. Column's strategy of Right is dominated.

6_2 The Nash equilibrium is
A. Up, Left
B. Up, Right
C. Down, Left
D. Down, Right
E. None of the above

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