斯坦福大学英属哥伦比亚大学 博弈论课程week3 problem set 3及其答案

Question 1

Iterated removal of strictly dominated strategies

Normal
1 \ 2	L	M	R
U	3,8	2,0	1,2
D	0,0	1,7	8,2

We say that a game is  dominance solvable, if iterative deletion of strictly dominated strategies yields a unique outcome. 

True or false: The previous game is dominance solvable. 
[Consider both pure strategies and mixed strategies.]

Your Answer		Score	Explanation
a) True;	Correct	1.00
b) False.
Total		1.00 / 1.00

Question 2

Iterated removal of weakly dominated strategies

In order to illustrate the problem that arises when iteratively eliminating  weakly dominated strategies, consider the following game:

Normal
1 \ 2	L	M	R
U	4,3	3,5	3,5
D	3,4	5,3	3,4

True or false: in the above game the order of elimination of  weakly dominated strategies does not matter (that is, the final outcome is the same regardless of the order in which weakly dominated strategies are eliminated.). [Hint: start the process of iterative elimination of  weakly dominated strategies by eliminating different strategies at the beginning of the process.]

Your Answer		Score	Explanation
a) True;
b) False.	Correct	1.00
Total		1.00 / 1.00

Question 3

Minimax 

Consider the matching-pennies game:

1\ 2	Left	Right
Left	2,-2	-2,2
Right	-2,2	2,-2

Which is a maxmin strategy for player 1:

Your Answer		Score	Explanation
a) Play Left.
b) Play Right.
c) Play Left and Right with probability 1/2.	Correct	1.00
d) It doesn't exist.
Total		1.00 / 1.00

Question 4

Minimax 

Consider the matching-pennies game:

1\ 2	Left	Right
Left	2,-2	-2,2
Right	-2,2	2,-2

Apply the Minimax theorem presented in lecture 3-4 to find the payoff that any player must receive in any Nash Equilibrium:

Your Answer		Score	Explanation
a) 2;
b) -2;
c) 1;
d) 0.	Correct	1.00
Total		1.00 / 1.00

Question 5

Correlated Equilibrium

1\ 2	B	F
B	2,1	0,0
F	0,0	1,2

Consider the following assignment device (for example a fair coin):

• With probability 1/2 it tells players 1 and 2 to play B, and with probability 1/2 it tells them to play F.
• Both players know that the device will follow this rule.

What is the expected payoff of each player when both players follow the recommendations made by the device? If one of players follows the recommendation, does the other player have an incentive to follow the recommendation as well?

Your Answer		Score	Explanation
a) Expected payoff =2; player has an incentive to follow the recommendation.
b) Expected payoff =1; player does not an incentive to follow the recommendation.
c) Expected payoff =1.5; player has an incentive to follow the recommendation.	Correct	1.00
d) Expected payoff =1.5; player does not have an incentive to follow the recommendation.
Total		1.00 / 1.00