Mixed Strategies : Use the following information to answer questions 10-14. Pena
ID: 1151894 • Letter: M
Question
Mixed Strategies: Use the following information to answer questions 10-14.
Penalty kicks are a great example of a setup where mixed strategies are played. Bayern Munich's forward Robert Lewandowski has two options when shooting a penalty: left and right (let's assume, for simplicity, that he does not shoot to the center). The goalkeeper must anticipate the shot. The probability he scores, given the goalkeeper's strategy and his own, is given in the following table. (Remember that Robert prefers a high probability, while the goalkeeper prefers a low probability!)
Goalkeeper
Anticipate Anticipate
Left Right
Left 0.4 0.7
Robert
Right 0.7 0.5
Question 11 (0.5 points)
Which of the following is true about this game?
Question 11 options:
There is a Nash equilibrium in pure strategies where each player has a dominant strategy.
There is no Nash equilibrium in pure strategies, but there is a Nash equilibrium in mixed strategies.
There is a Nash equilibrium in pure strategies where one of the two players has a dominant strategy.
Although there is a Nash equilibrium in pure strategies, neither player has a dominant strategy.
There is neither a Nash equilibrium in pure strategies nor in mixed strategies.
Save
Question 12 (0.5 points)
The following three questions will be asking about mixed strategies (that is, strategies where the players randomize across their options). What is the equilibrium probability that Robert will shoot left?
HINT: You need to find the equilibrium probability that makes the goalkeeper indifferent between anticipating to the left or right.
Question 12 options:
1/3
0
1
2/5
3/4
Save
Question 13 (0.5 points)
What is the equilibrium probability that the goalkeeper plays anticipate right?
Question 13 options:
1/3
3/5
1
1/2
0
Save
Question 14 (0.5 points)
What is the equilibrium probability that Robert will shoot right?
Question 14 options:
3/5
1/2
2/5
1/4
4/5
There is a Nash equilibrium in pure strategies where each player has a dominant strategy.
There is no Nash equilibrium in pure strategies, but there is a Nash equilibrium in mixed strategies.
There is a Nash equilibrium in pure strategies where one of the two players has a dominant strategy.
Although there is a Nash equilibrium in pure strategies, neither player has a dominant strategy.
There is neither a Nash equilibrium in pure strategies nor in mixed strategies.
Explanation / Answer
Answer:
11)
Option a is correct answer
12)
Option c is correct answer
13)
Option d is correct answer
14)
Option b is correct answer