Question

Mixed Strategies

Consider the following game between two players Bad-Boy and Good-Girl. Bad-Boy can either behave or misbehave whereas Good-Girl can either punish or reward. Below payoff matrix shows the game as pure strategies.

		Good Girl
		Reward	Punish
Bad Boy	Behave	5, 5	-5,-5
	Misbehave	10,-10	-10,-5

Question 41 (1 point)

What is the Nash equilibrium of the game in pure strategies?

Question 41 options:

	Behave-Reward
	Behave-Punish
	Misbehave-Punish
	There is no Nash equilibrium in pure strategies.

Question 42 (1 point)

Assume Bad Boy knows that Good Girl rewards 80% of the time. Then, if Bad Boy misbehaves 100% of the time, Bad Boy's expected payoff is equal to

Question 42 options:

	2
	4
	6
	8

Question 43 (1 point)

Assume Bad Boy knows that Good Girl rewards 80% of the time. Then, if Bad Boy misbehaves 100% of the time, Good Girl's expected payoff is equal to

Question 43 options:

	-5
	-6
	-7
	-8

Question 44 (1 point)

Assume Bad Boy knows that Good Girl rewards 80% of the time. Then, if Bad Boy misbehaves 100% of the time, which statement is true?

Question 44 options:

	Bad Boy exploits Good Girl being so nice
	Good Girl will feel exploited and consider a mixed strategy
	Both a. and b. are correct
	This is the best that Good Girl can do.

Question 45 (1 point)

Assume Good Girl wants to consider a mixed strategy such that she randomly chooses "Reward" and "Punishment" such that Bad Boy is indifferent between "Behave" and "Misbehave". With what probability should Good Girl choose play "Reward."

Question 45 options:

	1/2
	1/3
	1/4
	1/5

Question 46 (1 point)

Assume Good Girl knows that Bad Boy misbehaves 90% of the time. Then, if Good Girl punishes 100% of the time, Good Girl’s expected payoff is equal to

Question 46 options:

	1
	2
	3
	4

Question 47 (1 point)

Assume Good Girl knows that Bad Boy misbehaves 90% of the time. Then, if Good Girl punishes 100% of the time, Bad Boy’s expected payoff is equal to

Question 47 options:

	-9.5
	-8.5
	-7.5
	-7

Question 48 (1 point)

Assume Good Girl knows that Bad Boy misbehaves 90% of the time. Then, if Good Girl punishes 100% of the time, then which statement is true?

Question 48 options:

	Good Girl takes advantage of Bad Boy being so misbehaved
	Bad Boy will feel taken advantage of and consider a mixed strategy
	Both a. and b. are correct
	This is the best that Bad Boy can do.

Question 49 (1 point)

Assume Bad Boy wants to consider a mixed strategy such that he randomly chooses "Behave" and "Misbehave" such that Good Girl is indifferent between "Reward" and "Punish." With what probability should Bad Boy play "Behave."

Question 49 options:

	1/5
	2/5
	3/5
	4/5

Question 50 (1 point)

A game in which players choose their strategies randomly are called

Question 50 options:

	random games
	chance games
	no-clue games
	mixed-strategy games

Answer 1

Answer 41. There is no nash equilibrium in pure strategies.

Explanation- if good girl choose reward strategy, then bad boy will choose misbehave strategy because it will give him a higher payoff of 10. If good girl choose punish strategy then bad boy will choose behave strategy because it will give him higher payoff of -5.

If bad boy choose behave strategy, then good girl will choose reward strategy because it will give her higher payoff of 5. If bad boy choose misbehave strategy, then good girl will choose punish strategy because it will give her higher payoff of -5.

So we can see there is no pure nash equilibrium.