Question

In previous rounds of the Golden Balls game show, these players have built up a jackpot of £47,250. Now, they must decide how the jackpot will be distributed. Each player in this round of has two strategies: split or steal. The payoffs to each player depend on the strategies played:

• If both choose split, they each receive half the jackpot.
• If one chooses steal and the other chooses split, the steal contestant wins the entire jackpot and the split contestant leaves with nothing.
• If both choose steal, neither contestant wins any money.

Match the letters in the payoff matrix below to the appropriate values based on the payoffs presented above.

		LeeAnn
		split	steal
Chloe	split	B A	F E
	steal	D C	H G

Question 1 options:

A H G 123 C D E F 123 B

1. £47,250 2. £23,625 3. £0

Question 2 (1 point)

Refer to the payoff matrix you created for this game. Does LeeAnn have a dominant strategy? If so, what is her dominant strategy?

Question 2 options:

	a) Yes, steal
	b) Yes, split
	c) No, she has no dominant strategy

Question 3 (1 point)

Refer to the payoff matrix you created for this game. Does Chloe have a dominant strategy? If so, what is her dominant strategy?

Question 3 options:

	a) Yes, steal
	b) No, she has no dominant strategy
	c) Yes, split

Question 4 (1 point)

Identify any Nash equilibriums in this game.

Question 4 options:

	a) Chloe chooses steal; LeeAnn chooses split
	b) Chloe chooses split; LeeAnn chooses steal
	c) both players choose split
	d) both players choose steal

Question 5 (1 point)

Could the two players do better than the Nash equilibrium by colluding and choosing another strategy?

Answer 1

Answers:

Question 1:

Assuming, in each cell, the upper letter represents LeAnn's payoffs and the lower letter represents Chloe's payoff:

	LeAnn
Chloe		Split	Steal
Split	23,625; 23,625	0;   47,250
Steal	47,250;   0	0;   0

Answer:

A	2
H	3
G	3
C	1
D	3
E	3
F	1
B	2

where,
1. £47,250
2. £23,625
3. £0

Question 2:

a) Yes; steal

reason: LeAnn's dominant strategy is to steal because she gets a better payoff when she steals than splits (47,250 > 23,625). So, she will always choose to steal no matter what Chloe does.

Question 3:

a) Yes; steal

reason: Chloe's dominant strategy is to steal because she gets a better payoff when she steals than splits (47,250 > 23,625). So, she will always choose to steal no matter what LeAnn does.

Question 4:

d) both players choose steal.

reason: (Steal, Steal) is the Nash equilibrium because 'Steal' is the dominant strategy of both the players. Each player will steal no matter what the other player will do. So, Nash equilibrium is that both plyers steal. Pyoof will be (0, 0).

Question 5:

Yes, both players could collude and both decide to choose split. This way they could ensure they get a better payoff.