Nash Equlibrium Right answer!

[Snah]

Hi all,
Just a few days before the exam and I do not understand what is the better choice in a Nash equilibrium question.
If I put the prisoner dilemma as a example in a CFA exam, what will be the correct answer?
Obviously the best outcome for both is do not blame the other and spend few years in prison each, but the theory says that they will not cooperate and they will try to find the best outcome individually…
And then, if two companies at the same time cooperate and put high prices, the total outcome is much greater than if they put low price both (war price). But if they think in a selfish way, one could think, well I put the prices low and my outcome will be bigger than with both high. ( in that case the total outcome is lower than in a cartel situation).
I understand the theory what I do not understand is the correct answer for a question like “Two companies are into a collusive agreement, According to the Nash equilibrium, a low price is most likely charged by: both, one or neither”
Many thanks in advance.

 

[akthem]

In the case of an oligopoly (few firms, significant pricing power and high barriers to entry) where two firms collude to increase prices and therefore increase their profits, neither company has an incentive to cheat because the payoffs for colluding are greater than the payoffs for cheating.
In general, competing firms will likely match a price decrease but will not match a price increase (unless they collude).
If company A decides to lower their price, company B will likely lower their price as well to remain competitive.
If company A and company B collude and agree on a higher price, they both enjoy higher profits.

 

[Snah]

Thank you.
I see that logic, but Nash equilibrium says that participants of the market are interdepend BUT NOT COOPERATIVES.
That´s the reason I thought was a tricky question and the right answer was both (one will try to find the best profit lowering its price and the other company with react following that decision).
Also I based my answer in the prisoner dilemma, according Nash equilibrium, both will accuse each other (seeking the best individual outcome) and the overall result is worse that if both cooperate.
What do you think?

 

[akthem]

In the prisoner’s dilemma you would cheat (confess) because you would get less time in jail –> higher payoff than staying silent (more jail time).
In this question, if you cheat, you would lower your price, thus you would earn less money and your competitor will likely lower his price to match yours (reducing your price advantage) –> these two factors result in a lower payoff compared to not cheating (keeping the high price)

 

[Oscar]

akthem wrote:
In the prisoner’s dilemma you would cheat (confess) because you would get less time in jail –> higher payoff than staying silent (more jail time).
In this question, if you cheat, you would lower your price, thus you would earn less money and your competitor will likely lower his price to match yours (reducing your price advantage) –> these two factors result in a lower payoff compared to not cheating (keeping the high price)

Honestly I think the way the question is asked is not fair at all. Without delivering a payout scheme it could have been any of the four scenarios. Athem, your answer while it may be reasonable is a speculation.
In general a Nash equilibrum is found at the point where none of the participants in isolation can improve his position by changing his strategy. With this is mind it is very easy to find the equilibrium. However, as said you need to have the payoffs in the different scenarios.

Regards,
Oscar

 

[Snah]

’Oscar’ wrote:

akthem wrote:
In the prisoner’s dilemma you would cheat (confess) because you would get less time in jail –> higher payoff than staying silent (more jail time).
In this question, if you cheat, you would lower your price, thus you would earn less money and your competitor will likely lower his price to match yours (reducing your price advantage) –> these two factors result in a lower payoff compared to not cheating (keeping the high price)

Honestly I think the way the question is asked is not fair at all. Without delivering a payout scheme it could have been any of the four scenarios. Athem, your answer while it may be reasonable is a speculation.
In general a Nash equilibrum is found at the point where none of the participants in isolation can improve his position by changing his strategy. With this is mind it is very easy to find the equilibrium. However, as said you need to have the payoffs in the different scenarios.

Regards,
Oscar

So in the end, the anwser to choose is the one that both companies think selfishly.
Like here http://en.wikipedia.org/wiki/Prisoner's_dilemma
It is that right?
if not, Could you explain me by an example?

 

[Oscar]

In the classical prisoner’s dilemma that’s the case. In equilibrium nobody of the suspects can improve their payoffs by changing their strategy from cheating to not cheating. The result is that both will cheat in the end if there is no regulating mechanism (like trust or mutual control).
The strategies in equilibrium will however depend of the concrete payoffs under each strategy combination. And that’s why I think the question the way it is asked does not make real sense without a payoff matrix.
Hope not not have such a question in the exam.
Regards,
Oscar