Game Theory

[SPC]

Hi

I am practicing number of Game Theory Questions and appear to be making a few errors.

Perhaps someone can advise what exactly we are looking for when deciding which strategy Firm A should go for with respect to Firm B.
What is it exactly we are looking out for when comparing High (x1,y1) with Low (x2,y2)

All assistance is greatly appreciated!

 

[freddie]

Hi SPC

The payoff matrix shows the payoffs for each firm for each combination of strategies. So if Firm A is on the LHS and Firm B is on the top, then the payoffs might be:
High High (10,10) with 10 for Firm A and 10 for Firm B. High Low (-5, 15) with 5 for Firm A and 15 for Firm B
Low High (15, -5) with 15 for Firm A and -5 for Firm B. Low Low (0, 0) with 0 for Firm A and 0 for Firm B.

So, imagine we're Firm A. We say:
If B goes High, I could get 10 if I go High or 15 if I go Low, so I'd go Low.
If B goes Low, I could get -5 if I go High or 0 if I go Low, so I'd go Low.

In this case, there's a dominant strategy because whatever B does, it's always better for me to go Low.

If you do the same for B, we find that B has a dominant strategy too - to go Low.

Therefore Low Low becomes the dominant equilibrium. This is not a great position since both A and B make a payoff of 0. This illustrates the prisoners' dilemma and shows us why firms in oligopoly might be tempted to collude and agree to both go high.

Hope this helps.