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!
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.
