Suppose you are a firm in a duopoly and have to decide whether to produce a high
ID: 1217913 • Letter: S
Question
Suppose you are a firm in a duopoly and have to decide whether to produce a high quantity or a low quantity. Your profit depends not only on what you choose, but also on what your competitor chooses. Your profits are outlined in the table below, with your profit listed first, your competitor's profit listed second. Describe how your choice interacts with your competitor's choice, and why the profits are as outlined in the payoff matrix. What is the Nash Equilibrium (or Equilibrium) in this case? Explain how you solved for it.Explanation / Answer
3 This is a typical case of prisoners dilemma, in which a global optimum solution generally deviates from Nash equilibrium scenario since both parties choose a option which is best for them.
a. We are not sure what our competitor has chosen, it can be High Quantity (H) or Low Quantity (L).
Lets suppose he chooses H, then best case for us to choose H which gives us $5 profit
Lets suppose he chooses L, then best case for us to choose H which gives us $45 profit
So in either of the case we end up choosing H
b. In the similar way, our competitor is not sure about our strategy so he does following
Lets suppose we choose H, then best case for competitor to choose is H which gives him $5 profit
Lets suppose we chooses L, then best case for competitor to choose is H which gives him $45 profit
So in either of the case he end up choosing H
So Nash equilibrium is (H,H)
so both parties have to settle for $5 profit each