Question

Two firms, Small and Large, compete by price. Each can choose either a low price or a high price. The following payoff table shows the profit (in thousands of dollars) each firm would earn in each of the four possible decision situations:

		Small
		Low price	High price
Large	Low price	$1,000, $500	$375, $250
	High price	$550, –$100	$575, –$200

a) Is there a dominant strategy for Small? If so, what is it? Why?

b) Is there a dominant strategy for Large? If so, what is it? Why?

c)  What is the likely pair of decisions? What payoff will each receive?

Answer 1

A) If large chooses low price it is optimal for small to choose a low price.

If large chooses high price it is optimal for small to choose a low price.

So, dominant strategy for small is to choose a low price.

B) If small chooses low price it is optimal for large to choose a low price.

If small chooses high price it is optimal for large to choose a high price.

So, there is no dominant strategy for high.

C) Nash equilibrium provides the likely pair of decision.

Nash equilibrium in this case is both firms setting the low price. It is nash equilibrium because at this strategy no firm has any incentive to switch to some other strategy. Payoff for large firm will be 1000 and for small firm will be 500.