$1.)$ Two firms, Small and Large, compete by price. Each can choose either a low price or a high price. The following table shows the profit$($in thousands of dollars$)$ each firm would earn in each of the four possible decision situations:

$\backslash$table$[[,,$Large$],[,,$Low price,High price$],[$Small$,$Low price,$$200,$$$500,$$$600,$$$600],[,$$$0,$$$1,500,$$$400,$ $$1,000],[$High price,$$0,$$$1,500,$$$400,$ $$1,000]]$

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?