please help with "game theory"

Game theory (18 points)

In the market for widgets, there are only two firms. Both firms are considering the same strategies to increase their sales of widgets.

Strategy S, "social networks", focuses on increasing the visibility of widgets via social networks.

Strategy N, "newspapers", uses ads in newspapers.

Strategy L consists of doing nothing (leaving everything the same as is). Currently, the payoffs for firm A are 5 and the payoffs for firm B are 15.

If both firms adopt strategy S, payoffs for firm A are equal to 30 and payoffs for firm B are equal to 45. Both firms will have costs of 20 each when adopting this strategy.

If both firms adopt strategy N, payoffs for firm A are equal to 30 and payoffs for firm B are equal to 50. Both firms will have costs of 40 each when adopting this strategy.

If both firms adopt strategy L, their payoffs will stay the same as they are now.

a) Use the information provided above to complete the following payoff matrix - calculate the missing payoffs for the two firms and fill in the blanks. (6 points)

Firm B Firm A	S	N	L
S		0 for A 20 for B	20 for A 30 for B
N	15 for A 35 for B		10 for A 30 for B
L	25 for A 25 for B	5 for A 20 for B	5 for A 15 for B

b) What is the outcome in this game? Denote the equilibrium/equilibria in the payoff matrix. Describe (shortly) in words how you found the equilibrium/equilibria. (8 points)

c) Does any of the firms have a dominant strategy in this game? Briefly explain why or why not. (4 points)