Question

4. (30 Marks) Consider a game in which two firms choose either full scale (F) or niche (N) advertising campaigns. The payoffs from the possible strategy combinations are as follows:

Firm 2 F N Firm 1 F 200, 300-X 500, 100 N 300, 500-x 200, 200

Where x represents costs specific to firm 2 for undertaking a full scale advertising campaign.

A) Suppose the cost of the full campaign to firm 2 is x=250. Find the Pure Strategy Nash Equilibrium to the game. (10 marks)

B) For what values of x is niche a dominant strategy for firm 2? (10 marks)

C) For any value of x you found in B), determine the Pure Strategy Nash Equilibrium. Is the equilibrium unique? Why or why not? (5 marks)

D) In general, if firm 1 could increase firm 2’s full scale advertising costs (x) would it have an incentive to do so? Why or why not? (5 marks)

Answer 1

Let us see the payoff matrix:

*	*	Firm	2
*		F	N
Firm	F	200,300-x	500,100
1	N	300,500-x	200,200

Part A)

If x = 250,

*	*	Firm	2
*		F	N
Firm	F	200,50	500,100
1	N	300,250	200,200

The two Pure Strategy Nash Equilibria(PSNE) are (F,N) that is (500,100) and (N,F) that is (300,250) as no firm benefits from unilaterally changing their strategy.

Part B)

For N to be dominant for firrm 2, 300-x < 100 and 500 - x < 200

300-x<100 implies x>200

500-x<200 implies x>300

We have to take the intersection of x>200 and x>300

Hence our answer is x>300

Part C)

Let x = 400

Now, the payoff matrix will look like:

*	*	Firm	2
*		F	N
Firm	F	200,-100	500,100
1	N	300,100	200,200

Now since N is a dominant strategy for firm 2, Firm 2 will always choose N. Firm 1 knows this and it sees that choosing F over N is beneficial for Firm 1 (that is 500>200).

Hence our PSNE is (500,100). This equilibrium is unique because only one firm has a dominant strategy and other firm does not have a dominant strategy.

Part D)

Yes, firm 1 has an incentive to increase x as it is beneficial for firm 1 to shift the NE to (500,100) from (300,100) if (300,100) is currently the strategies(N,F) for both firms.

This is because firm 1 can earn a better payoff (500>300) in (F,N) than in (N,F)