Two firms compete by advertising. Given the profit matrix for this advertising game, identify each firm’s...

Two firms compete by advertising. Given the profit matrix for this advertising game, identify each firm’s best response to its rival’s possible actions. Does either firm have a dominant strategy? What is the Nash equilibrium?

		Firm 1
		Do Not Advertise	Advertise
Firm 2	Do Not Advertise	1 2	0 0
	Advertise	2 4	1 3

How does your answer change if Firm 1 gets 3 instead of 1 when both firms advertise?

Solutions

Expert Solution

Given that firm 2 do not advertise, firm 1's best response is do not advertise(1).
Given that firm 2 advertise, firm 1's best response is do not advertise(2).
So, firm 1's dominant strategy is do not advertise because it is always chosen by firm 1 irrespective of firm 2's strategy.

Given that firm 1 do not advertise, firm 2's best response is advertise(4).
Given that firm 1 advertise, firm 2's best response is advertise(3).
So, firm 2's dominant strategy is to advertise because it is always chosen by firm 2 irrespective of firm 1's strategy.

The NE is their dominant strategy equilibrium where firm 1 do no advertise and firm 2 advertises.

When firm 1 gets 3 when both firms advertise,
Given that firm 2 do not advertise, firm 1's best response is do not advertise(1).
Given that firm 2 advertise, firm 1's best response is advertise(3) because 3 > 2.
So, firm 1 does not have any dominant strategy because there is no strategy which is always chosen by it irrespective of firm 2's choice.

Now, the NE is for both firms to advertise because their best response occurs simultaneously when they both advertise.

Rahul Sunny answered 1 year ago

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