Consider the following game in which two firms A and B sell computing product and are...

Consider the following game in which two firms A and B sell computing product and are deciding whether to undertake advertising campaigns. The possible outcomes of this simultaneous one-shot game are illustrated by the payoff matrix (annual profit payoffs in millions). Note: Firm A's payoffs appear first in the payoff pairs:

Firm A	Firm B
	Strategy	Advertise	Don't Advertise
	Advertise	10, 5	15, 0
	Don't advertise	6, 8	20, 2

Use the payoff matrix to answer the questions below.

a. What is (are) the dominant strategy (strategies), if any, in this game? Justify your answer.

b. Identify the Nash equilibrium, if any, for Firm A and Firm B in this game. Justify your answer.

Expert Solution

a) Dominant strategy is a strategy for a player i.e. best response to all strategy profile of other player.

Firm A does not have any dominant strategy because it is not able to earn higher profit by choosing one strategy and without independence of strategy of other player.

Firm B has the dominant strategy of Advertising because it gives Firm B higher payoff irrespective of decision of Firm A. If B chooses to advertise then its payoff is either 5 or 8 which is greater than payoff when it chooses not to advertise.

b) Nash equilibrium is a strategy profile such that for each player given strategy, it is best response. Nash equilibrium is a set of strategies such that each player is doing their best given the strategy of other player.

If Firm A chooses to Advertise then best response of Firm B is to choose Advertise.

If Firm B chooses to Advertise then best response of Firm A is to choose Advertise.

So, (Advertise; Advertise) is the Nash Equilibrium.

Rahul Sunny answered 2 years ago

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