Question

Firm B Strategy 1 Strategy 2 Strategy 1: 24, 24 14, 30 Firm A Strategy 2: 30, 14 20, 20 1. (2 pts.) Does Firm A have a dominant strategy? _Yes_ If yes, which strategy? _Strategy 1_ 2. (2 pts.) Does Firm B have a dominant strategy? _No__ If so, which strategy? _ 3. (3 pts.)Are there any Nash equilibria? If there are any Nash equilibria, identify any and all of them.

Answer 1

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

Yes, Firm A has the dominant strategy of choosing Strategy 2 because it gives him higer payoff than Strategy 1 irrespective of decision of Firm B.

2. Yes, Firm B has the dominant strategy of choosing Strategy 2 because of higher payoff irrespective of decision of Firm A.

3. 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 Strategy 2 then best response of Firm B is to choose Strategy 2.

If Firm B chooses Strategy 2 then best response of Firm A is to choose Strategy 2.

So, (Strategy 2; Strategy 2) is the Nash Equilibrium.