Question

	Firm 2
		LOW	HIGH
Firm 1	LOW	$40,000     $40,000	$80,000     $10,000
	HIGH	$10,000     $80,000	$70,000     $70,000

1) What is the pure strategy Nash equilibrium (outcome) of the game?

2)Is the NE unique? If not, suggest a possible remedy to resolve the redundancy.

Answer 1

In the above problem, let us think that firm-1 starts with the strategy Low. Given firm-1's strategy, firm-2 will select the strategy Low as it gives him a higher pay off than the strategy High. Firm-1 will also stick to that strategy as deviating from that strategy to High will give him a lower pay off. So (40,000 40,000) is a nash equilibrium of the game.

Again, if Firm-1 chooses the strategy High. Given his strategy, Firm-2 will choose the strategy Low since it gives him a higher pay off than the other strategy. Again, Firm-1 will deviate from the strategy High to the strategy Low, which gives him a higher pay off. Thus Firm - 1 will move vertically upward to the strategy Low. Given Firm-1 chooses Low, Firm-2 will also choose low, since deviating from that strategy will give him a lower payoff.

Thus, both the Firms will choose the strategy Low with the pay off (40,000 40,000) finally, after starting from any of the strategies.

Thus (40,000 40,000) is the only Nash Equilibrium of the game and thus the Nash Equilibrium is unique.