Firm 2 is contemplating to enter the market in which Firm 1 operates. Firm 1 has two alternative choices, produce low output (L) or produce high output (H). Firm 2 has three alternative choices: not-enter (NO), produce low output (L) or produce high output (H). The profits earned are provided in the payoff matrix below.

			FIRM 2
		NO	L	H
FIRM 1	L	$5000, $0	$2500, $2000	$1500, $1500
	H	$3000, $0	$2500, -$200	$0, -$500

(i) In the above game, does Firm 1 & Firm 2 have a dominant strategy? Explain your answer. 

Assuming that both players choose their strategies simultaneously, what is the Nash Equilibrium of the above game and why? Make sure to also reproduce the payoff matrix in your answer and show the relevant workings on it to support your prediction. 

Suppose that the game is played sequentially with Firm 1 choosing their action first and Firm 2 choosing an action after Firm 1. Represent the game in extensive form (i.e. draw a decision tree which is also referred to as game tree) and using backward induction, analyse the action choice of each firm and predict the outcome of the game.