Two electricity firms, Firm 1 and Firm 2, are competing in the National Electricity Market by choosing the price to charge for each unit of power they produce. They can each choose to charge a high price (H), a medium price (M), or a low price (L). Charging a low price means they will make almost no revenue on the sale, and so make substantial negative profit. Charging a high or medium price will guarantee some profit, with the level of profit depending on the choice of the other firm. The payoff for each firm depending on their own action, and the action of their opponent, is given in the matrix below. H Firm 2 M L H 7 9 -5 7 4 4 Firm 1 M ++ 4 5 -5 9 5 0 4 0 L -5 CT -5 -5 a) Find all Nash Equilibria for this simultaneous game. Explain why cach is a Nash Equilibrium and briefly explain why there are no other Nash Equilibria. b) Suppose that, instead of acting simultaneously, Firm 1 sets prices first, and Firm 2 chooses it's price only after seeing the price of Firm 1. Draw the game tree for this sequential game. c) For the sequential game in part (b), find the unique Subgame Perfect Nash Equilibrium. d) For the sequential game in part (b), explain why the alternative strategy profile (H1, (M2, L2, L2)) (that is, the profile where Firm 1 sets a high price and Firm 2 sets a medium price if Firm 1 sets a high price, and sets a low price otherwise) is a Nash Equilibrium. Describe the non-credible threat being used in this strategy profile. e) Returning to the simultaneous game of parts (a) and (b); suppose the firms are not purely strategic players, but are level-k thinkers instead. Recall that a level-0 thinker would choose an action at random. What would be the action of a level-1 player, and why? What would be the action of a level-2 player, and why?