Consider the following game.
Two firms, 1 and 2, individually choose and simultaneously submit a bid price for a given product. They can submit either a high price or a low price. If both firms bid high, the resulting payoff for each firm is $80 million. If firm 1 bids low and firm 2 bids high, firm 1's payoff is $81 million and firm 2's payoff is $77 million. If both firms bid low, the resulting payoffs are $78 million for firm 1 and $76 million for firm 2. If firm 1 bids high and firm 2 bids low, firm 1's payoff is $77 million and firm 2's payoff is $79 million.
Note that if firm 1 bids high (H) and firm 2 bids low (L), then the corresponding pair of pricing strategies is (H, L).
a. Identify the pair of pricing strategies associated with a Nash equilibrium.
b. Using the definition of a Nash equilibrium, show why this pair of pricing strategies is a Nash equilibrium.