Question

2. Suppos e there are two firms in an oligopoly, Firm A both firms charge a low price, each earns and Firm B. If $2 million in profit. If both firms charge a high price, each earns $3 million in profit. If one firm charges a high price and one charges a low price, customers flock to the firm with the low price, and that firm earns $4 million in profit while the firm with the high price earns $1 million in profit. a. Draw a clearly labeled payoff matrix for this game and fill in each of the payoffs. Arrange the matrix so that Firm A is on the left, and make the upper-left set of strategies both firms choosing low prices. b. Identify the dominant strategy for each player, if one exists. c. Identify the Nash equilibria in this game, if any exist. d. Now suppose a tax on high-priced goods causes a $500,000 decrease in the payoffs received from charging a high price. Redraw the payoff matrix with adjustments for this change. (5 points)

Answer 1

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If firm A charges low price, it is optimal for firm B to charge a low price. If firm A charges high prices, it is optimal for firm B to charge a low price. So, dominant strategy for firm B is to charge a low price. Similarly, dominant strategy for firm A is to charge a low price. So, dominant strategy is (low price, low price) Nash Equilibrium is (low price, low price). At this strategy no firm has any incentive to deviate to some other strategy