Problem: Two firms, Coa, Inc. and Han, Inc., make up the entire aluminum industry and are interdependent competitors. This means that the payoffs to each firm depend on what the other firm does. Each firm faces a pricing choice—charge customers a limit price (lower) or a monopoly price (higher).
The payoffs, or profits, to each firm are listed in the table below. In each cell of the table, Coa’s payoff is listed first, and Han’s is listed second. For example, the lower right-hand cell of the table shows that, if both firms choose to charge the monopoly price, Coa receives $1.75 billion in profits and Han receives $3 billion. Each firm knows the payoffs that the other firm will receive.
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Han
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Limit price
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Monopoly price
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Coa
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Limit price
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1.5, 3.0
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2.5, 2.0
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Monopoly price
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1.0, 4.0
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1.75, 3.0
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(Payoffs are in billions of dollars.)
a. Is there a dominant strategy in this pricing game for Coa? If so, what is it?
b. Is there a dominant strategy in this pricing game for Han? If so, what is it?
c. Is there a Nash equilibrium in this pricing game? If so, what is it?
d. What is the best result (most profits) for the industry as a whole? How could it get there?