Questions:
Question 1
Suppose two competitors, Coa, Inc., and Han, Inc., are locked in a bitter pricing struggle in the aluminum industry. In the limit pricing payoff matrix, Coa can choose a given row of outcomes by offering a limit price ("up") or monopoly price ("down"). Han can choose a given column of outcomes by choosing to offer a limit price ("left") or monopoly price ("right"). Neither firm can choose which cell of the payoff matrix to obtain; the payoff for each firm depends upon the pricing strategies of both firms.
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Han
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Coa
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Pricing Strategy
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Limit Price
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Monopoly Price
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Limit Price
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$1.5 billion, $3 billion
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$2.5 billion, $2 billion
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Monopoly Price
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$1 billion, $4 billion
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$1.75 billion, $3 billion
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1.Is there a dominant strategy equilibrium in this problem? If so, what is it? Explain your answer fully.
2.Is there a Nash equilibrium in this problem? If so, what is it? Explain your answer fully.
Question 2
In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $500. If both players choose strategy B, each earns a payoff of $100. If player 1 chooses strategy A and player 2 chooses strategy B, then player1 earns $0 and player 2 earns $650. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $650 and player 2 earns $0.
a.Write the above game in normal form.
b.Find each player's dominant strategy, if it exists.
c.Find the Nash equilibrium (or equilibria) of this game
d.Rank strategy pairs by aggregate payoff (highest to lowest)