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Nash equilibrium

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Nash equilibrium is assessed.

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Dominant Strategy Equilibrium and Nash Equilibrium

Suppose two firms, Firm Y, Inc., and Firm X, Inc., are locked in a bitter pricing struggle in the bottled water industry. In strategy A, pricing payoff matrix, Firm Y can choose a given row of outcomes by offering A price ("up") or B price ("down"). Firm X can choose a given column of outcomes by choosing to offer A price ("left") or B 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.

Please see the attached document for the table with data and then consider:
a. Is there a dominant strategy equilibrium in this problem? If so, what is it? Please provide a detail explanation.
b. Is there a Nash equilibrium in this problem? If so, what is it? Please provide a detail explanation.

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