# Eliminating dominated strategies to find a Nash Equilibrium.

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.

Han

Coa Pricing Strategy Limit Price Monopoly Price

Limit Price $1.5 bil, $3 bil $2.5 bil, $2 bil

Monopoly Price $1 bil, $4 bil $1.75 bil, $3 billion

a. Is there dominant strategy equilibrium in this problem? If so, what is it?

b. Is there Nash equilibrium in this problem? If so, what is it?

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#### Solution Summary

The following examines a 2x2 payoff matrix and shows the process of eliminating dominated strategies to see if each player has a dominant strategy. Finally, this information is used to find the Nash Equilibrium.