# 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.

https://brainmass.com/economics/game-theory/dominant-strategy-equilibrium-and-nash-equilibrium-253778

#### Solution Preview

a.) There is a dominant strategy for firm X: choosing A. Because in the matrix, we find that X's payoff by choosing strategy A is always higher than ...

#### Solution Summary

In just over 100 words, this solution analyzes the dominant strategy equilibrium and the Nash equilibrium. Values are given to support the interpretations being made.