# Game Theory Problem

Rose and Cathy decide to play a matrix game. Each has two options, conveniently

called W and L. If both pick W, Cathy pays Rose $4; if both pick L, Cathy pays Rose $2; if Rose chooses L and Cathy chooses W, Cathy pays $1 to Rose; and finally, if Rose chooses W and Cathy chooses L, Rose pays Cathy $1. The payoff matrix for Rose can be represented as

$4 - $1

$1 $2,

where the first row and column represents choosing W and the second row and column represents choosing L. Also, Rose is the row player and Cathy is the column player. How should Rose and Cathy play this game?

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https://brainmass.com/math/discrete-math/game-theory-problem-36191

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Rose and Cathy decide to play a matrix game. Each has two options, conveniently called W and L. If both pick W, Cathy pays Rose $4; if both pick L, Cathy pays Rose $2; if Rose chooses L and Cathy chooses W, Cathy pays $1 to ...

#### Solution Summary

Given a payoff matrix, It is determined how a game should be played. The solution is detailed and well presented.

Dominant strategy

Suppose two competitors, Coa Inc., and Han, Inc., are locked in a bitter pricing struggle in the alumuninum 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 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 billion, $3 billion $2.5 billion, $2 billion

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

A. Is there a dominant strategy equilibrium in this problem? If so, what is it? Explain why the strategy you chose is the dominant strategy.

B. Is there a Nash equilibrium in this problem? If so, what is it? Explain.

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