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# Discussing the Dominant Strategy

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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.

Please see the attachment for the chart.

Questions:
a. Is there a dominant strategy equilibrium in this problem?
b. If there is a dominant strategy equilibrium, what is it?
c. Is there a Nash equilibrium in this problem?
d. If there is a Nash equilibrium, what is it?

https://brainmass.com/economics/general-equilibrium/discussing-the-dominant-strategy-299437

#### Solution Preview

Your questions a and b are the same. I am assuming that in (a) you are asking if there is a dominant strategy or not and in (b) you are asking if a dominant strategy equilibrium exists. ...

#### Solution Summary

This solution goes into a great amount of detail related to the economics question being asked. The solution is very easy to follow along and can be easily understood by anyone with a basic understanding of the concepts. This is all completed in about 135 words.

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## Game Theory #1 - Dominant Strategy/Nash Eq. (VHS vs. Betamax)

Please show all work and diagrams if necessary.

1) In the initial videocassette market (home use), there were two competing standards: Sony's Betamax and the VHS standard. Using hypothetical payoffs, we can analyze how both manufacturers can benefit from cooperation rather than competition. The following lists the payoffs for rival manufacturers and Sony in their decision to adopt one of the standards.

SEE WORD ATTACHMENT FOR PAYOFF MATRIX

a) Does Sony and/or the rival manufacturers have a dominant strategy? Explain.

b) Are there any Nash equilibria here? Explain and show how the equilibrium might be supported. Which outcome would Sony prefer, and why? Be sure to discuss cooperative vs. non-cooperative outcomes.

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