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# Nash Equilibrium: Coke and Pepsi Advertising Strategy

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1. Find the solution to the following advertising decision game between Coke and Pepsi, assuming the firms act independently.

Pepsi's budget
Low Medium High

Low 400; 400 320; 720 560; 600
Coke's
budget Medium 500; 300 450; 525 540; 500

High 375; 420 300; 378 525; 750

Questions:
1.
a. Does Coke have a dominant strategy? If yes, what is it?
b. Does Pepsi have a dominant strategy? If yes, what is it?
c. What is the likely outcome of this advertising decision problem? Verify that your answer is a Nash equilibrium by explaining why it is strategically stable.
d. Pepsi's highest payoff occurs when Coke and Pepsi both choose high ad budgets. Explain why Pepsi will not likely choose a high ad budget.
2. What is tacit collusion? How would the behavior of the firms differ from that of members of a cartel? Why would tacit collusion exist?

##### Solution Summary

Given the payoff matrix in an advertising war between Coke and Pepsi, this solution uses game theory to predict the likely outcome, including finding the Nash equilibrium.

##### Solution Preview

1.
a. Does Coke have a dominant strategy? If yes, what is it?

A dominant strategy means that Coke will get its best outcome by choosing that strategy no matter what Pepsi does. That is not the case here: if Pepsi chooses Low or Medium, Coke's best strategy is Medium, but if Pepsi chooses High, Coke's best strategy is Low.

b. Does Pepsi have a dominant strategy? If yes, what is it?

Pepsi also does not have a dominant strategy. If Coke chooses Low or Medium, Pepsi's best strategy is Medium, but if Coke chooses High, Pepsi's best strategy is low.

c. What is the likely outcome of this advertising decision problem? Verify that your answer is a Nash equilibrium by explaining why it is ...

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