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Nash Equilibrium Of a Coffee Company Rivalry

Little Kona is a small coffee company that is considering entering a market dominated by Big Brew. Each company's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price:

Big Brew
High Price Low Price
Little Kona Enter ($2,$3)millions ($1,$1)millions
Little Kona Don't Enter ($0,$7)millions ($0,$2)millions

a. Does either player in this game have a dominant strategy?

b. Does your answer to part (a) help you figure out what the other player should do? What is the Nash equilibrium? Is there only one?

c. Big Brew threatens Little Kona by saying, "If you enter, we're going to set a low price, so you had better stay out." Do you think Little Kona should believe the threat? Why or why not?

d. If the two firms could collude and agree on how to split the total profits, what outcome would they pick?

Solution Preview

a) Both players have a dominant strategy. See the attached file. Big Brew gets a higher payoff by charging a high price whether Little Kona enters or not. Little Kona gets a higher payoff by entering ...

Solution Summary

This solution shows how to use game theory and Nash equilibria to determine the best strategy for the dominant firm in the coffee industry and a new firm contemplating entering the industry.