Why do fast-food restaurants tend to cluster in the same immediate vicinity? Consider the following situation concerning the owners of two hamburger franchises, Burger Queen and Wally’s. Route 795 was recently extended from Baconsville to Hashbrowntown. Both franchise owners currently operate profitable restaurants in Hashbrowntown, a small town of about 25,000 residents.The exit off Route 795 is 5 miles from Hashbrowntown. Both franchise owners are considering moving their restaurants from the center of town to a location near the exit ramp. Regardless of location, we will assume that there is only enough business for two fastfood franchises to operate profitably. The franchise owners calculate that by relocating they will continue to receive some in-town business, but will also gain customers who use the exit as a rest stop. The payoff matrix for either strategy in this game is illustrated in Figure 10.10. The first entry in each cell of the payoff matrix refers to the payoff to Wally’s and the second entry refers to the payoff to Burger Queen. a. Does either franchise owner have a strictly dominant strategy? b. Is the solution to this game a Nash equilibrium?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.12P
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Why do fast-food restaurants tend to cluster in the same immediate vicinity? Consider the following situation concerning the owners of two hamburger franchises, Burger Queen and Wally’s. Route 795 was recently extended from Baconsville to Hashbrowntown. Both franchise owners currently operate profitable restaurants in Hashbrowntown, a small town of about 25,000 residents.The exit off Route 795 is 5 miles from Hashbrowntown. Both franchise owners are considering moving their restaurants from the center of town to a location near the exit ramp. Regardless of location, we will assume that there is only enough business for two fastfood franchises to operate profitably. The franchise owners calculate that by relocating they will continue to receive some in-town business, but will also gain customers who use the exit as a rest stop. The payoff matrix for either strategy in this game is illustrated in Figure 10.10. The first entry in each cell of the payoff matrix refers to the payoff to Wally’s and the second entry refers to the payoff to Burger Queen.

a. Does either franchise owner have a strictly dominant strategy?

b. Is the solution to this game a Nash equilibrium?

Burger Queen
Exit ramp Hashbrowntown
($150,000,
$150,000)
($1,000,000,
$100,000)
Exit ramp
Wally's
($100,000,
Hashbrowntown $1,000,000)
($250,000,
$250,000)
Payoffs: (Wally s, Burger Queen)
FIGURE 10.1o Payoff matrix for problem 10.7.
Transcribed Image Text:Burger Queen Exit ramp Hashbrowntown ($150,000, $150,000) ($1,000,000, $100,000) Exit ramp Wally's ($100,000, Hashbrowntown $1,000,000) ($250,000, $250,000) Payoffs: (Wally s, Burger Queen) FIGURE 10.1o Payoff matrix for problem 10.7.
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