. Consider the following "location game." There are two ice cream sellers (Seller 1 and Seller 2) in a small city. Residents are uniformly located on a straight street of length 1. The ice cream sellers need to choose where to set up their carts, and each resident will purchase one unit of ice cream from the nearest seller. The city council has fixed the price of the ice cream, and as a result, each seller just wants sell as much ice cream as possible. (a) We think of this "location game” as a simultaneous-move game, in which each player's payoff is the proportion of residents that buy from her cart. Is this game with discrete strategies or continuous strategies? Please state the set of (pure) strategies for both sellers. Is this game zero-sum or non-zero-sum? (b) Find all NE(s) of this game. (c) Is there an alternative pair of locations for the sellers such that the residents' total walking distance is reduced but neither seller is hurt? Is it an NE? (d) Suppose now that there are three ice cream sellers. Is there still an NE (in pure strategies)? If yes, please find it. If no, please explain why. (Hint: Consider strategy profiles in three categories: (i) three sellers locating at three different spots; (ii) two sellers locating at the same spot, one locating at a different spot; (iii) all three sellers locating at the same spot. Can you find profitable deviations in each of these situations?) (e) Suppose now that there are four ice cream sellers. Can you find an NE?
. Consider the following "location game." There are two ice cream sellers (Seller 1 and Seller 2) in a small city. Residents are uniformly located on a straight street of length 1. The ice cream sellers need to choose where to set up their carts, and each resident will purchase one unit of ice cream from the nearest seller. The city council has fixed the price of the ice cream, and as a result, each seller just wants sell as much ice cream as possible. (a) We think of this "location game” as a simultaneous-move game, in which each player's payoff is the proportion of residents that buy from her cart. Is this game with discrete strategies or continuous strategies? Please state the set of (pure) strategies for both sellers. Is this game zero-sum or non-zero-sum? (b) Find all NE(s) of this game. (c) Is there an alternative pair of locations for the sellers such that the residents' total walking distance is reduced but neither seller is hurt? Is it an NE? (d) Suppose now that there are three ice cream sellers. Is there still an NE (in pure strategies)? If yes, please find it. If no, please explain why. (Hint: Consider strategy profiles in three categories: (i) three sellers locating at three different spots; (ii) two sellers locating at the same spot, one locating at a different spot; (iii) all three sellers locating at the same spot. Can you find profitable deviations in each of these situations?) (e) Suppose now that there are four ice cream sellers. Can you find an NE?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Transcribed Image Text:2. Consider the following "location game." There are two ice cream sellers (Seller 1 and Seller 2) in
a small city. Residents are uniformly located on a straight street of length 1. The ice cream sellers
need to choose where to set up their carts, and each resident will purchase one unit of ice cream
from the nearest seller. The city council has fixed the price of the ice cream, and as a result, each
seller just wants sell as much ice cream as possible.
(a) We think of this "location game" as a simultaneous-move game, in which each player's payoff
is the proportion of residents that buy from her cart. Is this game with discrete strategies or
continuous strategies? Please state the set of (pure) strategies for both sellers. Is this game
zero-sum or non-zero-sum?
(b) Find all NE(s) of this game.
(c) Is there an alternative pair of locations for the sellers such that the residents’ total walking
distance is reduced but neither seller is hurt? Is it an NE?
(d) Suppose now that there are three ice cream sellers. Is there still an NE (in pure strategies)?
If yes, please find it. If no, please explain why.
(Hint: Consider strategy profiles in three categories: (i) three sellers locating at three different
spots; (ii) two sellers locating at the same spot, one locating at a different spot; (iii) all
three sellers locating at the same spot. Can you find profitable deviations in each of these
situations?)
(e) Suppose now that there are four ice cream sellers. Can you find an NE?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education