A bag of n players chooses one number between 0 and 10. The winner is the one who chooses the second smallest number. For example, if the selected numbers are [2, 2, 3, 5, 9, 10], the winner will be the one who chose 3. In the event that multiple people choose the second smallest number, the winner is randomly selected from among them. For example, if the selected numbers are [2,2, 2, 3, 3, 3, 3, 5, 9, 10], each player who chose 3 will win with a probability of 1/4. Even if everyone chooses the same number (meaning there is no second smallest number), the winner is randomly selected from among them. Each player wants to choose the number that will give them the greatest chance of winning. Find the Nash equilibrium for this problem.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question

A bag of n players chooses one number between 0 and 10. The winner is the one who chooses the second smallest number. For example, if the selected numbers are [2, 2, 3, 5, 9, 10], the winner will be the one who chose 3. In the event that multiple people choose the second smallest number, the winner is randomly selected from among them. For example, if the selected numbers are [2,2, 2, 3, 3, 3, 3, 5, 9, 10], each player who chose 3 will win with a probability of 1/4. Even if everyone chooses the same number (meaning there is no second smallest number), the winner is randomly selected from among them. Each player wants to choose the number that will give them the greatest chance of winning. Find the Nash equilibrium for this problem.

Expert Solution
steps

Step by step

Solved in 1 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
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)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
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-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education