Part (b) In a small town, two candidates, Alex and Bob, are running for mayor. Each candidate must simultaneously and independently decide whether to campaign in the North (N), the South (S), or the Central (C) district of the town. There are a total of 1000 votes in the North district, 1500 votes in the South district, and 2000 votes in the Central district. If both candidates campaign in the same district, they split the votes of that district evenly. If a candidate campaigns alone in a district, that candidate receives all the votes from that district. Each candidate's payoff is equal to the total number of votes they receive. For example, if Alex and Bob both campaigns in the Central district, then each get a payoff equal to 2000/2 = 1000. i. Using the above information, present the normal-form representation of the game via a payoff matrix. ii. Determine all Nash equilibria of this simultaneous move game and explain. iii. Determine whether Alex has a dominant strategy and explain. Page 8 of 9 iv. Determine whether Alex has a dominated strategy and explain. V. Suppose that game is played sequentially in which Alex will choose a strategy first and after observing Alex's choice, Bob will choose his strategy. Draw the game in extensive form (i.e., draw a game tree/decision tree) and apply backward induction to make a valid prediction about the play of the game. Explain your answer carefully.
Part (b) In a small town, two candidates, Alex and Bob, are running for mayor. Each candidate must simultaneously and independently decide whether to campaign in the North (N), the South (S), or the Central (C) district of the town. There are a total of 1000 votes in the North district, 1500 votes in the South district, and 2000 votes in the Central district. If both candidates campaign in the same district, they split the votes of that district evenly. If a candidate campaigns alone in a district, that candidate receives all the votes from that district. Each candidate's payoff is equal to the total number of votes they receive. For example, if Alex and Bob both campaigns in the Central district, then each get a payoff equal to 2000/2 = 1000. i. Using the above information, present the normal-form representation of the game via a payoff matrix. ii. Determine all Nash equilibria of this simultaneous move game and explain. iii. Determine whether Alex has a dominant strategy and explain. Page 8 of 9 iv. Determine whether Alex has a dominated strategy and explain. V. Suppose that game is played sequentially in which Alex will choose a strategy first and after observing Alex's choice, Bob will choose his strategy. Draw the game in extensive form (i.e., draw a game tree/decision tree) and apply backward induction to make a valid prediction about the play of the game. Explain your answer carefully.
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter18: Auctions
Section: Chapter Questions
Problem 4MC
Related questions
Question
Please correct answer and don't use hand raiting
Transcribed Image Text:Part (b)
In a small town, two candidates, Alex and Bob, are running for mayor. Each candidate must
simultaneously and independently decide whether to campaign in the North (N), the South (S),
or the Central (C) district of the town.
There are a total of 1000 votes in the North district, 1500 votes in the South district, and 2000
votes in the Central district. If both candidates campaign in the same district, they split the
votes of that district evenly. If a candidate campaigns alone in a district, that candidate
receives all the votes from that district. Each candidate's payoff is equal to the total number of
votes they receive. For example, if Alex and Bob both campaigns in the Central district, then
each get a payoff equal to 2000/2 = 1000.
i.
Using the above information, present the normal-form representation of the game via a
payoff matrix.
ii.
Determine all Nash equilibria of this simultaneous move game and explain.
iii.
Determine whether Alex has a dominant strategy and explain.
Page 8 of 9
iv.
Determine whether Alex has a dominated strategy and explain.
V.
Suppose that game is played sequentially in which Alex will choose a strategy first and
after observing Alex's choice, Bob will choose his strategy. Draw the game in extensive
form (i.e., draw a game tree/decision tree) and apply backward induction to make a
valid prediction about the play of the game. Explain your answer carefully.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
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: Applications, Strategies an…
Economics
ISBN:
9781305506381
Author:
James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
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: Applications, Strategies an…
Economics
ISBN:
9781305506381
Author:
James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:
Cengage Learning
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Microeconomics (MindTap Course List)
Economics
ISBN:
9781305971493
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Economics, 7th Edition (MindTap Cou…
Economics
ISBN:
9781285165875
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning