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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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.
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