Microeconomics (2nd Edition) (Pearson Series in Economics)
2nd Edition
ISBN: 9780134492049
Author: Daron Acemoglu, David Laibson, John List
Publisher: PEARSON
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Question
Chapter 13, Problem 5P
(a)
To determine
Reason for the men’s choice to not be a Nash equilibrium.
(b)
To determine
All men pursuing the same attractive woman is not a case of Nash equilibrium.
(c)
To determine
Reason for Nash equilibrium occurring when only one man asks the beautiful woman to dance.
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In 'the dictator' game, one player (the dictator) chooses how to divide a pot of $10 between herself and another player (the recipient). The recipient does not have an opportunity to reject the proposed distribution. As such, if the dictator only cares about how much money she makes, she should keep all $10 for herself and give the recipient nothing. However, when economists conduct experiments with the dictator game, they find that dictators often offer strictly positive amounts to the recipients.
Are dictators behaving irrationally in these experiments? Whether you think they are or not, your response should try to provide an explanation for the behavior.
Amir and Beatrice play the following game. Amir offers an amount of money z € [0, 1] to
Beatrice. Beatrice can either accept or reject. If Beatrice accepts, then Amir receives 1 - z
dollars and Beatrice receives a dollars. If Beatrice rejects, then both receive no money. As in
the Ultimatum Game, Amir cares only about maximizing the amount of money he receives.
Beatrice, on the other hand, detests Amir, and therefore cares about the amount of money
that both receive: if Amir receives y dollars and Beatrice receives a dollars, then Beatrice's
payoff is a-ay where a > 0.
(a) Find all pure strategy Nash equilibria of the game in which the two players choose
simultaneously (thus Beatrice accepts or rejects without seeing Amir's offer).
Solution: The NE are the strategy profiles in which Beatrice rejects and Amir's offer a
satisfies 2-a(1-x) ≤0, i.e. r ≤a/(1+a).
(b) Find all subgame perfect equilibria of the sequential game in which Amir first makes the
offer and Beatrice observes the offer…
You suspect that you are a price leader in the market. Moreover, you are considering expanding
your operations. H.R. Shovenstuff will observe your moves and then follow, but he is more
secretive so you will not know whether to price high or low after his pricing decision has been
made. Using the following game tree, solve for the Nash equilibrium.
High
Price
Shovenstuff
High
Price
Low
Price
You
High
Price
(2,1) (6,2)
Invest
Low
Price
Invest, High Price, High Price
O Invest, Low Price, High Price
Invest, Low Price, Low Price
O Don't Invest, High Price, High Price
Don't Invest, Low Price, High Price
LOW
Price
(2,4)
You
High
Price
(4,4)
Don't Invest
High
Price
Low
Price
Shovenstuff
Low
Price
You
High
Price
(8,1) (2.6)
Low
Price
(2,1)
Chapter 13 Solutions
Microeconomics (2nd Edition) (Pearson Series in Economics)
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