EBK INTERMEDIATE MICROECONOMICS AND ITS
12th Edition
ISBN: 9781305176386
Author: Snyder
Publisher: YUZU
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Chapter 15, Problem 8RQ
To determine
To explain:First player thought for second player and vice-versa in a separating equilibrium and in pooling equilibrium.
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Consider a signaling model in which the first player may be one of two types. What determines the other player’s beliefs about the first player’s type before observing the first-player’s signal? After observing the first player’s signal, what beliefs must the second player have about the first player’s type in a separating equilibrium? What beliefs must the second player have in a pooling equilibrium?
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…
Consider the signaling game below. Does the game have a perfect Bayesian equilibrium in
which all sender types play L?
Does there exist a perfect Bayesian equilibrium in which all sender types play R?
Explain.
1,1
1,00
2,1
0,0
0,0
14
Receiver
u
Receiver
14
L
L
L
(1/3)
1₂ R
(1/3)
R
(1/3)
R
14
Receiver
14
Receiver
U
0,1
0,0
1,1
1,0
0,0
2,1
Chapter 15 Solutions
EBK INTERMEDIATE MICROECONOMICS AND ITS
Ch. 15.2 - Prob. 1TTACh. 15.2 - Prob. 2TTACh. 15.2 - Prob. 1MQCh. 15.2 - Prob. 1.1MQCh. 15.2 - Prob. 2.1MQCh. 15.2 - Prob. 1.1TTACh. 15.2 - Prob. 2.1TTACh. 15.2 - Prob. 1.2TTACh. 15.2 - Prob. 2.2TTACh. 15.3 - Prob. 1MQ
Ch. 15.3 - Prob. 2MQCh. 15.4 - Prob. 1MQCh. 15.4 - Prob. 1.1MQCh. 15.4 - Prob. 2.1MQCh. 15.5 - Prob. 1TTACh. 15.5 - Prob. 2TTACh. 15.5 - Prob. 1MQCh. 15.5 - Prob. 2MQCh. 15 - Prob. 1RQCh. 15 - Prob. 2RQCh. 15 - Prob. 3RQCh. 15 - Prob. 4RQCh. 15 - Prob. 5RQCh. 15 - Prob. 6RQCh. 15 - Prob. 7RQCh. 15 - Prob. 8RQCh. 15 - Prob. 9RQCh. 15 - Prob. 10RQCh. 15 - Prob. 15.1PCh. 15 - Prob. 15.2PCh. 15 - Prob. 15.3PCh. 15 - Prob. 15.4PCh. 15 - Prob. 15.5PCh. 15 - Prob. 15.6PCh. 15 - Prob. 15.7PCh. 15 - Prob. 15.8PCh. 15 - Prob. 15.9PCh. 15 - Prob. 15.10P
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