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1. A Nash equilibrium is a set of strategies that are mutual:
a.
best responses.
b.
dominant strategies.
c.
Pareto optima.
d.
all of the above.
2. The difference between a Nash equilibrium strategy and a dominant strategy is:
a.
nothing; they are synonymous.
b.
the former is stable but the latter is unstable.
c.
the former must be a best response to all others' strategy profiles, whereas the latter need only be a best
response to others' Nash equilibrium strategies.
d.
the former need only be a best response to others' Nash equilibrium strategies, whereas the latter must be a
best response to all others' strategy profiles.
3. Nash equilibria:
a.
always exist in pure strategies.
b.
generally come in even numbers.
c.
always exist in finite games.
d.
all of the above.
4. The strategy profile in which both players remain silent in the Prisoners' Dilemma can be described as:
a.
non-Pareto optimal and unstable.
b.
Pareto optimal and unstable.
c.
non-Pareto optimal and stable.
d.
Pareto optimal and stable.
5. Which statement is true of the Battle of the Sexes game?
a.
It is a coordination game.
b.
The mixed-strategy Nash equilibrium provides players with lower expected payoffs than other equilibria.
c.
The first mover has an advantage in the sequential version.
d.
All of the above.
6. What are the pure-strategy Nash equilibria of the following game?
Player 2
A
B
C
Player 1
A
4, 4
0, 5
0, 0
B
5, 0
1, 1
0, 0
C
0, 0
0, 0
3, 3
a.
Both play A.
b.
Both play B.
c.
Two equilibria: both play B in one and both play C in the other.
d.
Two equilibria: 1 plays B and 2 plays A and vice versa.
7. In the mixed-strategy Nash equilibrium of the following game in which players randomize between B and C and do not
play A at all, what is the probability that each plays B?
Player 2
A
B
C
Player 1
A
4, 4
0, 5
0, 0
B
5, 0
1, 1
0, 0
C
0, 0
0, 0
3, 3
a.
3/4
b.
1/2
c.
1/4
d.
1/3
8. In a mixed-strategy Nash equilibrium, a player is willing to randomize because:
a.
this confuses opponents.
b.
he or she is indifferent between the actions in equilibrium.
c.
the actions provide the same payoffs regardless of what the other player does.
d.
he or she does not know what the other player is doing.
9. Consider a version of the Tragedy of the Commons in which herder 1 and 2 simultaneously choose to graze quantities
of sheep and , respectively. If herder 1's payoff function is , his or her best response function is:
a.
.
b.
.
c.
.
d.
.
10. Consider a version of the Tragedy of the Commons in which herder 1 and 2 simultaneously choose to graze quantities
of sheep and , respectively, and in which the payoff functions are for 1 and
for 2. The Nash equilibrium is :
a.
100.
b.
60.
c.
40.
d.
33.3.
11. A subgame-perfect equilibrium:
a.
is not a Nash equilibrium; it is a refinement of Nash equilibrium.
b.
is an equilibrium concept used in simultaneous games.
c.
is a special sort of Nash equilibrium.
d.
can be ruled out using backward induction.
12. The difference between a Nash equilibrium and a subgame-perfect equilibrium is:
a.
the former requires rational play both on and off the equilibrium path but the latter requires rational play only
on the equilibrium path.
b.
the former requires rational play only on the equilibrium path but the latter requires rational play both on and
off the equilibrium path.
c.
Nash equilibria are a subset of the subgame-perfect equilibria.
d.
nothing; they are synonyms.
13. Consider a sequential game in which the police move first, choosing which of two sites to defend, and
, against terrorism. After observing this choice, the terrorist moves second, choosing which site to attack. The
attack only succeeds against an undefended target. A successful attack on causes more damage than against
. The police's objective is to minimize and the terrorist's to maximize damage. What outcome characterizes
the subgame perfect equilibrium?
a.
Cannot tell without more information
b.
Police defends , and terrorist attacks
c.
Police defends , and terrorist attacks
d.
Police randomize between targets
14. For an infinitely repeated game promising A per period with continuing cooperation, B for the one period gain from
cheating and C per period for the non-cooperative solution (B > A > C) will have a subgame perfect Nash equilibrium in
trigger strategies providing:
a.
b.
c.
d.
15. The general message of the folk theorems is:
a.
Nash equilibria may not be sustainable over many replications of a game.
b.
payoffs that are unambiguously preferred to Nash equilibria may be sustainable over many replications of a
game.
c.
credible threats may inhibit the achievement of mutually beneficial outcomes over many replications of a
game.
d.
just plain folk play the best games.
16. A game of incomplete information is distinct from one of complete information in that players:
a.
do not observe each others' actions.
b.
do not know each others' payoff functions.
c.
do not know the timing of moves.
d.
use mixed strategies.
17. Which of the following is a true statement about signaling games?
a.
In a separating equilibrium, the second mover's posterior beliefs are the same as his priors.
b.
In a separating equilibrium, Bayes' rule cannot be used to compute posterior beliefs (because it produces an
undefined answer).
c.
In a pooling equilibrium, both the first and second movers choose the same action.
d.
In a pooling equilibrium, the second mover learns nothing from the first mover's action.
18. In the separating equilibrium of the Spence education signaling game in which the high type gets an
education, which is a true statement about the firm's posterior belief that the worker who shows up with no
education is the low type?
a.
b.
c.
d.
19. In experimental tests of the ultimatum game:
a.
the proposer often offers an even split of the "pie", and responders often reject smaller offers, consistent with
the predictions of game theory.
b.
the proposer often offers an even split of the "pie", and responders often reject smaller offers, in contrast to the
predictions of game theory.
c.
the proposer often offers an unfair split, taking the lion's share of the "pie" for him or herself, and responders
often accept such offers, consistent with the predictions of game theory.
d.
the proposer often offers an unfair split, taking the lion's share of the "pie" for him or herself, and responders
often accept such offers, in contrast to the predictions of game theory.
20. How does the dictator game differ from the ultimatum game?
a.
The responder can dictate whether the offer is accepted or not.
b.
The responder has no choice but to accept the proposal.
c.
The experimenter takes over the proposer's role, inserting an offer designed to test a hypothesis.
d.
If the responder rejects, the proposer obtains the whole "pie."
