Deck 6: Strategy and Game Theory

Question 1

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.

Answer 1

B

Question 2

A Nash equilibrium is a set of strategies that are mutual

A)best responses.
B)dominant strategies.
C)Pareto optima.
D)All of these answers are correct.

Answer 2

A

Question 3

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?

A)3/4.
B)1/2.
C)1/4.
D)1/3.

Answer 3

A

Question 4

The general message of the folk theorems is that

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.

Question 5

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.

Question 6

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.

Question 7

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.

Question 8

Cheap talk

A)has no bearing on games; only "real" actions matter.
B)can transmit information in certain equilibria,but only if players' interests are sufficiently distinct.
C)can transmit information in certain equilibria,but only if players' incentives are sufficiently aligned.
D)always leads to the best equilibrium for the "talker".

Question 9

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)δ > B/(A + C).
B)δ > (B - A)/(B - C).
C)δ > B/(A - C).
D)δ > A/(B + C).

Question 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.If herder 1's payoff function is ,his or her best response function is

A) .
B) .
C) .
D) .

Question 11

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 these answers are correct.

Question 12

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.

Question 13

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.

Question 14

Nash equilibria

A)always exist in pure strategies.
B)generally come in even numbers.
C)always exist in finite games.
D)All of these answers are correct.

Question 15

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.

Question 16

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.

Question 17

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.

Question 18

What are the pure-strategy Nash equilibria of the following game?

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.