Deck 3: Focal-Point and Evolutionary Equilibria

Question 1

A focal-point equilibrium:

A) May be a possible solution to a game involving multiple Nash equilibria.
B) Cannot exist in the presence of multiple Nash equilibria.
C) Results when two players follow a secure strategy.
D) Only applies to multistage games.
E) None of the above.

Answer 1

May be a possible solution to a game involving multiple Nash equilibria.

Question 2

A focal-point equilibrium is possible for:

A) Static games with a unique Nash equilibrium.
B) Static games with multiple Nash equilibria.
C) Static games in which there are no Nash equilibrium does not exist.
D) Zero-sum games.
E) None of the above.

Answer 2

Static games with multiple Nash equilibria.

Question 3

A strategy profile that is a focal-point equilibrium:

A) Is said to be self-fulfilling because the players recognize that it is in their best interest to adopt it.
B) Is the outcome of a coordination game because the players are attempting to implicitly coordinate their strategy choices to achieve a mutually beneficial outcome.
C) Because the players share a common understanding of the context within which the game is being played.
D) All of the above.
E) None of the above.

Answer 3

All of the above.

Question 4

Coordination games:

A) Are noncooperative games in which the players attempt to their coordinate their strategies.
B) Are cooperative games in which the players' lack a common frame of reference.
C) Involve dynamic equilibrium strategy profiles in which successful strategies replace unsuccessful strategies.
D) Sometimes have a focal-point equilibrium.
E) Answers a and d are correct.

Question 5

-Consider the noncooperative, static game depicted in Figure 3.1. Two hunters are stalking bear or raccoon. Each could hunt raccoon alone, or they can coordinate their efforts and hunt bear. Sharing a bear is preferred to sharing a raccoon. The payoffs in this game are measured in units of satisfaction. If larger payoffs are preferred, the Nash equilibrium strategy profile for this game is:
I. {Bear, Bear}.
II. {Raccoon, Raccoon}.
III. {Bear, Raccoon}.
IV. {Raccoon, Bear}.
Which of the following is correct?

A) I only.
B) II only.
C) III or IV only.
D) III and IV only.
E) I and II only.

Question 6

-Consider the noncooperative, static game depicted in Figure 3.1. Two hunters are stalking bear or raccoon. Each could hunt raccoon alone, or they can coordinate their efforts by hunting bear. Sharing a bear is preferred to sharing a raccoon. The payoffs in this game are measured in units of satisfaction. If larger payoffs are preferred, the most likely focal-point equilibrium for this game is:
I. {Bear, Bear}.
II. {Raccoon, Raccoon}.
III. {Bear, Raccoon}.
IV. {Raccoon, Bear}.
Which of the following is correct?

A) I only.
B) II only.
C) III only.
D) IV only.
E) I and II only.

Question 7

-Consider the noncooperative, static, pricing game depicted in Figure 3.2. Firms A and B can charge a high price or a low price for their products. Payoffs are in thousands of dollars. If larger payoffs are preferred, the Nash equilibrium strategy profile for this game is: I. {High price, High price}.
II) {High price, Low price}.
III) {Low price, High price}.
IV) {Low price, Low price}.
Which of the following is correct?

A) I only.
B) II only.
C) II or III only.
D) II and III only.
E) I and IV only.

Question 8

-Consider the noncooperative, static, pricing game depicted in Figure 3.2. Firms A and B can charge a high price or a low price for their products. Payoffs are in thousands of dollars. If larger payoffs are preferred, the most likely focal-point equilibrium for this game is:
I. {High price, High price}.
II. {High price, Low price}.
III. {Low price, High price}.
IV. {Low price, Low price}.
Which of the following is correct?

A) I only.
B) II only.
C) II or III only.
D) II and III only.
E) IV only.

Question 9

-Consider the pie-sharing game depicted in Figure 3.3. Greta has baked an apple pie for her two sons Hans and Frans. Hans and Frans simultaneously ask for a slice of the pie. Greta tells her sons that they can have any size slice they want as long as their slices do not exceed the entire pie. On the other hand, if their combined requests exceed the size of the pie then they each get nothing. This game has _____ Nash equilibria.

A) 0
B) 1
C) 2
D) 3
E) 4

Question 10

-Consider the pie-sharing game depicted in Figure 3.3. Greta has baked an apple pie for her two sons Hans and Frans. Hans and Frans simultaneously ask for a slice of the pie. Greta tells her sons that they can have any size slice they want as long as their slices do not exceed the entire pie. On the other hand, if their combined requests exceed the size of the pie then they each get nothing. The most likely focal-point equilibrium for this game is:

A) {No pie, No pie}.
B) {1/4 pie, 3/4 pie}.
C) {3/4 pie, 1/4 pie}.
D) {1/2 pie, 1/2 pie}.
E) {Whole pie, Whole pie}.

Question 11

In games involving multiple Nash equilibria, several qualitative factors appear to be important in explaining the existence of a focal-point equilibrium, including:
I. Distribution of payoffs.
II. Equity. III. Diversity.
IV. Fairness.
V. Uniqueness.
Which of the following is correct?

A) I, II and III only.
B) II, III and IV only.
C) III, IV and V only.
D) I, II and IV only.
E) II, III and V only.

Question 12

A Nash equilibrium:

A) Always results in the best possible payoff for all players.
B) Occurs when each player adopts a strategy that is the best response to a strategy adopted by a rival.
C) Occurs when a player cannot improve his or her payoff by switching strategies.
D) Both b and c are correct.
E) None of the above.

Question 13

-Brad and Angelina are trying to decide how to spend an evening. Brad would prefer to spend an evening at the opera. Angelina would spend the evening attending a professional wrestling match. They could, of course, go their separate ways, but would rather spend the evening together. Figure 3.4 summarizes the payoffs from alternative strategy profiles. This game has _____ Nash equilibrium strategy profiles.

A) 0
B) 1
C) 2
D) 3
E) 4

Question 14

-Brad and Angelina are trying to decide how to spend an evening. Brad would prefer to spend an evening at the opera. Angelina would spend the evening attending a professional wrestling match. They could, of course, go their separate ways, but would rather spend the evening together. Figure 3.4 summarizes the payoffs from alternative strategy profiles. The most likely focal-point equilibrium strategy profile for this game is:

A) {Opera, Opera}.
B) {Opera, Wrestling}.
C) {Wrestling, Opera}.
D) {Wrestling, Wrestling}.
E) It is not possible to answer this question without additional information.

Question 15

-Brad and Angelina are trying to decide how to spend an evening. Brad would prefer to spend an evening at the opera. Angelina would spend the evening attending a professional wrestling match. They could, of course, go their separate ways, but would rather spend the evening together. Figure 3.4 summarizes the payoffs from alternative strategy profiles. What is the strategy profile for this game if Brad and Angelina adopt a minimax regret strategy?

A) {Opera, Opera}
B) {Opera, Wrestling}
C) {Wrestling, Opera}
D) {Wrestling, Wrestling}.

Question 16

-Brad and Angelina are trying to decide how to spend an evening. Brad would prefer tospend an evening at the opera. Angelina would spend the evening attending aprofessional wrestling match. They could, of course, go their separate ways, but would rather spend the evening together. Figure 3.4 summarizes the payoffs from alternative strategy profiles. What is the strategy profile for this game if Brad and Angelina adopt a maximin strategy?

A) {Opera, Opera}
B) {Opera, Wrestling}
C) {Wrestling, Opera}
D) {Wrestling, Wrestling}.

Question 17

-Ben and Jennifer are trying to decide how to spend an evening. Ben would like to attend a ballet performance. Jennifer would like to go to a hockey game. While they could spend the evening apart, they would prefer to spend the evening together. Figure 3.5 summarizes the payoffs from alternative choices. This game has _____ Nash equilibrium strategy profiles.

A) 0
B) 1
C) 2
D) 3.
E) 4

Question 18

-Ben and Jennifer are trying to decide how to spend an evening. Ben would like to attend a ballet performance. Jennifer would like to go to a hockey game. While they could spend the evening apart, they would prefer to spend the evening together. Figure 3.5 summarizes the payoffs from alternative choices. The most likely focal-point equilibrium strategy profile for this game is:

A) {Ballet, Ballet}.
B) {Ballet, Hockey}.
C) {Hockey, Ballet}.
D) {Hockey, Hockey}.
E) It is not possible to answer this question without additional information.

Question 19

-Ben and Jennifer are trying to decide how to spend an evening. Ben would like to attend a ballet performance. Jennifer would like to go to a hockey game. While they could spend the evening apart, they would prefer to spend the evening together. Figure 3.5 summarizes the payoffs from alternative choices. What is the strategy profile for this game if Ben and Jennifer adopt a minimax regret strategy?

A) {Ballet, Ballet}.
B) {Ballet, Hockey}.
C) {Hockey, Ballet}.
D) {Hockey, Hockey}.

Question 20

-Ben and Jennifer are trying to decide how to spend an evening. Ben would like to attend a ballet performance. Jennifer would like to go to a hockey game. While they could spend the evening apart, they would prefer to spend the evening together. Figure 3.5 summarizes the payoffs from alternative choices. What is the strategy profile for this game if Ben and Jennifer adopt a maximin strategy?

A) {Ballet, Ballet}.
B) {Ballet, Hockey}.
C) {Hockey, Ballet}.
D) {Hockey, Hockey}.

Question 21

-Consider the Cold War game depicted in Figure 3.6 involving a first and second strike nuclear strategies where !4 represents total annihilation, !L represents significant but "acceptable" losses, and G_US and G_SU represent positive gains to the U.S. and the Soviet Union, respectively. The equilibrium strategy profile(s) for this game is(are):
I. {First strike, First strike}.
II. {Second strike, Second strike}.
III. {First strike, Second strike}.
IV. {Second strike, First strike}.
Which of the following is correct?

A) I only.
B) II only.
C) I and II only.
D) III and IV only.
E) This game does not have a equilibrium strategy profile.

Question 22

-Consider the Cold War game depicted in Figure 3.6 involving a first and second strike nuclear strategies where !4 represents total annihilation, !L represents significant but "acceptable" losses, and G_US and G_SU represent positive gains to the U.S. and the Soviet Union, respectively. If the players in this game are assumed to be rational, the most likely focal-point equilibrium strategy profile for this game is:
I. {First strike, First strike}.
II. {Second strike, Second strike}.
III. {First strike, Second strike}.
IV. {Second strike, First strike}.
Which of the following is correct?

A) I only.
B) II only.
C) I and II only.
D) III and IV only.
E) This game does not have a equilibrium strategy profile.

Question 23

-Consider the Cold War game depicted in Figure 3.6 involving a first and second strike nuclear strategies where !4 represents total annihilation, !L represents significant but "acceptable" losses, and G_US and G_SU represent positive gains to the U.S. and the Soviet Union, respectively. The strategy profile:

A) {First strike, First strike} constitutes a Nash equilibrium because neither player can improve its payoff by switching strategies.
B) {Second strike, Second strike} constitutes a Nash equilibrium because neither player can improve its payoff by switching strategies.
C) {First strike, First strike} is a Nash equilibrium because both players have a strictly dominant strategy.
D) Both a and b are correct.
E) None of the above are correct.

Question 24

-Consider the Cold War game depicted in Figure 3.6 involving a first and second strike nuclear strategies where !4 represents total annihilation, !L represents significant but "acceptable" losses, and G_US and G_SU represent positive gains to the U.S. and the Soviet Union, respectively. Both players have:

A) A weakly dominant first strike strategy.
B) A weakly dominant second strike strategy.
C) Neither player has a weakly dominant strategy.
D) Both players have a strictly dominant strategy.
E) Both players have nondominant strategies.

Question 25

-Consider the Cold War game depicted in Figure 3.6. If both players have a weakly dominant strategy, the equilibrium strategy profile for this game is:
I. {First strike, First strike}.
II. {Second strike, Second strike}.
III. {First strike, Second strike}.
IV. {Second strike, First strike}.
Which of the following is correct?

A) I only.
B) II only.
C) I and II only.
D) III and IV only.
E) This game does not have a equilibrium strategy profile.

Question 26

The qualitative factors that help to explain the existence of a focal-point equilibrium include:

A) Symmetry and uniqueness.
B) Distribution of payoffs
C) Equity
D) Efficiency and fairness
E) All of the above.

Question 27

The existence of a focal-point equilibrium:

A) Provides an explanation as to why explicit collusion is not possible.
B) Explains why explicit collusion is necessary.
C) Suggests that implicit collusion may be possible.
D) Implies the existence of an evolutionary equilibrium.
E) Is only possible for cooperative, static games.

Question 28

When attempting to identify a unique focal-point equilibrium in static games:

A) If one identifying principle suggests a unique Nash equilibrium and another suggests multiple Nash equilibria, the first principle tends to dominate.
B) If one identifying principle suggests multiple Nash equilibria and another suggests a unique Nash equilibrium, the first principle tends to dominate.
C) Explicit agreements may come about through a process of adaptive expectations.
D) Implicit agreements may come about through a process of backward induction.
E) Observing how others have played the game in the past should not provide affect a players current and future moves.

Question 29

Framing:

A) Refers to the idea that players often make decisions using a familiar frame of reference.
B) Refers to the idea that players make decisions with less than perfect information.
C) Has something to do with oil paintings.
D) Is a prisoners' dilemma problem in which one player attempts to gain an advantage by attempting to maneuver a rival into an untenable situation.
E) Answers a and b above.

Question 30

An evolutionary equilibrium:

A) Is a solution to games with imperfect information in which players move without knowledge of previous moves of the other players..
B) Is a Bayesian Nash equilibrium.
C) Is a population-dynamic equilibrium strategy profile that results when successful strategies replace unsuccessful strategies.
D) Is found using the backward induction solution algorithm.
E) All of the above are correct.

Question 31

-Consider the Hawk-Dove Game in Figure 3.7. Suppose that the costs (c) and benefits (b)of aggressive behavior $10 and $12, respectively. The evolutionary equilibrium for this game is:

A) {Hawk, Hawk}.
B) {Dove, Dove}.
C) {Hawk, Dove}.
D) {Dove, Hawk}.
E) Answers c or d above

Question 32

-Consider the Hawk-Dove Game in Figure 3.7. Suppose that the costs (c) and benefits (b)of aggressive behavior $12 and $10, respectively. The evolutionary equilibrium for this game is:

A) {Hawk, Hawk}.
B) {Dove, Dove}.
C) {Hawk, Dove}.
D) {Dove, Hawk}.
E) Answers b or c above