# Quiz 15: Introduction to Game Theory

Business

Q 1Q 1

One possible explanation for low voter turnouts during elections is
A)the cost of voting is too high
B)there are rarely any good candidates
C)the free rider problem
D)do not vote" is the dominant strategy

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Multiple Choice

D

Q 2Q 2

When a phone line is cut off in the middle of a conversation, and neither party returns the call, this is an example of:
A)low payoffs on the game.
B)a best response function.
C)multiple Nash equilibrium.
D)a Nash equilibrium.

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Multiple Choice

D

Q 3Q 3

During the Cold War, the United States and Russia's Mutual Assured Destruction (MAD)equilibrium:
A)did not require rhetoric to function.
B)required the second strike to be automatic.
C)meant that one party wins and the other party is losing.
D)did not suffer from a credibility problem since both sides survived that war.

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Multiple Choice

B

Q 4Q 4

A poker player:
A)should never bluff
B)should optimize the mix of bluffing.
C)should rely on flair, not on mixed strategies.
D)should bluff on every hand.

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Multiple Choice

Q 5Q 5

In a game of plain complements:
A)there is no relationship between a player's strategy and the payoff of the other player.
B)there is a positive relationship between the players' payoffs.
C)there is a negative relationship between a player's strategy and the payoff of the other player.
D)there is a positive relationship between a player's strategy an the payoff of the other player.

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Multiple Choice

Q 6Q 6

Which of the following does not represent a strategic behaviour?
A)Build a factory with higher than needed capacity to deter possible entrants.
B)Spend heavily on advertising to signal a quality product.
C)Price below marginal cost to drive competitors out of business.
D)Choose output so that marginal revenue equal marginal cost.

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Multiple Choice

Q 7Q 7

Predicting behavior after it was determined that a comet will destroy life on earn in the next three days:
A)does not require the use of game theory.
B)does not require the use of Nash equilibrium.
C)is best accomplished using a repeated interaction setup.
D)can be done best using the last period problem.

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Multiple Choice

Q 8Q 8

All but which of the following constitutes a Nash equilibrium?
A)collusive solution
B)Cournot equilibrium
C)noncooperative equilibrium
D)Bertrand equilibrium

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Multiple Choice

Q 9Q 9

Choosing a mixed strategy entails:
A)a channel of communication between the players.
B)using an incomprehensible strategy.
C)randomly generating a strategy by optimally combining pure strategies.
D)simply using pure strategies.

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Multiple Choice

Q 10Q 10

The essence of game theory as used in economics:
A)refers to learning how to make money by gambling in a casino.
B)is to gain insights into the strategic interaction of economic players.
C)boils down to a few principles that can be applied in any economic model.
D)is to help building a sophisticated theory with no relevance for the real world.

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Multiple Choice

Q 11Q 11

Two firms are selling the same product. Each has a choice of setting a high price or a low price. If they both set high prices, they make $150 each. If they both set low prices, they each make $125. If one sets a low price and the other sets a high price, then the player with the low price makes $200, while the player with the high price makes $100. The Nash equilibrium of this game is:
A)one to set high price and the other to set low price.
B)there does not exist a Pure Strategy Nash Equilibrium for this game
C)both choosing high price.
D)both choosing low price.

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Multiple Choice

Q 12Q 12

The Nash equilibrium in a game of plain substitutes with simultaneous moves:
A)entails strategy values that "are too large".
B)is Pareto- optimal.
C)entails strategy values that "are too small".
D)results from a game of mutual positive externalities.

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Multiple Choice

Q 13Q 13

Strategic interaction refers to:
A)the fact that economic actors' interaction affects the outcome.
B)the fact that economic actors plan ahead.
C)the fact that economic actors are rational actors.
D)the fact that economic actors maximize an objective function.

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Multiple Choice

Q 14Q 14

Your psychology class meets Monday to Thursday. On Thursday your prof tells you that you will have a surprise quiz next week. What day will you have the quiz?
A)Tuesday
B)Monday
C)Wednesday
D)Thursday

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Multiple Choice

Q 15Q 15

If a government provides an exporting firm with subsidies:
A)changes the payoff matrix in the foreign market.
B)unambiguously increase the welfare of the domestic economy.
C)it does not signal that it does not believe in free markets.
D)it will provide that firm with less incentives to be competitive.

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Multiple Choice

Q 16Q 16

John Nash:
A)is a Canadian basketball player.
B)is a fictional movie character.
C)is an American mathematician who received the Nobel prize in Economics.
D)is an American economist.

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Multiple Choice

Q 17Q 17

In a game of plain substitutes with simultaneous moves, the lens of missed opportunity is:
A)a set of possible outcomes that are inferior to the Nash equilibrium.
B)a lens- shaped area situated to the southwest of the Nash equilibrium.
C)attainable in a one- shot game.
D)a set of possible outcomes that involve higher strategies values by both players.

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Multiple Choice

Q 18Q 18

A player that makes a move first:
A)has usually an advantage unless there is a zero- sum game.
B)has always a substantial advantage.
C)can use surprise to her advantage.
D)has never a substantial advantage.

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Multiple Choice

Q 19Q 19

Strategies players use in a game:
A)represent levels of prices chosen by firms competing in a market.
B)represent choices in general.
C)represent levels of investment by two rival firms.
D)represent quantities chosen by firms being part of a given market.

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Multiple Choice

Q 20Q 20

Once the state environmental protection agency devises its new policy to protect the environment, firms decide whether to remain in the state or move their operations to a neighboring state. In the language of game theory, this is an example of:
A)a cooperative game.
B)a Prisoner Dilemma game.
C)a threat.
D)a sequential game.

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Multiple Choice

Q 21Q 21

An equilibrium strategy combination is:
A)a set of dominant strategies.
B)obtained when one player's own strategy maximizes that player's own payoff.
C)a set of strategies containing the best responses of every player to the other players' best responses.
D)a fortunate turn of events.

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Multiple Choice

Q 22Q 22

In numerous business courses, but very few economics courses, there are group projects. The Nash equilibrium for group projects is
A)for everyone to put in as little effort as possible
B)to coerce the poorest student to exert effort
C)for the best student to do all the work
D)the best student to coordinate the work of the others

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Multiple Choice

Q 23Q 23

In a duopoly, each firm is likely to choose a strategy which gives each firm:
A)the highest profit.
B)a different profit.
C)the lowest profit.
D)a profit which depends on random events.

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Multiple Choice

Q 24Q 24

The analysis of games of plain substitutes and complements:
A)proves that most social relationships lead to achieving full economic potential.
B)is a diagnostic tool needed to define optimal outcomes.
C)show the need for a better equilibrium concept other than the Nash equilibrium.
D)indicate the direction of the bias introduced by the pursuit of self- interest.

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Multiple Choice

Q 25Q 25

In a game of chicken where where two people drive their cars at each other.Both have the choice of either driving straight or swerving. The first person to swerve loses. What is the dominant strategy?
A)both people swerve
B)there isn't one
C)neither person swerves
D)one person swerves

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Multiple Choice

Q 26Q 26

In a game of plain complements:
A)the cross- effects in the payoff functions are positive.
B)there is no lens of missed opportunities.
C)there are mutual negative externalities.
D)the cross- effects in the payoff functions are negative.

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Multiple Choice

Q 27Q 27

The case of waste disposal in most cities in North America can be modeled as a prisoner dilemma:
A)because city households are hostile to each other.
B)due to the high incidence of crime in the city.
C)if certain conditions regarding the cost and benefits of proper disposal are met.
D)in all cases.

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Multiple Choice

Q 28Q 28

In games of plain complements with simultaneous moves the Nash equilibrium is
A)Pareto efficient if preferences are well behaved
B)is Pareto optimal compared to all other equilibria
C)Pareto efficient if there are no spillover effects
D)not Pareto efficient

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Multiple Choice

Q 29Q 29

In which of the following would we expect that there is no dominant strategy?
A)the use of performance enhancing drugs in professional sports
B)the game of tick tack toe
C)advertising in oligopoly
D)the game output and keep

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Multiple Choice

Q 30Q 30

Two athletes contemplating the simultaneous use of performance enhancing drugs:
A)play a game of plain complements.
B)play a game other than prisoner's dilemma.
C)show poor sportsmanship.
D)will end up using too much drugs.

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Multiple Choice

Q 31Q 31

A player's payoff depends:
A)both on his action and other players' action.
B)on luck.
C)on the strategies chosen by the other players.
D)on his own strategy.

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Multiple Choice

Q 32Q 32

Often, oligopolists act without the benefit of communication. As a result they choose strategies that lead to lower profits than what could have been achieved with cooperation. This situation is known as:
A)the minimax strategy.
B)the collusion outcome.
C)the prisoner's dilemma.
D)a compromise.

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Multiple Choice

Q 33Q 33

The solutions to the problems signaled by the analysis of games of plain substitutes and complements:
A)can be found by further pursuing the self- interest of the participating actors.
B)lie in the search for institutions that solve social dilemmas.
C)can always be solved by the government intervention.
D)lie outside the realm of game theory.

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Multiple Choice

Q 34Q 34

Team production results in:
A)significant individual effort towards the common goal.
B)a Nash equilibrium that is Pareto- optimal.
C)a Nash equilibrium that is not Pareto- optimal.
D)a compassionate view of the world.

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Multiple Choice

Q 35Q 35

Team production is an example of:
A)a game of plain substitutes.
B)a game of chicken.
C)a game of coordination.
D)a game of plain complements.

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Multiple Choice

Q 36Q 36

The strategies are ranked by each player according to the:
A)levels of profit.
B)likelihood of success.
C)value of payoffs.
D)consumption patterns.

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Multiple Choice

Q 37Q 37

A dominated strategy:
A)is the strategy of all the other players except the dominant one.
B)is the strategy with the lowest payoff.
C)is the worst strategy for a player, regardless of what the other players in the game are doing.
D)is the one the player with smallest clout always uses.

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Multiple Choice

Q 38Q 38

Subgame perfection
A)is a concept applied to complex on- shot games.
B)yields several equilibria.
C)is obtained via forward induction.
D)is a refinement of Nash equilibrium.

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Multiple Choice

Q 39Q 39

The dominant strategy:
A)is the second best strategy.
B)is the best strategy for a given player, whatever the other players are doing.
C)is the best strategy of the dominant player.
D)is the strategy yielding the highest payoff.

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Multiple Choice

Q 40Q 40

A game with a mixed strategy Nash equilibrium:
A)has no pure strategy equilibria.
B)may or may not have a pure strategy equilibria.
C)does not have well- defined best response functions.
D)will always have a pure strategy equilibria.

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Multiple Choice

Q 41Q 41

The best response function is:
A)the strategy that increases the payoff.
B)the strategy that best uses the available information.
C)the strategy that leads to the highest payoff regardless of what the other players do.
D)the strategy that maximizes one's payoff given the action of the other players.

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Multiple Choice

Q 42Q 42

Battle of the sexes is a:
A)game of chicken.
B)variant of the prisoner's dilemma game.
C)coordination game.
D)famous novel.

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Multiple Choice

Q 43Q 43

The equilibrium arrived at in the prisoner's dilemma game is a:
A)Nash equilibrium.
B)Bertrand equilibrium.
C)collusive equilibrium.
D)Cournot equilibrium.

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Multiple Choice

Q 44Q 44

Which of the following is true?
A)Inefficient bribe- taking in highly regulated economies can be regarded as a game of plain substitutes.
B)The demand for bribes is an increasing function of the sum of bribes.
C)Inefficient bribe- taking in highly regulated economies result in bribes that are efficient.
D)Bribing is immoral but it has beneficial social role.

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Multiple Choice

Q 45Q 45

Which of the following is true?
A)All games have at least a dominated strategy.
B)All games have at least a dominant strategy.
C)Games may or may not end up having dominated or dominating strategies.
D)A Nash equilibrium in pure strategies requires at least a dominating strategy.

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Multiple Choice

Q 46Q 46

Cooperation is more likely to arise in repeated prisoner dilemma games:
A)when value the present gains highly.
B)when players are more patient.
C)when a one- time gain from cheating is large.
D)when players interact seldom.

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Multiple Choice

Q 47Q 47

The Nash equilibrium in a game of plain complements with simultaneous moves:
A)entails strategy values that "are too small".
B)entails strategy values that "are too large".
C)is Pareto- optimal.
D)results from a game of mutual negative externalities.

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Multiple Choice

Q 48Q 48

The non Pareto- optimal equilibria characterizing games of plain substitutes and complements:
A)yield conflicting results.
B)social interactions may lead to unattractive outcomes.
C)indicate that Adam Smith's invisible hand works properly.
D)imply that pursuing self- interest always achieve the full economic potential.

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Multiple Choice

Q 49Q 49

A dominant strategy is:
A)always a winning strategy.
B)never part of a Nash equilibrium.
C)always part of a Nash equilibrium.
D)sometime part of a Nash equilibrium.

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Multiple Choice

Q 50Q 50

A dominant strategy means that:
A)One player makes the best move given the move of the other player.
B)A player does not consider the moves available to the other player in making his decision.
C)It is the best response regardless of the strategy picked by the other player.
D)One player is aggressive while the other is passive.

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Multiple Choice

Q 51Q 51

A Nash equilibrium occurs when:
A)each firm is doing the best it can given its opponents' actions.
B)there is no dominant firm in a market.
C)each firm chooses the strategy that maximizes its minimum gain.
D)a player can choose a strategy that is optimal regardless of its rivals' actions.

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Multiple Choice

Q 52Q 52

A strategy combination:
A)is a list of strategies, one for each player in the game.
B)is a different name for a mixed strategy.
C)is a sophisticated strategy used by a player.
D)is a sequence of moves by a player .

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Multiple Choice

Q 53Q 53

A dominant strategy is one that:
A)combines pure and mixed strategies.
B)is chosen by the player regardless of the best response by the other player.
C)brings losses for the player.
D)restricts the freedom of choice.

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Multiple Choice

Q 54Q 54

A coordination game:
A)covers most market situations.
B)cannot yield a Nash equilibrium.
C)usually has more than one equilibrium.
D)result in a final outcome that is uncertain.

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Multiple Choice

Q 55Q 55

The Nash equilibrium in a prisoner's dilemma game:
A)has few real- life applications.
B)does not necessarily lead to jail time for the players.
C)is the set of the dominant strategies for all players.
D)is Pareto- optimal.

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Multiple Choice

Q 56Q 56

Which of the following types of games are likely to exhibit mixed strategy equilibria?
A)games of coordination
B)games of discoordination
C)any game that is properly formatted.
D)prisoner dilemma games.

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Multiple Choice

Q 57Q 57

The prisoner's dilemma:
A)is characterized by several Nash equilibria.
B)yields a Pareto- optimal equilibrium.
C)can be used to model a variety of economic settings.
D)does not have many real- life applications.

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Multiple Choice

Q 58Q 58

The following mathematical properties should characterize the payoff functions:
A)discrete
B)continuous and quasi- concave
C)continuous and quasi- convex
D)bounded

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Multiple Choice

Q 59Q 59

In the game of PUT (P)and KEEP (K)each child was given nine dollars and, if they chose to put it back, six dollars was added to the nine and the two children shared the total pot of money. What is the dominant strategy?
A)(K, K)
B)(P, K)
C)(K, P)
D)(P, P)

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Multiple Choice

Q 60Q 60

If voting is costly yet it has no intrinsic value, voting in an election:
A)is a patriotic duty.
B)is a dominant strategy.
C)is a dominated strategy.
D)is neither a dominated strategy nor a dominant strategy.

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Multiple Choice

Q 61Q 61

In the game of PUT (P)and KEEP (K)each child was given nine dollars and, if they chose to put it back, six dollars was added to the nine and the two children shared the total pot of money. Which exchange a has the highest joint payoff?
A)(P, K)
B)(P, P)
C)(K, K)
D)(K, P)

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Multiple Choice

Q 62Q 62

A one shot game in a prisoner's dilemma game:
A)the prisoner has a chance of confessing before being shot.
B)implies there are no consequences to decisions outside the payoffs mentioned in the game.
C)allows players to punish opposing player for choosing to fink.
D)players repeatedly interact with each other.

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Multiple Choice

Q 63Q 63

Competitive equilibrium and Nash equilibrium:
A)are such that competitive equilibria are a subset of Nash equilibria.
B)are such that Nash equilibria are a subset of competitive equilibria.
C)are not related.
D)are inconsistent with each other.

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Multiple Choice

Q 64Q 64

By willingly eliminating some strategies from the strategy set ("burning some bridges"), a player:
A)can never create a strategic advantage.
B)is showing goodwill.
C)may create strategic advantage in certain cases.
D)is shooting himself in the foot since more options are better than fewer.

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Multiple Choice

Q 65Q 65

The normal form of the game is:
A)the game's outcome in the simplest form.
B)the game's outcome in a matrix form.
C)a combination of equilibrium strategies that is most likely.
D)the game's outcome in a tree form.

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Multiple Choice

Q 66Q 66

In the case of the team production, the best response functions:
A)do not intersect.
B)are positively sloped.
C)pass through the origin.
D)are negatively sloped.

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Multiple Choice

Q 67Q 67

A Nash equilibrium is:
A)individually rational.
B)collectively rational.
C)irrational.
D)both collectively and individually rational.

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Multiple Choice

Q 68Q 68

The outcome of a prisoner's dilemma game is:
A)sub- optimal, even the players are acting rational.
B)cooperative.
C)sub- optimal, since they are irrational.
D)optimal, since players are acting rational.

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Multiple Choice

Q 69Q 69

In a game of plain substitutes:
A)there is a negative relationship between the players' payoffs.
B)there is no relationship between a player's strategy and the payoff of the other player.
C)there is a positive relationship between a player's strategy an the payoff of the other player.
D)there is a negative relationship between a player's strategy and the payoff of the other player.

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Multiple Choice

Q 70Q 70

The prisoner's dilemma game:
A)leads to a Pareto efficient outcome.
B)refers to the interaction between police and criminals.
C)has few practical applications due to its simplicity.
D)is a game of dominant strategies.

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Multiple Choice

Q 71Q 71

Provide one example for each of the following: 1)a game of plain substitutes, 2)a game of plain complements, 3)a game of discoordination

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Essay

Q 72Q 72

Why is the prisoner's dilemma touted as one of the most famous and equally important example of games in economics (but also in political science, biology, philosophy, etc.)?

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Essay

Q 73Q 73

Consider the classic prisoner's dilemma problem where both players get a payoff of - 1 if they're silent, both get a payoff of - 6 if they fink, and if only one finks that person receives the payoff of zero and the one that remains silent gets a payoff of - 9. When the two prisoners are kept separated the Nash equilibrium is for both to think. Does the Nash equilibrium change if the prisoners are permitted to discuss their choice in advance but are still required to plead separately?

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Essay

Q 74Q 74

Present a real life example that can be understood better if modeled as a prisoner's dilemma.

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Essay

Q 75Q 75

In the 1983 MGM movie Wargames, starring Matthew Broderick and Ally Sheedy, a supercomputer is programmed to simulate global thermonuclear war. Using game theory predict the dominant strategy determined by the computer.

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Q 78Q 78

Annie and Peter have two strategies each at their disposal: top and bottom. For the strategy combinations (top, top)and (top, bottom), the payoff is (0,100)in each case, where the first position refers to Annie, and the second to Peter. Similarly, for (bottom, top)the payoff is (- 20, - 50), while for (bottom, bottom)is (60, 60). Is there a Nash equilibrium in pure strategies? Is there a dominant strategy Nash equilibrium?

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Essay

Q 79Q 79

Currently, there is an incumbent monopoly in the market. Next year, a potential entrant may enter. The incumbent needs to make a decision on whether or not it should spend $50 to lobby the government into passing legislation which places a lump- sum tax of $100 on the potential entrant if it enters. If the potential entrant stays out of the market it makes zero profit and the incumbent firm makes a monopoly profit, Profit

_{m}>0, minus expenditures on lobbying if any ($50 or $0). If the potential entrant enters the market, it gets duopoly profit, Profit_{d}=$200, minus the tax if any, and the incumbent gets duopoly profit minus the lobbying costs if any. a)Show the game in extensive form. What strategies will be played? b)Suppose the tax on the potential entrant is $210 instead of $100. Repeat part A. How large must Profit_{m}_{ }be for the monopolist to want to lobby?Free

Essay

Q 80Q 80

Firms Alba Inc. and Bute Inc. are duopolists selling firecrackers. Each of them has the option to charge high prices or low prices. Alba was longer in the business and its cost structure allows for higher profits. Also, Alba enjoys a strong reputation among customers and is able to charge higher prices. For the strategy combination (high, high)the payoff is (200,120), where the first position refers to Alba, and the second to Bute. Similarly, for (high, low)the payoff is (100,150), for (low, high)the payoff is (50, 0), while for (low, low)is (50, 25).
a)What is the dominant strategy for each firm?
b)Find the Nash equilibrium.
c)Can Alba induce Bute to charge a high price by threatening to charge a low price otherwise?

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Essay

Q 81Q 81

Maya and Allen contemplated going to one of the two parties their school buddies organize that night. Just before deciding what party to attend, Allen's cell phone went dead. Now they have to come up with a way to find each other. In their minds, it was as if they play the following game. Each has a choice between two parties, the big one and the small one. The payoffs are as follows: for the strategy combination (big, big)the payoff is (200,200), where the first position refers to Maya, and the second to Allen. Similarly, for (big, small)the payoff is (0, 0), for (small, big)the payoff is (0, 0), while for (small, small)is (500, 500).
a)Does this game have a dominant strategy Nash equilibrium?
b)What are the two pure strategy equilibria?
c)How is this game referred to among game theorists?
d)Is there an equilibrium that is Pareto superior to the other? If yes, is there a possibility Maya and Allen will choose it?

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Essay

Q 82Q 82

Fergie and Abdul were caught by the police in the vicinity of a robbery site. The police have a strong feeling the two individuals are the actual robbers, but they do not have a way to prove it yet. In the absence of hard evidence, the prosecutor can convict them of only a minor offence, with only a year in prison. The police put the two in separate rooms and try to offer them incentives to confess: if one of the robbers does so, he would go
scot- free while the other goes to prison for 10 years. If both confess the prosecutor will be able to put both in prison for 5 years. As a result, each partner in crime has two options: to confess or to remain silent.
Note: here payoffs are in years of prison, so less is better.
a)Represent this game in normal form. Are there dominant strategies for these robbers?
b)What s the Nash equilibrium of this game?
c)How is this game called?
d)What exactly is the dilemma that the two robbers have? Is there a way to get around this problem

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Essay

Q 83Q 83

Hamilton and Virginia have two strategies each a their disposal: top and bottom. For the strategy combination (top, top)the payoff is (60,20), where the first position refers to Hamilton, and the second to Virginia. Similarly, for (top, bottom)the payoff is (0, 0), for (bottom, top)the payoff is (0, 0), while for (bottom, bottom)is (20, 60). What is the mixed strategy equilibrium for this one- shot game?

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