Econ Chapter 13

A Beautiful Mind​, a movie about John​ Nash, fails to properly demonstrate a Nash equilibrium. It attempts to do so in a bar scene where men at a bar​ (Nash and his​ friends) plan to ask women to dance. There is one beautiful woman that the men consider the most​ attractive, as well as several other women. Nash assumes less attractive women will only accept an offer to dance if the man extending the offer has not first been rejected by the beautiful woman. In the​ movie, Nash proposes that all the men agree not to ask the beautiful woman in the first place. Given this​ information, which of the following is true of​ Nash's proposal?

-It will not result in a Nash equilibrium because each man will choose to deviate from the plan.

Assume that the beautiful woman will accept only one dance proposal and only one man asks the beautiful woman to dance. Given this​ information, which of the following statements is​ true?

-There will be a Nash equilibrium because only one man will ask the beautiful woman to dance and the rest of the men will ask the other women.

A​ zero-sum game is when​ ___________. What is not an example of a real life zero sum​ game?

-the sum of the payoffs is zero. -free market transaction.

A Nash equilibrium is​ ___________. How is a Nash equilibrium different from a dominant strategy​ equilibrium? Identify the key​ assumption(s) made about a Nash equilibrium. ​(Check all that apply.​)

-when players choose strategies that are best responses to the strategy of others. -For a given​ game, there can only be one dominant strategy equilibrium but multiple Nash equilibriums. -All players understand the game and the payoffs associated with each strategy. -All players understand that other players understand the game.

The movie initially shows all the men asking the beautiful woman to dance. Given this​ information, will this situation result in a Nash​ equilibrium?

No, because most of the men will get rejected by the beautiful woman.

Is a​ player's best response in a game the same as his dominant​ strategy?

Not necessarily. If a player has a dominant​ strategy, then it is his best​ response; however, every best response is not always a dominant strategy.

Although there are many examples of game theory in the real​ world, how well do you think specifics like payoff​ matrices, Nash​ equilibrium, and dominant strategies translate to​ reality? Which of the following are potential reasons game theory differs from​ reality? ​(Check all that apply.​)

Payoffs are determined by the attitudes and feelings of individuals as well as by their monetary returns. One player may be more​ cunning, wiser, or more experienced than another.

All of the following statements are true about​ simultaneous-move games​ except:

Players know their​ opponent's choices.

A trust game is a sequential​ prisoners' dilemma. This means that it is likely that the outcome of the game is not socially efficient. Which of the following factors would likely result in a more socially efficient outcome in real​ life?

Reputational concerns.

What is backward​ induction?

The procedure of solving an​ extensive-form game by first considering the last​ mover's decision.

What is the difference between a pure strategy and a mixed​ strategy?

-A pure strategy involves choosing one​ action, while a mixed strategy involves choosing different actions randomly according to preassigned probabilities.

Why might game theory not always be an accurate predictor of​ real-world situations?

We do not always know the exact​ payoffs, since payoffs involve attitudes and feelings as well as monetary gains.

The​ prisoners' dilemma is​ ____________ with a​ ____________ equilibrium that is not the best outcome for both players.

a simultaneous move​ game; dominant strategy.

Economic agents​ (for example, consumers or​ firms) often do things that at first glance seem to be inconsistent with their​ self-interest. People tip at restaurants when they are on vacation even if they have no intention to return to the same place.​ Firms, sometimes, install costly pollution abatement equipment voluntarily. These deviations from Nash predictions can most likely be explained if​ __________.

an​ individual's benefits are defined not only by her own payoffs but also by the payoffs of others.

In real life​ extensive-form games:

both integrity and vengeance can be used as commitments.

In a​ zero-sum game the players are better off by​ ________. Which of the following is not an example of a​ zero-sum game? ​(Check all that apply.​)

choosing a mixed strategy because it enables randomization A trade agreement that increases gains for both of the nations involved. A brutal and terrible war between two nations that significantly impaired civil life.

In a trust game that is only played​ once, you would be most inclined to trust someone who​ ____________. Suppose there is a new website called​ Badtipper.com, where restaurant servers post pictures of bad tippers along with scathing commentary. Knowledge of this website is most likely to change the behavior of individuals with a​ ____________.

claims she gains happiness from helping others. low degree of social preferences.

When developing a dominant strategy in a​ simultaneous-move game, a​ player:

devises the same best response to every possible strategy of the other player.

The tragedy of the commons can be modeled as a​ prisoners' dilemma game when the​ __________.

dominant strategy equilibrium leads to the destruction of a common resource.

More than one Nash equilibrium is possible​ if:

each​ player's best response changes based on the other​ player's strategy.

When can backward induction be used to arrive at the equilibrium for a​ game? In the case​ of,

extensive form games.

A dominant strategy equilibrium is​ ____________.

he combination of strategies where each strategy is a dominant strategy.

Dominant strategy equilibria can result in negative consequences in real life​ when:

it is in the best interest of a firm to not clean up its pollution providing its competitor does.

A​ first-mover advantage occurs if​ __________. Suppose you were playing​ rock-paper-scissors as an extensive from​ game; first you choose​ rock, or​ paper, or​ scissors, and then your opponent makes a choice. Is there a​ first-mover advantage in this​ game? Two firms are thinking of entering a new market. If one enters it will be successful but if a second enters both will suffer very large losses. Is there a​ first-mover advantage in this​ game?

the first mover to act in a sequential game gets a benefit from doing so. No, if you show your move first you will lose every time. Yes. The firm that goes first can enter and the firm that goes second will have no incentive to enter.

A dominant strategy equilibrium exists​ if:

the relevant strategy for each player is a dominant strategy.

One significant difference between​ extensive-form and​ simultaneous-move games​ is:

the timing of moves changes in​ extensive-form games.

When relating dominant strategies to real life​ experiences:

there seems to be a direct relationship.

Suppose that a player has a dominant strategy. Would she choose to play a mixed strategy​ (such as playing two strategies each with probability​ 50-50)? Why or why​ not?

​No, because it would involve choosing actions other than the dominant strategy.

All of the following statements about real life game theory are true​ except:

A pure strategy is usually best.

Which of the following statements about backward induction is​ true?

Each player tries to deduce the​ other's moves by looking forward.

In a Nash​ equilibrium:

neither player can change strategy and improve his or her payoff.