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.