Chapter 13: Game Theory and Strategic Play

All of the following statements are true about​ simultaneous-move games​ except: A. Players know their​ opponent's choices. B. Players pick their actions at the same time. C. Players know the entire payoff matrix. D. Players know the payoffs for both players.

A. Players know their​ opponent's choices.

The​ prisoners' dilemma is​ ____________ with a​ ____________ equilibrium that is not the best outcome for both players. A. a simultaneous move​ game; dominant strategy. B. a simultaneous move​ game; submissive strategy. C. an​ extensive-form game; dominant strategy. D. an​ extensive-form game; submissive strategy.

A. a simultaneous move​ game; dominant strategy.

The tragedy of the commons can be modeled as a​ prisoners' dilemma game when the​ __________. A. dominant strategy equilibrium leads to the destruction of a common resource. B. Nash equilibrium is equal to the common resource equilibrium. C. common resource equilibrium is the dominant strategy for public goods. D. Nash equilibrium is greater than the dominant strategy equilibrium.

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

In a Nash​ equilibrium: A. neither player can change strategy and improve his or her payoff. B. both players can change strategy and improve their payoffs. C. player A can change strategy and improve his or her payoff. D. player B can change strategy and improve his or her payoff.

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

A​ zero-sum game is when​ ___________. A. the sum of the payoffs is zero. B. the Nash equilibrium is dominant. C. the outcome of a payoff matrix is uncertain. D. the dominant strategy is a payoff.

A. the sum of the payoffs is zero.

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? A. ​No, because it would involve choosing actions other than the dominant strategy. B. ​No, because a mixed strategy would not use preassigned probabilities for the various actions. C. ​Yes, because a mixed strategy would involve choosing a single action. D. ​Yes, a mixed strategy would be optimal if one of its actions were the dominant strategy.

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

A​ zero-sum game means it is not is possible for both players to find an optimal strategy with a given​ move; therefore, a Nash equilibrium does not does exist.

A​ zero-sum game means it is not possible for both players to find an optimal strategy with a given​ move; therefore, a Nash equilibrium does not exist.

1. The movie initially shows all the men asking the beautiful woman to dance. Given this​ information, will this situation result in a Nash​ equilibrium? A. ​Yes, because each man would not be better off by asking another woman to dance. B. ​No, because most of the men will get rejected by the beautiful woman. C. ​Yes, because each man would be better off by asking the beautiful woman to dance. D. ​No, because most of the men will not get rejected by the beautiful woman. 2. 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? A. There will be no Nash equilibrium because most of the men would be rejected by the beautiful woman. B. There will be a Nash equilibrium because each man will be better off asking the beautiful woman to dance. C. There will be no Nash equilibrium because if two men ask the beautiful woman to​ dance, both of them might end up dancing with her. D. 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.

1. B 2. D

All of the following statements about real life game theory are true​ except: A. A pure strategy is usually best. B. Real life contestants may not be evenly matched. C. Subjective feelings may make payoffs less exact. D. Real life events may not have clear payoffs.

A. A pure strategy is usually best.

Identify the key​ assumption(s) made about a Nash equilibrium. ​(Check all that apply.​) A. All players understand that other players understand the game. B. All players understand the game and the payoffs associated with each strategy. C. Some players are smarter than others. D. Some players will occasionally behave illogically.

A. All players understand that other players understand the game. B. All players understand the game and the payoffs associated with each strategy.

Which of the following statements about backward induction is​ true? A. Each player tries to deduce the​ other's moves by looking forward. B. It eliminates the need for predetermined payoffs. C. There can still be more than one equilibrium. D. The first move has to be made before any strategy can be foreseen.

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

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? A. It will not result in a Nash equilibrium because each man will choose to deviate from the plan. B. It will result in a Nash equilibrium because each man will choose not to deviate from the plan. C. It will result in a Nash equilibrium because each man will ask the beautiful woman to dance. D. It will not result in a Nash equilibrium because each man will be better off asking the beautiful woman to dance.

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

What is the difference between a pure strategy and a mixed​ strategy? A. A pure strategy involves choosing an action before other players choose their​ actions, while a mixed strategy involves choosing an action simultaneously with other players. B. A pure strategy involves choosing one​ action, while a mixed strategy involves choosing different actions randomly according to preassigned probabilities. C. A pure strategy is a best response to other​ players' actions, while a mixed strategy is a random response that may not be a best response. D. A pure strategy involves choosing an action independently of other​ players' actions, while a mixed strategy involves choosing an action that is dependent on other​ players' actions.

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

How is a Nash equilibrium different from a dominant strategy​ equilibrium? A. Nash equilibriums are​ mathematical, while dominant strategy equilibriums are quantitative. B. For a given​ game, there can only be one dominant strategy equilibrium but multiple Nash equilibriums. C. Dominant strategy equilibriums are​ mathematical, while Nash equilibriums are quantitative. D. For a given​ game, there can only be one Nash equilibrium but multiple dominant strategy equilibriums.

B. For a given​ game, there can only be one dominant strategy equilibrium but multiple Nash equilibriums.

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.​) A. Game theory is just an abstraction and cannot represent reality. B. Payoffs are determined by the attitudes and feelings of individuals as well as by their monetary returns. C. The formulator the Nash​ equilibrium, John​ Nash, eventually became mentally unbalanced. D. People are not driven by​ self-interested payoffs in general. E. One player may be more​ cunning, wiser, or more experienced than another.

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

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​ __________. A. there is some financial incentive to do so. B. an​ individual's benefits are defined not only by her own payoffs but also by the payoffs of others. C. players have reputational​ concerns, and they value trustworthy behavior. D. people value the payoffs to other individuals more than their own payoffs.

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

When developing a dominant strategy in a​ simultaneous-move game, a​ player: A. devises multiple strategies for the best response of the other player. B. devises the same best response to every possible strategy of the other player. C. devises multiple strategies for every possible strategy of the other player. D. devises the same best response to a possible response of the other player.

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

A dominant strategy equilibrium exists​ if: A. the outcome is in the best interest of both players. B. the relevant strategy for each player is a dominant strategy. C. the payoff for each choice is equal. D. the payoff for each player is equal.

B. the relevant strategy for each player is a dominant strategy.

When relating dominant strategies to real life​ experiences: A. there seems to be an inverse relationship. B. there seems to be a direct relationship. C. there does not seem to be a relationship. D. Nash equilibria cannot exist in real life.

B. there seems to be a direct relationship. Just as people get better at finding the optimal strategy as they become more familiar with a​ game, so,​ too, do they get closer to the optimal strategy of any real life game as they gain experience.

Why should you use a mixed strategy to play rock-paper-scissors? A. Mixed strategy has the advantage of requiring less effort to generate an optimal outcome. B. Random behavior generally leads to a Nash equilibrium. C. Predictable behavior by one player can be taken advantage of by the other player. D. Pure strategy is a more efficient way to reach higher payoff outcomes.

C. Predictable behavior by one player can be taken advantage of by the other player.

What is backward​ induction? A. The methodology supporting an​ extensive-form representation of a game. B. It involves choosing one particular action for a situation. C. The procedure of solving an​ extensive-form game by first considering the last​ mover's decision. D. The theory that represents​ extensive-form games when the Nash equilibrium specifies the order of play.

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

Dominant strategy equilibria can result in negative consequences in real life​ when: A. it is in the best interest of a firm to clean up its pollution providing its competitor does not. B. it is in the best interest of two competing firms not to clean up their pollution. C. it is in the best interest of a firm to not clean up its pollution providing its competitor does. D. it is in the best interest of two competing firms to clean up their pollution.

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

A dominant strategy equilibrium is​ ____________. A. when players pick their actions at the same time. B. the payoffs for each action that a player can take. C. the combination of strategies where each strategy is a dominant strategy. D. the best response to every possible strategy of the other player.

C. the combination of strategies where each strategy is a dominant strategy.

One significant difference between​ extensive-form and​ simultaneous-move games​ is: A. one player gets to react to the other in a​ simultaneous-move game. B. backward induction cannot be used in​ extensive-form games. C. the timing of moves changes in​ extensive-form games. D. ​simultaneous-move games allow for more strategy.

C. the timing of moves changes in​ extensive-form games. An​ extensive-form game is a representation that specifies the order of play in a game.​ Extensive-form games introduce the sense of timing that is missing in​ simultaneous-move games. This sense of timing is relevant for negotiations in which different players make offers to one another over time​ (sequentially). Backward induction is the procedure of solving an​ extensive-form game by first considering the last​ mover's decision.

A Nash equilibrium is​ ___________. A. when players pick their actions at the same time. B. one best response to every possible strategy of the other​ player(s). C. when players choose strategies that are best responses to the strategy of others. D. when prisoners confess because of unfair sentencing​ guidelines, which lead to heterogeneous dominant strategies.

C. when players choose strategies that are best responses to the strategy of others.

Is a​ player's best response in a game the same as his dominant​ strategy? A. ​Yes, if a​ player's best responses depend on the strategy choices of other​ players, then a​ player's best response will be the same as his dominant strategy. B. ​Yes, if a player has a dominant​ strategy, then it is his best​ response, and every best response is always a dominant strategy. C. ​No, the key concept of game theory is finding a best response in each​ game, so that each best response leads to a Nash equilibrium. D. 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.

D. 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.

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? A. Financial incentives. B. Posing a credible threat to other players. C. Lack of trust. D. Reputational concerns.

D. Reputational concerns.

In real life​ extensive-form games: A. a​ short-term bluff is better than a​ long-term reputation. B. a lack of trust often drives a social optimum. C. the​ first-mover advantage​ can't be affected. D. both integrity and vengeance can be used as commitments.

D. both integrity and vengeance can be used as commitments.

More than one Nash equilibrium is possible​ if: A. player​ B's strategy is not optimum but player​ A's strategy is. B. player​ B's payoff differs from player​ A's payoff. C. neither​ player's strategy is optimum. D. each​ player's best response changes based on the other​ player's strategy.

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

What is not an example of a real life zero sum​ game? A. ​rock-paper-scissors. B. thermonuclear war. C. ​heads-or-tails. D. free market transaction.

D. free market transaction.

A​ first-mover advantage occurs if​ __________. A. the first mover to act in a strategic game reaches the Nash equilibrium. B. the first mover to act in a sequential game reaches the dominant strategy equilibrium. C. the first mover to act in a strategic game reaches the dominant strategy equilibrium. D. the first mover to act in a sequential game gets a benefit from doing so.

D. the first mover to act in a sequential game gets a benefit from doing so.