MOODLE QUIZ THREE Flashcards
A strategy that is always best for a player, regardless of what others players choose to do is called a:
Question 1Select one:
first mover advantage.
Nash strategy.
tit-for-tat strategy.
dominant strategy.
The correct answer is: dominant strategy.
Which is the following is true about the relationship between a dominant strategy equilibrium and a Nash equilibrium?
Question 2Select one:
A dominant strategy equilibrium is just another name for a Nash equilibrium.
A Nash equilibrium and a dominant strategy equilibrium cannot occur at the same time.
A Nash equilibrium is always a dominant strategy equilibrium.
A dominant strategy equilibrium is always a Nash equilibrium.
Your answer is correct.
A dominant strategy is a strategy that gives a player a payoff that is higher than the payoff the player could receive from any other strategy, regardless of the strategy played by the other players. A dominant strategy equilibrium occurs where both players have a dominant strategy.
A Nash equilibrium is a set of strategies in which each player is doing the best they can, given the actions of the other players. Following a dominant strategy leads to an outcome where the player is doing the best they can, given the actions of the other players (even though, when a strategy is dominant, it actually doesn’t matter what the other players do).
So, if both players have a dominant strategy, and therefore there is a dominant strategy equilibrium, then both players are also doing the best they can, given the actions of the other players. That means that a dominant strategy equilibrium is always a Nash equilibrium.
However, not all Nash equilibriums require dominant strategies. So, not all Nash equilibriums are dominant strategy equilibriums.
The dominant strategy equilibrium is just a special case of the Nash equilibrium.
The correct answer is: A dominant strategy equilibrium is always a Nash equilibrium.
As discussed in class, in the famous prisoners’ dilemma, both prisoners acting in their own self-interest leads to:
Question 3Select one:
an outcome that is not best for either prisoner.
an outcome that is best for both prisoners collectively and individually.
an outcome that is best for both prisoners individually, but not collectively.
an outcome that is best for both prisoners collectively, but not individually.
Your answer is correct.
In the famous prisoners’ dilemma game, both prisoners would be better off if they stayed silent. However, both prisoners have a dominant strategy to confess. Acting in their own self-interest would mean that each prisoner confesses. This leads to a bad outcome for both prisoners - an outcome that is not best for either prisoner.
The correct answer is: an outcome that is not best for either prisoner.
Which of the following could best be described as a real-world example of a prisoners’ dilemma game?
Question 5Select one:
Evacuating the building in case of fire, where every person has an incentive to rush for the exit, but if everyone rushes then the chances of injuries increase.
None of these is correct.
Two café firms competing for customers, where both firms have a dominant strategy to offer high quality coffee, and the outcome results in high profits for both firms.
Two farmers on properties that are distant from each other, where neither farmer needs to consider the actions of the other.
A prisoners’ dilemma exists when players choices, while acting in their own self-interest and choosing their dominant strategy, result in an outcome that is worse for all players than if they cooperated.
In these examples, that is the case for a fire evacuation, since every person rushing for the exit leads to an outcome (injuries) that is not good for all. This is an example of a prisoners’ dilemma.
The two café firms are not in a prisoners’ dilemma, since their dominant strategy leads to a preferred outcome (high profits).
The two farmers are not in a prisoners’ dilemma, since their choices do not affect each other at all.
The correct answer is: Evacuating the building in case of fire, where every person has an incentive to rush for the exit, but if everyone rushes then the chances of injuries increase.
In a game where there are no Nash equilibriums in pure strategy,:
Question 9Select one:
no player will have a dominant strategy.
All of these are correct.
there will generally be a mixed strategy equilibrium.
all players would be best to randomise their choice of strategy.
In a game where there are no Nash equilibriums in pure strategy, there will generally be a mixed strategy equilibrium. The mixed strategy equilibrium involves all players randomising their choice of strategy. Almost by definition, in a game with a mixed strategy equilibrium no player will have a dominant strategy (because if they did, then they must choose the dominant strategy rather than randomising, because randomising would make them worse off).
The correct answer is: All of these are correct.
In a sequential game, the subgame perfect Nash equilibrium (if any) can be found using:
Question 10Select one:
repeated game theory.
backward induction.
dominant strategies only.
a payoff table.
In a sequential game, we solve for the subgame perfect Nash equilibrium by first working out what the last player will do, then working backwards to figure out what the first player will do. This is referred to as backward induction.
Payoff tables are used in simultaneous games, not sequential games.
Backward induction allows us to solve for subgame perfect Nash equilibrium even when there are no dominant strategies.
The correct answer is: backward induction.
In a repeated game, if a player starts out cooperating in the first play and then after that they choose the same strategy their opponent chose in the previous play, they are playing a:
Question 11Select one:
repeated equilibrium strategy.
grim strategy.
tit-for-tat strategy.
dominant strategy.
In a tit-for-tat strategy, a player starts out cooperating in the first play of the repeated game, and then after that they choose the same strategy their opponent chose in the previous play.
In a grim strategy, a player starts out cooperating in the first play of the repeated game, and then after the first time their opponent defects (doesnt’ cooperate), the player never cooperates again.
A dominant strategy is a strategy that is always better for a player, no matter what the other player chooses to do.
The correct answer is: tit-for-tat strategy.
In a repeated prisoners’ dilemma game, the players may be able to cooperate to achieve the optimal outcome. However, this outcome is likely to rely on trust, because:
Question 12Select one:
the cooperative outcome is the long-run Nash equilibrium.
there is still an incentive to cheat on any agreement.
there is no alternative but to trust the other players.
All of these are correct.
In the standard prisoners’ dilemma game, both players have a dominant strategy to confess. If they both cooperated and remained silent, they would both be better off. However, because of the dominant strategies, there is a dominant strategy equilibrium (also a Nash equilibrium), where both players confess. Neither prisoner would cooperate and remain silent, unless they could be sure that the other prisoner would cooperate as well. This problem is common to all prisoners’ dilemma games.
Cooperating requires each player to trust the other player. That is because there is an incentive to cheat on any agreement (because not cooperating is a dominant strategy that leads to a higher payoff for the individual player).
However, that does not mean that there is no alternative to trusting the other players. A player can simply choose their dominant strategy and not cooperate. That way, they are never taken advantage of.
The cooperative outcome is also not a Nash equilibrium, regardless of whether there is cooperation or not. The Nash equilibrium remains for all players not to cooperate.
The correct answer is:
there is still an incentive to cheat on any agreement.
