In Section 4.5 we played a game called Volunteer’s Dilemma.
Example4.6.1.A Volunteer’s Dilemma.
One example of a Volunteer’s Dilemma is the game where everyone chooses “1 point” or “5 points.” If at least one person writes down 1 point, then everyone gets the number of points they wrote down. If no one chooses 1 point, then everyone gets 0 points. Choosing “1 point” is considered volunteering or cooperating. Choosing to not volunteer and take “5 points” is defecting.
You should note that it is difficult to put this game into a matrix form since payoffs depend on whether there is at least one volunteer or cooperator.
In this section we will compare Class-wide Prisoner’s Dilemma with Volunteer’s Dilemma. In particular, we want to think about the effect cooperating and defecting have on the group of players. How does one player’s choice affect everyone else? What happens to the group if there is a single cooperator or a single defector? What happens if everyone cooperates or everyone defects? We will use the payoffs for Prisoner’s Dilemma from Section 4.3 and Table 4.4.1, given again in the following table.
Table4.6.2.Class-wide Prisoner’s Dilemma (again).
Player 2
Cooperate
Defect
Driver 1
Cooperate
\((3, 3)\)
\((0, 5)\)
Defect
\((5, 0)\)
\((1, 1)\)
Activity4.6.1.Effect of a single defector in Class-wide Prisoner’s Dilemma.
In Class-wide Prisoner’s Dilemma, Table 4.6.2, what effect does one defector have on the group? In other words, if a single player defects, how many points does he cost each of the other players?
Activity4.6.2.Effect of everyone’s defection in Class-wide Prisoner’s Dilemma.
In Class-wide Prisoner’s Dilemma, Table 4.6.2, what effect does everyone’s defection have on the group? In other words, what is the most points lost by the group if everyone defects?
Activity4.6.3.Effect of your defection in Class-wide Prisoner’s Dilemma.
In Class-wide Prisoner’s Dilemma, Table 4.6.2, what effect could your own defection have on the group? In other words, how many points does the group lose if you defect instead of cooperate? You may need to consider different cases depending on how many cooperators there are. For example what if there are no cooperators? What if there are no defectors? What if there are some of each?
Activity4.6.4.Effect of a single defector in Volunteer’s Dilemma.
In Volunteer’s Dilemma, with the payoffs given in Example 4.6.1, what effect does one defector have on the group? In other words, if there is a single defector, how many points do each of the other players lose?
Activity4.6.5.Effect of everyone’s defection in Volunteer’s Dilemma.
In Volunteer’s Dilemma, with the payoffs given in Example 4.6.1, what effect does everyone’s defection have on the group? In other words, if everyone defects, how many points does the group lose?
Activity4.6.6.Effect of your defection in Volunteer’s Dilemma.
In Volunteer’s Dilemma, with the payoffs given in Example 4.6.1, what effect could your own defection have on the group? In other words, how many points does the group lose if you defect instead of cooperate? You may need to consider different cases depending on how many cooperators there are. For example what if there are no cooperators? What if there are no defectors? What if there are some of each?
Now that we’ve considered how an individual decision can affect the group, we can think about what the most rational strategy is in a multiplayer Prisoner’s Dilemma or a Volunteer’s Dilemma.
Activity4.6.7.Rationality in Class-wide Prisoner’s Dilemma.
Considering your answers above and to previous work with Prisoner’s Dilemma, in Class-wide Prisoner’s Dilemma, which is more rational, to be a cooperator or a defector? Why?
Activity4.6.8.Everyone is rational in Class-wide Prisoner’s Dilemma.
Whichever strategy you chose in Activity 4.6.7, explain what would happen if everyone was the most rational. Is it now more rational to do the opposite?
Activity4.6.9.Rationality in Volunteer’s Dilemma.
Considering your answers above, in Volunteer’s Dilemma, which is more rational, to be a cooperator (volunteer) or a defector? Why?
Activity4.6.10.Everyone is rational in Volunteer’s Dilemma.
Whichever strategy you chose in Activity 4.6.9, explain what would happen if everyone was the most rational. Is it now more rational to do the opposite?
Activity4.6.11.Class-wide Chicken.
Volunteer’s Dilemma can also be called Class-wide Chicken. Try to describe this class-wide game in terms of “swerving” and “going straight.” How do the payoffs for Volunteer’s Dilemma relate to the payoffs for Chicken?
Even though the Class-wide Prisoner’s Dilemma and the Volunteer’s Dilemma games were played with multiple players, each game was only played once. In the next section we look at what might happen if we repeatedly play Prisoner’s Dilemma with the same opponent.
Reading QuestionsCheck Your Understanding
1.
Consider the Volunteer’s Dilemma in which each player can choose 1 point or 0 points. If no one chooses 0, everyone loses 10 points. If at least one person chooses 0, every player gets the points they chose. A player who chooses 0 is a
cooperator.
Choosing 0 allows the group to benefit.
defector.
Who benefits most by a player choosing 0, the individual or the group?
2.
Consider the Volunteer’s Dilemma in which each player can choose 1 point or 0 points. If no one chooses 0, everyone loses 10 points. If at least one person chooses 0, every player gets the points they chose. A player who chooses 1 is a
cooperator.
Who benefits most by a player choosing 1, the individual or the group?
defector.
Choosing 1 allows the individual to benefit but risks a negetive payoff for everyone.
3.
Consider the Volunteer’s Dilemma in which each player can choose 1 point or 0 points. If no one chooses 0, everyone loses 10 points. If at least one person chooses 0, every player gets the points they chose. Suppose you are playing this game in a class of 20 people. If everyone chooses 0, how many points does each person get?
4.
Consider the Volunteer’s Dilemma in which each player can choose 1 point or 0 points. If no one chooses 0, everyone loses 10 points. If at least one person chooses 0, every player gets the points they chose. Suppose you are playing this game in a class of 20 people. If no one chooses 0, how many points does each person get?
5.
Consider the Volunteer’s Dilemma in which each player can choose 1 point or 0 points. If no one chooses 0, everyone loses 10 points. If at least one person chooses 0, every player gets the points they chose. Suppose you are playing this game in a class of 20 people. If one person chooses 0 and 19 choose 1, how many points does a defector get?
6.
Consider the Volunteer’s Dilemma in which each player can choose 1 point or 0 points. If no one chooses 0, everyone loses 10 points. If at least one person chooses 0, every player gets the points they chose. Suppose you are playing this game in a class of 20 people. If one person chooses 1 and 19 choose 0, how many points does a defector get?
7.
True or False: In the Volunteer’s Dilemma in which players choose 1 point or 0 points and if no one chooses 0, everyone loses 10, a cooperator will get 0 points no matter what anyone else does.
True.
Since a cooperator guarantees everyone gets the points they chose, the cooperator get 0 no matter what anyone else does.
False.
Since a cooperator guarantees everyone gets the points they chose, the cooperator get 0 no matter what anyone else does.
8.
True or False: In the Volunteer’s Dilemma in which players choose 1 point or 0 points and if no one chooses 0, everyone loses 10, a defector will get 1 point no matter what anyone else does.
True.
A defector only gets 1 point if someone else chose 0.
False.
A defector only gets 1 point if someone else chose 0.
9.
Consider the class-wide or multiplayer Prisoner’s Dilemma with the following payoff matrix
where every player is playing the game against every other player. Suppose you are playing this game in a class of 20 people. If everyone chooses Row/Column 1, how many points does each person get?
12.
Consider the class-wide or multiplayer Prisoner’s Dilemma with the following payoff matrix
where every player is playing the game against every other player. Suppose you are playing this game in a class of 20 people. If no one chooses Row/Column 1, how many points does each person get?
13.
Consider the class-wide or multiplayer Prisoner’s Dilemma with the following payoff matrix
where every player is playing the game against every other player. Suppose you are playing this game in a class of 20 people. If one player chooses Row/Column 1 and 19 choose Row/Column 2, how many points does a defector get?
14.
Consider the class-wide or multiplayer Prisoner’s Dilemma with the following payoff matrix
where every player is playing the game against every other player. Suppose you are playing this game in a class of 20 people. If 19 players chooses Row/Column 1 and one chooses Row/Column 2, how many points does a defector get?
15.
True or False: In the multiplayer Prisoner’s Dilemma with payoff matrix
