## Section 4.6 Volunteer's Dilemma

¶In Section 4.5 we played a game called Volunteer's Dilemma.

###### Example 4.6.1. 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, given again in Table 4.6.2.

Player 2 | |||

Cooperate | Defect | ||

Driver 1 | Cooperate | \((3, 3)\) | \((0, 5)\) |

Defect | \((5, 0)\) | \((1, 1)\) |

###### Exercise 4.6.3. Effect of a single defector in Class-wide Prisoner's Dilemma.

In *Class-wide Prisoner's Dilemma* 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?

###### Exercise 4.6.4. Effect of everyone's defection in Class-wide Prisoner's Dilemma.

In *Class-wide Prisoner's Dilemma* 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?

###### Exercise 4.6.5. Effect of your defection in Class-wide Prisoner's Dilemma.

In *Class-wide Prisoner's Dilemma* 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?

###### Exercise 4.6.6. 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?

###### Exercise 4.6.7. 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?

###### Exercise 4.6.8. 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.

###### Exercise 4.6.9. 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?

###### Exercise 4.6.10. Everyone is rational in Class-wide Prisoner's Dilemma.

Whichever strategy you chose in Exercise 4.6.9, explain what would happen if everyone was the most rational. Is it now more rational to do the opposite?

###### Exercise 4.6.11. 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?

###### Exercise 4.6.12. Everyone is rational in Volunteer's Dilemma.

Whichever strategy you chose in Exercise 4.6.11, explain what would happen if everyone was the most rational. Is it now more rational to do the opposite?

###### Exercise 4.6.13. 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.