CHAPTER 12 GAME: A Public Goods Game
Often groups work together to produce a good that is shared among all group
members. A pure public good is non-rivaled and non-excludable, meaning that
one person’s consumption does not rule out another’s consumption and no one
can be excluded from consuming the good. With a public good a free rider
problem can arise when an individual is not contributing a fair share or
consuming too much. Though we often think of a public good as something we
all share (e.g., a national park), we can gain insights on small group behavior
from public goods experiments. Many of us who have worked in groups, on a
class project for school, as a member of a team of employees, or as an executive
board member, understand the aversion felt for a free rider and the desire not to
be taken advantage of. Earlier in the chapter we noted that some shareholders
may be inclined to free ride on other shareholders, leaving the monitoring of
managers to others.
Public goods games have taken many forms.1 The instructions that follow
are for a simple public goods game.2 Students are placed in groups of four
members.
Each student is given 20 francs and given the opportunity to
contribute to a “group project” over a series of periods. A student is better off
contributing nothing to the project but all members of the group are better off if
everyone contributes. Contributions can take any integer value from 0 to 20 and
students keep whatever they do not contribute. For each franc contributed to the
group, every group member earns 0.40 francs. So, when one student contributes
a franc, the group earns 1.6 francs (4 times 0.40). A purely self-interested student
For an extensive review of public goods experiments see Kagel J. H., and A.
Roth, 1995, The Handbook of Experimental Economics (Princeton University Press,
Princeton, NJ).
1
We thank Ernst Fehr for sharing his original experimental instructions
(translated into English) which provided the basis for the instructions given here.
2
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will contribute nothing to the project because the individual return to a
contribution of one franc is less than one franc. Pro-social subjects, however, will
contribute their entire endowment to increase social welfare.
Contribution rates observed in the literature begin at about one-half of
students’ endowments but decline quickly over time. Some people are free
riders and never contribute, while others contribute more than would be
expected. These people may not be purely selfless, with their driving concern
being reciprocity.3
An interesting extension of this experiment provides
punishment opportunities. With the ability to punish low contributors who are
free riders, contributions to the project are high.4
Importantly, a social
mechanism that is threatening induces people to cooperate so that higher
contribution rates are expected and observed. It is also important to recognize
that social norms have a greater impact on behavior as social distance decreases.5
If the students are allowed to communicate or even simply know the members of
their group, again contribution rates should increase.
The experiment is easy to implement in class and students enjoy
discussing among themselves what they learned about their own willingness to
contribute and how others behave. The instructor might also discuss extensions
of the basic design, such as punishment and reduced social distance, and ask
students to consider how these factors might impact behavior. To conduct the
experiment you will need the instruction sheets which follow. As with other
classroom experiments, this experiment will be most effective if it is conducted
See Henrich, J., R. Boyd, S. Bowles, C. Camerer, E. Fehr, and H. Gintis, eds.,
2004, Foundations of Human Sociality (Oxford University Press, Oxford, UK).
3
See Fehr, E., and S. Gachter, 2000, “Cooperation and punishment in public
goods experiments,” American Economic Review 90(4), 980-994.
4
See Charness, Gary, and Uri Gneezy, 2003, “What’s in a name? Anonymity and
social distance in dictator and ultimatum games,” Working paper, University of
Chicago.
5
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several weeks before social forces are covered in class so that students are not
familiar with the material. As is likely, if the number of student participants is
not a multiple of four, the instructor can choose to include monitors, or form
groups of size three or five. While true monetary incentives are, of course,
preferred, this experiment has been conducted in class without incentives and
the results were similar to those reported in the literature.
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STUDENT INSTRUCTIONS
You have been asked to participate in a decision-making experiment. During the
experiment your entire earnings will be calculated in francs.
The experiment is divided into different periods.
In all, the experiment
consists of 10 periods. In each period the participants are divided into groups of
four. You will therefore be in a group with 3 other participants. The composition
of the groups will be randomly determined by the monitors but will remain the
same for all ten periods.
In the experiment today you have to decide how many francs you would like
to contribute to a project. At the end of each period you are informed of the
contributions to the project by the members of your group. The remainder of the
instructions explains exactly how the experiment is conducted.
Each participant is given a decision form, which is included with your
instructions. At the beginning of each period each participant receives 20 francs.
We call this your endowment. Your task is to decide how to use your
endowment. Each period you are asked to decide how many of the 20 francs you
want to contribute to a group project and how many you want to keep for
yourself. In column (2) of the decision form you record the number of francs you
want to contribute to the project (any integer between 0 and 20). As soon as you
decide how many francs to contribute to the project, you have also decided how
many francs you keep for yourself: You keep (20 - your contribution) francs.
After recording your contribution your decision cannot be revised.
When you are finished recording your contribution for a period, turn your
page over and raise your hand. A monitor will collect the decision forms and
record the total amount of francs contributed by all four group members to the
project (including your contribution) in column (3).
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Your income consists of two parts:
1) Francs that you have kept for yourself (20 – column (2)) where one franc
contributed equals one franc in earnings.
2) Your earnings (in francs) from the project, calculated as 0.4 times the total
contribution of all 4 group members to the project.
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The income of each group member from the project is calculated in the same
way, so that each member of your group receives the same income from the
project. Suppose the sum of the contributions of all group members is 60 francs.
In this case each member of the group receives an income from the project of:
0.4*60 = 24 francs. If the total contribution to the project is 9 francs, then each
member of the group receives an income of 0.4*9 = 3.6 francs from the project.
For each franc you keep for yourself you earn an income of 1 franc. Suppose
instead that you contributed this franc to the project. Then, the total contribution
to the project would rise by one franc. Your income from the project would rise
by 0.4*1=0.4 francs. The income of the other group members would also rise by
0.4 francs each, so that the total income of the group from the project would rise
by 1.6 francs. Your contribution to the project therefore raises the income of the
other group members. In the same way, you earn an income for each franc
contributed by the other members to the project. For each franc contributed by
any member you earn 0.4*1=0.4 francs.
You will have 30 seconds to record your contribution to the project each
period. The monitor will then collect the Decision Forms and record the group’s
contribution. You can then compute how many francs you have earned in the
period.
Practice Exercise
1. Each group member has an endowment of 20 francs. Nobody (including
yourself) contributes any francs to the project in period 3. What are:
Your income in period 3? _________
The income of each of the other group members in period 3? _________
2. Each group member has an endowment of 20 francs. You contribute 20 francs
to the project in period 7. All other group members each contribute 20 francs to
the project in period 7. What are:
Your income in period 7? _________
The income of each of the other group members in period 7? _________
3. Each group member has an endowment of 20 francs. You contribute nothing
to the project in period 10. The other three group members contribute together a
total of 30 francs to the project, with each contributing 10 francs. What are:
Your income in period 10? _________
The income of each of the other group members in period 10? _________
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STUDENT ANSWER SHEET
Decision Form
Code Number:
__________
(1)
Period
(2)
Your
contribution to
the project
[0 to 20 francs]
(3)
Total group
francs
[0 to 80]
(4)
Your earnings
from the
project
[0.40* column
(3)]
(5)
Your earnings
for the period
[20 - column
(2)
+ Column (4)]
1
2
3
4
5
6
7
8
9
10
Total earnings [sum of column (5)]
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duplicated, or posted to a publicly available website, in whole or in part.