Transcript Andreoni: Cooperation in Public

Andreoni:
Cooperation in Public-Goods Experiments:
Kindness or Confusion
Economics 328
Spring 2005
What are Public Goods?
What Can Experiments Tell Us About Them?

Pure public goods




Non-excludable
Non-rival
For public goods, the marginal social
benefit always exceeds the marginal
private benefit. Hence, theory predicts
under-provision.
What do experiments bring to the study of
public goods?



Tight control over the environment
How do real individuals’ decision vary from
theory (and how can the theory then be
modified)?
Market design
Voluntary Contribution Mechanism: Theory

For laboratory experiments, voluntary contribution mechanisms
(VCM) are the most frequently studied version of a public goods
problem.



N players.
Initial endowment = Ei.
Players simultaneously decide how much to contribute to a public
pool.

Let xi be the amount contributed. Payoffs are given by the following
formula.
 N 
R i = E i – xi + V   x j 
 j1 

The variable V is called the marginal per capita return (MPCR).
Voluntary Contribution Mechanism: Theory

To simplify, assume the return on contributions is linear:
Ri = Ei – xi +

 N 
V∙  x j 
 j1 
If we have 1/N < V < 1, we have a public goods problem.
Individually, each player is best off giving nothing to the
public good, but collectively the players are best off
donating their entire endowments.
Voluntary Contribution Mechanisms: Results


Even though the theory predicts no
contributions, experimenters general
observe substantial contribution
levels.
Consider the data shown to the
right, taken from Isaac and Walker
(1988).




Group size either equals 4 or 10.
H denotes MPCR = .75 and L
denotes MPCR = .3.
In all cases, there are large
amounts contributed to the public
good, although the amount does
predictably decline with experience.
What forces might be driving these
high contribution rates?
Experience Effects


Generally, although not always, experimenters find that contribution rates
decrease with experience. There are two likely explanations . . .
Learning.



Inexperienced subjects may erroneously contribute to the public good, not realizing that
their payoff is maximized by not contributing.
As they realize their mistake, they contribute less and contribution rates fall.
Strategic play

Suppose it is considered likely that some individuals are “reciprocal altruists.”



In English, I am willing to contribute to the public good as long as others contribute.
This is not the behavior of a “rational” individual.
It then becomes profitable for a rational individual to pretend to be a reciprocal altruist.


By developing a reputation for being this type, the player can induce contributions by other rational
players.
Because it is costly to maintain a reputation and because the value of maintaining a reputation
shrinks as the end of an experiment approaches, we would expect contribution rates to fall over time
as individuals stop maintaining their reputations.
Experience Effects

To separate these two hypotheses,
Andreoni (1988) ran a “partners and
strangers” experiment.




In the partners treatment, subjects
play with the same five person
group for all ten rounds of the
experiment.
In the strangers treatment, there is
random rematching of groups in
every round. This should reduce
the benefits of building a reputation.
In fact, contributions decline in both
treatments and average
contributions are actually somewhat
higher in the strangers treatment.
These results suggest that learning
is driving the decline in contribution
rates and that high contribution
rates cannot solely be attributed to
strategic concerns.
MPCR



Marginal per capita Return (MPCR): Suppose that subjects’ predilection
for contributing to public goods could be explained by a standard model
of consumer choice. It should then be true that the marginal rate of
substitution between private and public goods equals the ratio of prices
for these goods.
Since an increase in V, the MPCR of public goods, is equivalent to
decreasing the price of public goods, an increase in V should
unequivocally lead to more public goods being provided.
With very few exceptions, this is what experimenters observe. (Of
course, a cynic might also note that increasing V reduces the cost of
erroneously donating to the public good.)
Group Size

Group Size: One can imagine an increase in group size cutting
either way. On the one hand, every dollar contributed to the
public good now generates greater group benefits (holding
MPCR fixed). On the other hand, sustaining cooperation is
usually more difficult in large groups –monitoring is more
difficult and punishing defectors involves a difficult coordination
problem. There has been relatively little systematic examination
of the effect of group size on contributions, largely due to the
difficulties and expense of such experiments. There are good
papers on this topic by Isaac and Walker (1988) and by Isaac,
Walker, and Williams (1991). Their results suggest that
increased group size will lead to higher contributions, although
this effect interacts with the MPCR.
Communication

Communication: The theory does not predict that allowing pre-play
communication should have any effect on contributions. However,
early work by psychologists (Dawes, McTavish, and Shaklee, 1977)
showed that cooperation in N-person games is increased by
allowing pre-play communication. A large number of studies have
found similar effects in public goods games (Dawes, McTavish, and
Shaklee, 1977; Isaak, McCue, and Plott, 1985; Isaak and Walker,
1988 & 1991). Moreover, with communication contribution rates
increase over time. Recent work by psychologists (Dawes, Orbell,
and van de Kragt, 1987, 1988, and 1990) indicates that
communication works either by allowing for multilateral promises
(coordination from a game theorist’s point of view) or by generating
group identity.
Andreoni (1995):
Cooperation in Public-Goods Experiments:
Kindness or Confusion

Research Question: The preceding literature had established that
subjects would contribute to public goods in VCM games. Two leading
hypotheses had emerged for why.



One possibility is other-regarding preferences – reasons such as kindness,
altruism, or warm-glow. This is similar to the ideas we have seen proposed for
ultimatum games. Rather than only caring about themselves, people also care
about the payoffs of others. Here, instead of being jealous when others get
more than themselves, they are concerned when others get less.
The other possibility is subject error (confusion). For unsophisticated subjects,
it may not be immediately that contributing money to the public good is a
dominated strategy. (This may not just be a failure to understand the
mathematics. Many real world settings are similar to the public goods games,
but give people incentives to contribute to the public good.) Declining
contribution rates could reflect subjects becoming less confused.
Andreoni’s experiments are designed to separate out these two
hypotheses.
Experimental Design and Procedures

For all treatments subjects play 10 rounds of a standard VCM game. The MPCR
for all of the treatments is .5. Subjects played in fixed groups of five (partners).
There were three treatments:



Regular: This is a standard VCM game, with subjects paid their experimental earnings.
Rank: In this treatment, subjects’ cash earnings are based on the rank of the
experimental earnings. Subjects are shown the conversion table, so they know that
their cash payoffs are solely determined by their rank. This treatment eliminates any
incentive for cooperation and largely reduces the effects of “kindness.”
RegRank: It is possible that just knowing about ranks (without it affecting one’s cash
payoff) might change behavior. The RegRank treatment controls for this. It is
identical to the regular treatment except that subjects are told their rank.
Initial Hypotheses



If contribution to the public good is driven solely by confusion, we
should expect the regular and rank treatments to yield (statistically)
indistinguishable behavior.
If kindness is playing an important role, we should expect lower
contribution rates in the rank treatment.
If there is no confusion present, we should expect no contributions in
the rank treatment.
Results


The percentage of subjects’ endowments contributed to the public good and the percentage
of the subjects contributing something to the public good can consistently be ranked from
top to bottom: Regular, RegRank, and Rank. These differences are statistically significant.
The differences narrow over time, but this must happen as contribution rates are falling.
While there are always at least some contributions in the rank treatment, these
contributions die out to virtually nothing by the final round. This suggests that little
confusion is left by the end of the experiment. Indeed, Andreoni attributes virtually all of
the early cooperation to confusion (81% in round 1). This percentage drops steadily with
experience. For experienced subjects, cooperation is rough 50% kindness, 50% confusion.
Conclusions

Both kindness and confusion play some role in generating contribution
in public goods games. Roughly half of these contributions seem to be
directly due to kindness, with the proportion increasing over time.
These results indicate that an examination of other-regarding
preferences is necessary to understand contribution in public goods
games.
Some Recent Work



Conditional Cooperators: There is an increasingly large body of evidence that
subjects in public goods games are “conditional cooperators” or “reciprocal
altruists.” In other words these subjects are more willing to contribute if they
think others will also be contributing. Fischbacher, Gächter, and Fehr (2001)
provide a nice example of this.
Punishments: Fehr and Gächter (2002) study a public goods game with
punishments, much like the game you played in Block 3 of Tuesday’s
experiment. The presence of these punishments doesn’t change the game’s
equilibrium. None the less, they find that individuals frequently punish freeriders and that the overall level of contribution is dramatically increased by the
presence of punishments.
Social Sanctions: There has been an increasing interest among economists in
social norms – behaviors supported more by social approval or disapproval than
monetary incentives. Rege and Telle (2002) provides evidence that social
sanctions of a very weak sort can greatly increase contributions in public goods
games. This is the treatment we studied in Block 2.