1. Andreoni: Cooperation in Public-Goods Experiments: Kindness or Confusion
Economics 328
Spring 2005

2. 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

3. 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.
Ri = Ei – xi + V
The variable V is called the marginal per capita return (MPCR).

4. Voluntary Contribution Mechanism: Theory
To simplify, assume the return on contributions is linear:
Ri = Ei – xi + V∙
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.

5. 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?

6. 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.

7. 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.

8. 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.)

9. 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.

10. 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.

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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 free-riders 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.