Unit 4 Strategic interactions and social dilemmas

4.8 Repeated interaction: Social norms, reciprocity, and peer punishment in public good games

Free-riding today on contributions by other members of one’s community may have consequences tomorrow or years from now. From year to year, some people may acquire a reputation for being uncooperative, which may influence the behaviour of others. Ongoing relationships are an important feature of social interactions that is not captured in the models we have used so far: life is not a one-shot game.

Best responses may be different in a repeated game. Imagine how differently things would work out if the pest control game were repeated every season—even with self-interested preferences. Anil and Bala would consider what had happened in the past when making choices today, and also the impact of today’s choices on what might happen in the future. Suppose that Bala had used IPC last season. What is Anil’s best response when he is considering whether to use Toxic Tide or IPC this year? He would reason like this:

If I use IPC, like Bala did last season, then maybe Bala will continue to do so in future. If I use Toxic Tide—raising my profits this year—Bala is more likely to use Toxic Tide next year. So unless I am extremely impatient for income now, I’d better go for IPC.

Bala could reason in the same way. So they might continue playing IPC forever.

Question 4.9 Choose the correct answer(s)

Four farmers are deciding whether to contribute to the maintenance of an irrigation project. For each farmer, the cost of contributing is $10. But for each farmer who contributes, all four of them will benefit from an increase in their crop yields, so they will each gain $8 per farmer that contributes.

Read the following statements and choose the correct option(s).

  • If all the farmers are selfish, none of them will contribute.
  • If one of the farmers, Kim, cares about her neighbour (Jim) just as much as herself, she will contribute $10.
  • In a one-shot game, if Kim is altruistic and contributes $10, the others might contribute too, even if they are selfish.
  • If the farmers have to reconsider this decision every year, they might choose to contribute to the project even if they are selfish.
  • Do Not Contribute is a dominant strategy for all the farmers: whatever the others do, their own benefit from contributing is $8, but the cost is $10.
  • If Kim is the only one who contributes, all farmers will receive $8. If Kim cares about Jim just as much as herself, then her pay-off is the sum of what she receives ($8) and what Jim receives ($8), which is $16. Since $16 is higher than the cost of contributing ($10), Kim will contribute.
  • Whatever Kim does, the dominant strategy for a purely self-interested farmer in the one-shot public good game is Do Not Contribute.
  • If the farmers have an ongoing relationship, they may all decide to contribute, to gain the future benefits of continued cooperation. If any of the neighbours failed to contribute in any year, cooperation would break down. Knowing this, they would have an incentive to contribute in the present.

A public good experiment

Laboratory experiments demonstrate that people can sustain high levels of cooperation in repeated public good games, if they have opportunities to target free-riders once it becomes clear who is contributing less than the norm.

An experiment that mimics the costs and benefits from contribution to a public good was conducted in cities around the world. In this experiment, participants play ten rounds of a public good game similar to the irrigation game involving Kim and the other farmers. They are randomly sorted into small groups, typically of four people who don’t know each other. In each round, each participant is given $20. They are asked to decide on a contribution from their $20 to a common pool of money. The pool is a public good: for every dollar contributed, each person in the group receives $0.40, including the contributor.

Imagine that you are playing the game, and you expect the other three members of your group each to contribute $10. Figure 4.14a shows how you might decide whether to do the same. Unfortunately for the group, your pay-off is higher if you contribute nothing. And unfortunately for you, the same applies to the other members. If the players were self-interested, we would expect them all to free-ride.

Three other players contribute $10 I contribute nothing I contribute $10
My return from their contributions 12 (= 30 × 0.4) 12 (= 30 × 0.4)
Plus benefit from my own contribution 0 4 (= 10 × 0.4)
Plus the money that I keep 20 10
Total $32 $26

Figure 4.14a Comparing the pay-offs from free-riding and contributing $10.

That is not what happened in this experiment. After each round, the players were told the contributions of other members of their group. The lines in Figure 4.14b represent the evolution over time of average contributions in each location around the world. In every round, players contribute more than $0, although the amount contributed declines over time and varies across places.

In this line chart, the horizontal axis shows time period, ranging from 1 to 10, and the vertical axis shows the average contribution in dollars, ranging from 0 to 16. Lines for 16 cities are shown: Copenhagen, Dnipropetrovs’k (Dnipro), Minsk, St. Gallen, Muscat, Samara, Zurich, Boston, Bonn, Chengdu, Seoul, Riyadh, Nottingham, Athens, Istanbul, and Melbourne. In all cities, average contributions start high, ranging from 8 to 14 in period 1, but steadily decline each period, ranging from 1 to 9 in period 10.

Figure 4.14b Worldwide public goods experiments: contributions over 10 periods.

Benedikt Herrmann, Christian Thoni, and Simon Gachter. 2008. ‘Antisocial Punishment Across Societies’. Science 319 (5868): pp. 1362–67.

Focus on Chengdu in the interactive graph. Players contributed $10 on average initially, but after four rounds the amount began to decline. In every population where the game was played, contributions to the pool were high in the first period, although much more so in some cities (Copenhagen) than in others (Melbourne). This is remarkable: if you care only about your own pay-off, contributing nothing at all is the dominant strategy. One possible explanation for the high initial contributions is that the participants in the experiment were altruistic. But the difficulty (or, in Hardin’s words, the tragedy) is obvious. Everywhere, contributions decreased over time.

In some cities (Copenhagen, Bonn, and St. Gallen) this trend is very evident. In others (Muscat, Riyadh, or Athens) contributions are still high at the end of the experiment. Contributions to the common pool vary widely across societies.

Altruism is not the most plausible explanation of these results. Altruistic players would care about the pay-offs received by others in all periods independently of the actions of other players, maintaining their contributions over time to ensure benefits for all. But it appears that contributors decreased their level of cooperation if they observed that others were free-riding. They cared about how others behaved.

The role of social norms

People make decisions according to their own individual preferences—the likes, dislikes, attitudes, feelings, and beliefs that motivate them (including social preferences, such as altruism). But their preferences may be influenced by social norms.

A social norm is an understanding that is shared among most members of a community about how people should behave towards each other in particular circumstances. Giving gifts on birthdays to close family members and friends is a social norm in many communities, as are conventions that also apply among strangers, like ‘waiting in line’.

In the situations modelled by public good games, many people are happy to contribute when they observe others contributing. This suggests that they are influenced by social norms: for example that people ought to contribute for the good of the group, or that outcomes should be fair.

A preference to be kind to or to help others who are kind and helpful, and to withhold help and kindness from people who are not helpful or kind.

The most convincing reason for falling contributions in later rounds of the experiment is that players whose contributions were initially high were disappointed that others did not follow a social norm of reciprocity by raising their contributions in return. The disappointed players responded—according to the same norm—by lowering their own contributions.

If people care strongly about social norms, they may wish to punish those who violate them, even if the cost to themselves is high. In the experiment in Figure 4.14b, the only way to punish free-riders was to stop contributing. To test what would happen if players could punish each other directly, the experimenters introduced a punishment option. After observing the contributions of their group, individual players could punish other players by making them pay a $3 fine. The punisher remained anonymous, but had to pay $1 per player punished.

Figure 4.14c shows the effect. For the majority of players, including those in China, South Korea, northern Europe, and the English-speaking countries, contributions were higher when they had the opportunity to punish free-riders.

In this line chart, the horizontal axis shows time period, ranging from 1 to 10, and the vertical axis shows the average contribution in dollars, ranging from 0 to 16. Lines for 16 cities are shown: Copenhagen, Dnipropetrovs’k (Dnipro), Minsk, St. Gallen, Muscat, Samara, Zurich, Boston, Bonn, Chengdu, Seoul, Riyadh, Nottingham, Athens, Istanbul, and Melbourne. In all cities, average contributions range from 6 to 16 in period 1 and stay steady at their initial levels in all subsequent periods.

Figure 4.14c Worldwide public goods experiments with opportunities for peer punishment.

Benedikt Herrmann, Christian Thoni, and Simon Gachter. 2008. ‘Antisocial Punishment Across Societies’. Science 319 (5868): pp. 1362–67.

In some cities, the threat of punishment was sufficient to prevent contributions falling over time. But in Melbourne, where contributions fell rapidly to below $2 in the previous experiment, players were able to use punishment to raise the average from $8 initially to $16 before the end.

When people engage in a common project—whether pest control, irrigation, or reducing carbon emissions—everyone has something to gain if they cooperate, but also something to lose when others free-ride. This experiment illustrates how, even in large groups of people, repeated interactions, social norms, and social preferences (with or without penalty mechanisms) can support high levels of contribution to the public good.

Exercise 4.9 Exploring the data from the worldwide public goods experiments

In this exercise, you will be using Excel to explore how contributions in the public goods experiments (shown in Figures 4.14b and 4.14c) have changed over the course of the game and after punishment was introduced.

Download and save the spreadsheet containing the data for Figures 4.14b and 4.14c.

  1. Choose one figure (either 4.14b or 4.14c) and use the data to plot a line chart with contribution on the vertical axis and period on the horizontal axis. (For help on how to do this task in Excel, use this walk-through.)
  2. For Figure 4.14b, calculate the difference between the starting and ending values. Which country had the largest, and which country had the smallest change in contributions after ten periods? Do the same for Figure 4.14c. Did contributions increase, decrease, or stay the same when players could punish each other?
  3. Now choose three countries in the data. Calculate and compare the difference between contributions in the game with and without punishment. Did players in your chosen countries contribute more in every period when there was punishment? Why would it be reasonable to think that the differences we see are due to the punishment option, rather than other explanations?

The Experiencing Economics ebook contains a public good game that instructors can play with students in the classroom or during synchronous online teaching. Visit the instructor’s section to find a step-by-step guide for running the game.