# Unit 4 Strategic interactions and social dilemmas

## 4.6 Public good games and cooperation

In the pest control game, self-interest—ignoring the costs and benefits of their own decisions for the other player—led Anil and Bala to an outcome that neither would have wanted.

Their problem is hypothetical, but it captures a real dilemma facing people around the world whose actions can benefit or harm their neighbours. For example, many farmers in south-east Asia rely on shared irrigation facilities that require constant maintenance and new investment. Each farmer faces the decision of how much to contribute to these activities, which benefit the entire community. But a farmer who does not contribute will still benefit from the contribution of others.

Imagine there are four farmers who are deciding whether to contribute to an irrigation project.

For each farmer, the cost of contributing to the project is $10. Every contribution of$10 increases the crop yield on each of the four farms by $8. This is a strategic interaction: the action of one farmer affects the pay-offs of the others. Now consider the decision facing Kim, one of the four farmers. Her pay-off is the increased crop yield from the project—which depends on how many farmers contribute—minus the cost of her own contribution. For example, suppose two other farmers contribute. Figure 4.8 shows how to calculate Kim’s pay-offs, depending on her own decision. If she doesn’t contribute, she will receive a benefit of$8 from each of the two contributions and incur no costs herself. Her total pay-off is $16. If she contributes too, she receives an additional benefit of$8 (and so do the other three farmers). But it will cost her $10, reducing the pay-off to$14.

Two other players contribute Kim does not contribute Kim does contribute
Benefit from the contribution of others 16 16
Plus benefit from her own contribution + 0 + 8
Minus cost of her contribution – 0 – 10
Total $16$14

Figure 4.8 When two others contribute, Kim’s pay-off is lower if she contributes too.

Figure 4.9 shows Kim’s pay-offs, calculated the same way, for each possible case as the number of other contributors varies from 0 to 3. The figure shows that however many other farmers contribute, Kim’s pay-off is higher if she does not contribute herself (red bars) than if she does (blue bars).

Figure 4.9 Kim’s pay-offs in the irrigation game.

A good like an irrigation system is ‘public’ in the sense that all members of a group benefit equally, irrespective of their own contribution. For more about public goods, with other examples, see Unit 10.

public good game
A public good game is a game in which individual players can take an action that would be costly to themselves, but would produce benefits for all players (including themselves).

The irrigation game is an example of a public good game: when one individual bears a cost to provide a good, everyone receives a benefit. This creates a social dilemma. Whatever other people decide, Kim makes more money if she doesn’t contribute than if she does. In a public good game, each player can free-ride on the contributions of others.

The irrigation game is a case of the prisoners’ dilemma with more than two players. As in the pest control game, each farmer’s decision has external effects on other farmers. If the farmers care only about their own monetary pay-off, there is a dominant strategy equilibrium in which no one contributes and all pay-offs are zero. Yet if all contributed, each would get \$22. Everyone would benefit if everyone cooperated, but cooperation cannot be an equilibrium because each farmer would do better by free-riding on the others.

### Exercise 4.7 Free-riding in the public good game

Group projects in the workplace share similar features to the irrigation game. Suppose you and two other colleagues can each choose to Work or Not Work on a task. Each person’s output is £90 for Work and £0 for Not Work, while the cost of effort is £40 for Work and £0 for Not Work. The total output is shared equally between the three of you.

1. Draw a chart like Figure 4.9 to compare your pay-offs from Work and Not Work, when the number of other colleagues choosing Work is 0, 1, and 2. Use your chart to show that Not Work is a dominant strategy.
2. Suggest some ways to address the free-rider situation in this scenario.

### Is this a good model?

Around the world, farmers and fishing people facing similar decisions have nevertheless chosen to invest, or cooperate, making all those affected better off. Behaviour does not always correspond to the predictions of the prisoners’ dilemma game with self-interested preferences.

The evidence gathered by Elinor Ostrom, a political scientist, and other researchers on common irrigation projects in India, Nepal, and other countries, shows that people do cooperate, although the degree of cooperation varies. In some communities, a history of trust encouraged cooperation—in others, inequality discouraged it. In south India, for example, villages with extreme inequalities in land and caste status had more conflicts over water usage. Less unequal villages maintained irrigation systems better: it was easier to sustain cooperation.1

Ostrom studied how communities managed common property resources, such as inshore fisheries, grazing lands, or forest areas, thereby challenging the prevailing wisdom that informal collective ownership of resources would necessarily lead to a ‘tragedy of the commons’. She emphasized the distinction between common property and open access:

• Common property involves a well-defined community of users who can in practice, if not under the law, prevent outsiders from exploiting the resource.
• Open-access resources such as ocean fisheries or the earth’s atmosphere can be exploited without restrictions, other than those imposed within states acting alone or through international agreements.
social norm
An understanding that is common to most members of a society about what people should do in a given situation when their actions affect others.

She discovered great diversity in how common property is managed. Some communities were able to devise rules and draw on social norms to enforce sustainable resource use and maintenance, while others failed to do so. Ostrom found that individuals would willingly bear considerable costs to punish violators of rules or norms.

As the economist Paul Romer put it, Ostrom recognized the need to ‘expand models of human preferences to include a contingent taste for punishing others’. She developed simple game-theoretic models in which individuals have social preferences, caring directly about trust and reciprocity. And she looked for the ways in which people faced with a social dilemma changed the rules, so that the strategic nature of the interaction was transformed.

Aside from studying real-world behaviour, economists have conducted laboratory experiments to investigate why people might cooperate rather than defect in prisoners’ dilemma situations. Around 20% or more of players in one-shot two-player prisoners’ dilemma games choose to cooperate. One possible explanation is that they feel altruistic towards their opponent. It has also been observed that playing repeatedly against the same opponent increases the likelihood of cooperation to around 50%: players who think their opponent may be altruistic may want to develop a reputation for cooperating themselves, so that their opponent will continue to cooperate in future rounds. 2 3

So far in our game-theoretic models, we have assumed that people are purely self-interested, and played the game only once. In the next two sections, we will explore how altruism, repeated interaction, and social norms can be incorporated into our models, to make them consistent with the evidence of cooperative behaviour.

### Great Economists Elinor Ostrom

Elinor Ostrom (1933–2012), a political scientist, was a co-recipient of the 2009 Nobel Prize for economics (the first woman to receive this award). She was not well known among economists, but some, like Vernon Smith—an experimental economist who had previously received the prize—recognized her originality, scientific common sense, and willingness to listen carefully to data.

Ostrom’s entire academic career was focused on the central role of property. Ronald Coase established that when one person’s actions affected the welfare of others, the need for government regulation depended on whether property rights were clearly delineated. Ostrom explored the middle ground where communities, rather than individuals or formal governments, held property rights.

Ostrom drew on a unique combination of case studies, statistical methods, game-theoretic models with unorthodox ingredients, and laboratory experiments to try to understand how tragedies of the commons could be averted. Much of her career was devoted to identifying the criteria for success, and using theory to understand why some arrangements worked better than others.

Economists had explained the diversity of outcomes using the theory of repeated games, which predicts that self-interested individuals can sustain cooperative outcomes when they interact repeatedly. But this theory was not a satisfying explanation for Ostrom, partly because it predicted that any other outcome, including rapid depletion, could also arise. More importantly, she knew that sustainable use was enforced by actions that clearly deviated from the hypothesis of material self-interest.

Through a pioneering series of experiments, she confirmed the widespread use of costly punishment in response to excessive resource extraction, and demonstrated the power of communication and the critical role of informal agreements in supporting cooperation.4

### Question 4.5 Choose the correct answer(s)

Read the following statements about Elinor Ostrom’s ideas and choose the correct option(s).

• Elinor Ostrom challenged the view that collectively owned resources would suffer from a ‘tragedy of the commons’.
• Open-access resources can be more easily exploited than common property.
• Elinor Ostrom found certain conditions under which communities could successfully manage their common property.
• Elinor Ostrom confirmed the theory that sustainable resource use can be explained by repeated interactions by self-interested individuals.
• She studied ways that the tragedy of the commons could be averted.
• Unlike open-access resources, common property involves a well-defined community of users that can prevent outsiders from exploiting the resource.
• She found that communication and informal agreements were important, as well as costly punishment in response to excessive resource extraction.
• She showed that sustainable use was enforced by actions that cannot be explained by purely self-interested behaviour, such as costly punishment.
1. Elinor Ostrom. 2000. ‘Collective Action and the Evolution of Social Norms’. Journal of Economic Perspectives 14 (3): pp. 137–58.

2. James Andreoni and John H. Miller. 1993. ‘Rational Cooperation in the Finitely Repeated Prisoner’s Dilemma: Experimental Evidence’. The Economic Journal 103 (418): pp. 570.

3. Harris Cooper, Barbara Nye, Kelly Charlton, James Lindsay, and Scott Greathouse. 2016. ‘The Effects of Summer Vacation on Achievement Test Scores: A Narrative and Meta-Analytic Review’. Review of Educational Research 66 (3): pp. 227–268.

4. Elinor Ostrom, James Walker, and Roy Gardner. 1992. ‘Covenants With and Without a Sword: Self-Governance is Possible’. The American Political Science Review 86 (2).