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Twenty years after the declarations from the Earth Summit in Rio, the world faces an unattenuated host of problems that threaten the goal of sustainable development. The challenge to cooperatively solve socio-ecological problems has been portrayed in Garrett Hardin’s essay “The Tragedy of the Commons”. While this paper remains controversial, it has inspired a vast number of theoretical, experimental, and empirical contributions that have clarified the mechanisms of collective action problems and suggested ways to overcome these. This article reviews the recent game-theoretic research in this field.

Hardin’s paper “The Tragedy of the Commons” [

Hardin’s paper has in many ways coined the term for this very common problem where benefits from an action are private but the costs are borne by all. However, an analysis of the problem that Hardin formulated does in fact not yield a “Tragedy of the Commons” as it is conventionally understood in game-theoretic terms. Neither does “freedom in a commons bring ruin to all” [

Two themes run through this review, namely the issues of coordination and cooperation. Let me introduce these concepts with the help of two examples. Consider first the following situation: There are two actors (players): One who likes to listen to Stravinsky, and another, who likes to listen to Bach. Now picture that both are at work and agree to go a concert (both prefer to go to a concert together rather than alone) but they have not decided where to meet. So, if Player 1 goes to the Bach concert and his partner goes there, too, 1 gets a payoff of 2 and Player 2 gets a payoff of 1. If Player 1 go to the Stravinsky concert and Player 2 goes there too, 1 get a payoff of 1 and 2 gets a payoff of 2. But if Player 1 goes to the Bach concert and Player 2 goes to the Stravinsky concert (or vice versa), both are alone and get a payoff of zero. (See

Bach or Stravinsky: A game of coordination.

This is very different in the second example, the “Prisoner’s dilemma”. The story here is that there are two robbers that have been caught, but the police have no evidence who the main culprit is. If both robbers cooperate and do not talk, the police cannot do anything and both robbers get only a slight punishment. If however one of the robbers defects and speaks to the police and tells the officers that the other one did it while he was merely standing by, the defector will be set free and the other robber will go to jail for a long sentence. If both robbers talk to the police, both will get punished, although they do get some reduction as they have talked to the police. (See

Prisoner’s dilemma: A game of cooperation.

How do non-cooperative games play out in situations where a good is shared by all? Let me start out by quoting the original passage in Hardin’s article that is the basis of his metaphor. It is a situation where a group of herdsmen put cows on a common pasture:

As a rationale being, each herdsman seeks to maximize his gain. Explicitly or implicitly, more or less consciously, he asks, “what is the utility to me of adding one more animal to my herd?” This utility has a negative and a positive component.

(1) The positive component is a function of the increment of one animal. Since the herdsman receives all the proceeds from the sale of the additional animal, the positive utility is nearly +1.

(2) The negative component is a function of the additional overgrazing created by one more animal. Since, however, the effects of overgrazing are shared by all [...], the negative utility for any particular decision-making herdsman is only a fraction of −1.

Adding together the component particular utilities, the rational herdsman concludes that the only sensible course for him to pursue is to add another animal to his herd. And another; and another... But this is the conclusion reached by each and every rational herdsman sharing a commons. Therein is the tragedy. Each man is locked into a system that compels him to increase his herd without limit—in a world that is limited. Ruin is the destination towards which all men rush, each pursuing his own best interest in a society that believes in the freedom of the commons. Freedom in a commons brings ruin to all. [

Partha Dasgupta [

An essay to capture Hardin’s game in normal form.

There are several issues with Hardin’s metaphor. First, it is not clear who is “all”. Commonly, “all” is interpreted as “open-access”, meaning that there are no barriers to enter the pasture and that the number of players is in fact indeterminate. Under open access, effort will enter until all rents/profits are dissipated. There are two things to say about this argument: First, common property is not nobody’s property. Quite to the opposite, common property belongs to an often well-defined group of people and in many cases institutions and social norms exist that regulate the harvesting/extraction of the communally owned property, so that it is managed in a more or less sustainable way. Second, if the characterization of open-access is correct, then the individual actor plays such a small part that his actions have only a negligible effect on the other players. In this case, Game Theory plays no role.

Furthermore, Hardin’s metaphor is criticized on the grounds that it contains a dynamic dimension which should be treated explicitly. For example, Brekke

In order to discuss the effect of non-cooperative harvesting, one needs a benchmark of optimal dynamic resource management. Consider therefore the canonical model of renewable resource use [

Equation (1) says that the objective of a social planner is to maximize the Net-Present-Value from harvesting the resource by choosing the appropriate level of effort _{max}

We can see that it is linear in the control variable E so that whenever the term in the squared brackets is negative, it is best to set effort to zero, and whenever the term in the squared brackets is positive, it is best to set effort to its maximum level (technically, the optimal strategy is of the bang/bang type):

In other words, when the initial stock level is low, it is optimal to let the stock grow until it has reached the optimal level and then just take out what is re-growing in equilibrium. In contrast, with a high initial stock size, the stock is “harvested down” to the optimal level as fast as possible.

Turning to a dynamic game, one sees that the problem for player

Let me illustrate the outcome of a game with two symmetric players (see, for example [

Stock development under optimal and non-cooperative management. (

Now let me turn to a game where the players are asymmetric in the sense that player ^{i }<c^{j}

Stock development under non-cooperative management. (

Considering a situation where there are three or more asymmetric players, the stock will be reduced until the first (least efficient) player leaves the fishery. But the two remaining players can also not cooperate on keeping the stock at that level. The situation will be just as before and only the most efficient player will remain in the fishery. He or she obtains some rents, but these are limited by the threat of re-entry of the second-most efficient player. It is plain to see that as the number of players with unique marginal effort cost increases, rents will be dissipated, but all rents will only be dissipated as this number tends to infinity.

To sum up, although Hardin’s simile of the pasture’s problem does not lend itself to a formal model while maintaining the same properties that Hardin claimed, formal dynamic models can be constructed that lead to the total dissipation of rents.

Among the most prominent scholars who have criticized Hardin’s essay and its dismal implications is the Nobel laureate Elinor Ostrom. She highlights that Hardin’s essay is overly pessimistic and warns that those who blindly advocate formal property rights solutions might do more harm than good. There are many empirical examples of successful community management and introducing formal property rights and other external laws in these regimes might crowd out existing informal arrangements. There is by now also ample evidence from lab-experiments that people are not only rational, narrowly self-interested maximizers. In many lab-games, where self-interest would dictate zero contributions to a public good, many people actually do contribute significant sums. Thus, there are not only “rational maximizers” but also “conditional cooperators” and “willing punishers”. To quote Ostrom [

In her work, Ostrom identifies a series of factors that are crucial for success, which can be paraphrased as follows (for an original elaboration see [

To illustrate, imagine that a prisoner’s dilemma game (

Illustration of two-phase punishment scheme in [

When all players follow this two-phase punishment scheme, no player has an incentive to stray from the path of cooperation, but also note that—and this is important—a deviating player has no incentive to not accept the punishment and all other players have no incentive to not punish. This two-phase punishment strategy ensures cooperation as long as the rents from cooperating are large enough, there are not too many players, and the future is not discounted too heavily.

In many ways, the climate problem is the “tragedy of the commons” in inverse: Here the benefits (avoidance of dangerous climate change) are public but the costs (of abatement) are private. Hence every country has an incentive to free-ride on the abatement effort of the others. As the local commons analyzed in the previous section, the climate problem is essentially a dynamic stock problem. That is, the strategic interactions play out over the level of the stock variable that is shared by all players. However, cooperation in the climate commons is extremely difficult to establish and enforce. It fails on almost all aspects that Ostrom found to be critical for successful management. In particular, the climate system differs from the local commons discussed above, namely, it is a global commons. This implies that the damages from climate change are potentially unbounded, whereas in a local commons the players could always secure themselves a payoff of zero. They could simply leave the fishery, but one cannot leave this planet (at least not today).

In the following, I will discuss three recent papers that deal with different aspects of establishing cooperation in the commons. In the first paper, Heitzig

In contrast, Mason

The last paper I want to mention on this topic is a working paper from Scott Barrett [

However, when the location of the threshold is uncertain, then coordination is ineffective. Technically speaking, the expected damage function is continuous again. Figuratively speaking, the players are walking towards the edge of a cliff, but it is so foggy that they do not see anything and do not know where exactly to stop. Then each individual has an incentive to just take one more tiny step. We are back again in a situation where cooperation is necessary, but very difficult to enforce.

This is clearly an exiting and most important area of research. One approach could be to merge the idea of a relative punishment scheme to enforce cooperation with a more realistic modeling of the climate change situation by means of a dynamic game. Progress towards solving the collective action problems that humanity faces will only be made if both the natural and social aspects of the respective problem are appreciated and understood. A deep understanding in turn is only possible when people with different points of view come together and discuss. It is exactly by raising discussion, by provoking research, and by providing a focal point of consent or dissent that Hardin’s metaphor of the “Tragedy of the Commons” has deeply inﬂuenced the way we think about current socio-ecological challenges. One may object to his analysis and his conclusions, but as pointed out in the epigraph to his article, achieving sustainable development still requires, at its root, a change of human relationships with the environment.

I would like to thank Nils Christian Stenseth for his support and comments on earlier versions of this manuscript. This research is funded by NorMER, a Nordic Centre of Excellence for Research on Marine Ecosystems and Resources under Climate Change.