Tragedy of the Commons – Part 2

Tragedy of the Commons is the natural extension of the Prisoner’s Dilemma to an arbitrary number of players. Just as we used Prisoner’s Dilemma as a model to understand the limitations of pairwise cooperation¹, so too Tragedy of the Commons is an essential model for understanding the limitations of group cooperation.

The abstract definition is as follows. A ‘game’ is classified as a ‘Tragedy of the Commons’ if it satisfies the following abstract conditions: There are an arbitrary number of ‘players’. Each player decides between two options – to either ‘cooperate’ or ‘defect’. Each player considers the outcome in which they defect better than the outcome in which they cooperate, regardless of how everyone else plays. Also each player considers the outcome in which everyone cooperates, better than the outcome in which everyone defects. Then, by the very definition, the only rational strategy is to defect, and so a group of rational players all defect and are therefore worse off than a group of irrational players who all choose to cooperate.

The example which gave the Tragedy of the Commons it’s name was the hypothetical consequence of unregulated grazing on common land. More generally, the Tragedy of the Commons applies to any situation where people have open access to some scarce and valuable natural resource, without any system of regulation². The argument is that every individual is better off taking more than is sustainable (defecting) than exercising restraint (cooperating), and this is the same regardless of how many people choose to cooperate. If everyone cooperates the resource can be sustained, but if everyone defects, taking as much as they want, the resource is over-exploited to the point of depletion. The logical end for a community of rational self-interested individuals is therefore the depletion, or possibly elimination, of the common resource – a real tragedy of the commons. A concrete example of this kind of tragedy of the commons is the hunting of a species to extinction, which is a repeating pattern in human history. As Matt Ridley puts it³: “The rational individual would – did – kill the last two mammoths on the planet because he would know that another individual would get them if he did not”. As an even more concrete example, there was the collapse of the cod fishing industry that happened in the Grand Banks fishery off the coast of Newfoundland in 1990; this happened because rapid advancements of fishing technology in the 1960s meant people could catch more fish than was sustainable and there was no system of regulation in place to control it.

Many examples for which the Tragedy of the Commons is a useful model are of this kind⁴. But if you think outside the box you can find examples of the tragedy of the commons everywhere, that meet the abstract definition, but aren’t necessarily like this. My favourite example to stretch the mind, is the example of tall trees⁵. Why do rain forest trees expend so much energy getting so tall, when they could all be half the size and still all get the same amount of light? It’s a classic tragedy of the commons. Each tree can either ‘cooperate’ and stay a modest size or ‘defect’ and get a bit taller than all the other trees. Natural selection selects for trees which ‘defect’ because they get more light, and this is the sense in which defecting is the best option for each tree. And yet all trees cooperating is ‘better’ for every tree than all trees defecting because they all get the same amount of light but all expend less energy. Therein lies the ‘tragedy’.

As another example, consider the case of a university course which is marked relatively (meaning a student’s grade is determined by their relative position in the year group). Hypothetically you could imagine it would be possible for the students to make a pact to all study two days less e.g. never study at the weekend. This would be a great pact as theoretically if all students cooperate and observe the pact then all students are better off since their grade is theoretically the same but they don’t have to ever study on weekends. But it could never work, even hypothetically, because it’s a tragedy of the commons; for each student the individual benefit of ‘defecting’ and studying at the weekend beats the individual benefit of cooperating, and so the collective benefit of cooperating can never be realised.

I’m particularly interested in examples, such as the above, where a Tragedy of the Commons limits the possibility of group cooperation. A canonical example of group cooperation which is a tragedy of the commons is the ‘public goods game’. In this game, each player can opt in to invest in a public good (‘cooperate’) or opt out (‘defect’). The public good creates a return on investment proportional to the amount invested, but the benefits of the public good are available equally to everyone, including those who don’t contribute⁶. Then, under the assumption that the shared return is not enough to justify a single contribution, defecting is better than cooperating, at the individual level, because a defector receives the benefits of the public good without the costs, but at the same time everyone cooperating is better for every individual than everyone defecting because everyone gets a return they wouldn’t otherwise have been able to get individually. This predicts a tragedy of missed opportunity where no-one invests in the public good. This situation closely resembles the collection of taxes to fund public services; and the ‘lesson’ of the tragedy of commons in this situation, is that public services would not be possible without taxes being enforced.

We should acknowledge that not all examples of group cooperation can be modelled by a Tragedy of the Commons, which makes it much easier to see how certain examples of group cooperation can be compatible with natural selection. We can model the general case of group cooperation, by a generalisation of the ‘public goods game’. As in the special case we considered above, which I will call the ‘linear public goods game’ to differentiate it, every player has the option to contribute to a public good, the benefits of the public good are available to all equally, and there exists some level of contribution such that it is a better outcome for everyone than when no-one contributes, but we will no longer assume that the benefit is proportional to the number of contributors and instead allow it to depend in an arbitrary way on the number of contributors. This to me captures the essential properties of group cooperation – that there is some benefit that it is impossible to achieve individually, and this benefit is equally available to all. There are a couple of interesting special cases to this. One we have already seen, the ‘linear public goods game’, leads to a tragedy of the commons.

A second special case is one that much more accurately models ‘teamwork’, such as collaborative hunting or even collaborative warfare, both of which are not unique to humans. In the extreme simple case of this, there is only a payoff when everyone contributes, and this payoff more than exceeds the cost of contributing. The abstraction of this kind of situation is known as a ‘stag hunt’⁷. This is very different to a tragedy of the commons because now the optimal move depends on the play of everyone else; if you know everyone else is going to cooperate, you should cooperate, but if you think anyone else is going to defect you should defect. Also unlike the tragedy of the commons, if you can all communicate your plan to cooperate, you have no reason to suspect anyone would deviate from this because they can not benefit in doing so; it’s foolproof to free-riders. You may still think that, even though group cooperation can be ‘rational’ in this case, it could not spread by natural selection because there is no relative advantage to an individual within the group; while it’s true that the cooperation instinct cannot spread within a static group, it can spread through the species; this is not invoking group-selection as it does not require groups to be static, but rather just the fact that natural selection is not always a zero-sum⁸ game, especially within the boundary of a single group.

A third special case is the case where the benefit of just a single ‘cooperator’ is enough to justify the cost. In this case everyone should want to ‘cooperate’, regardless of what everyone else does, but to make it more interesting we assume that only one individual’s ‘cooperation’ is required for the public good to be ‘produced’⁹. This situation is known as a ‘Volunteer’s Dilemma’¹⁰. Since it feels unnatural to call a single individual’s contribution a ‘cooperation’, we usually use the terms ‘volunteer’ and ‘ignore’ instead of ‘cooperate’ and ‘defect’ in this context. Examples of the volunteer’s dilemma include the case where the public good is exposing a criminal, which may only require one person to report it, or the case where the public good is a lighthouse which may only require one person to build it. Again a volunteer’s dilemma is not like a tragedy of the commons. While it’s true that it’s better to ignore if someone else volunteers, because you get the benefit without the cost, it is not best to ignore if no-one volunteers, because even for an individual the benefit of volunteering outweighs the costs. Again, unlike a tragedy of the commons, your optimal move depends on how everyone else plays and the result is that the two strategies ‘volunteer’ and ‘ignore’ can naturally exist in equilibrium. While the volunteer’s dilemma isn’t like a ’cooperation’ in the sense of requiring more than one contributor, it is in the sense that the benefits are shared equally among the group. Again, it is not contradictory to natural selection for volunteering tendencies to exist, for the same reason it is not contradictory for cooperation in ‘stag hunts’ to exist – because natural selection is not always a zero-sum game.

In the two player case of the tragedy of the commons – the prisoner’s dilemma – we saw in the previous part that cooperation could be natural in the context of repeat play; there is unfortunately no analogue of this for general group sizes because the larger the group sizes, the larger the proportion of mixed groupings where defectors can benefit from cooperators. In short, we can not rely on goodwill alone to solve a tragedy of the commons, unless perhaps in the context of a war against a neighbouring group where a united effort is essential. The way human societies solve a tragedy of the commons is with politics¹¹, and conversely I think this is one of politics’ main purposes. In general this involves agreeing on a system, and correspondingly having measures in place to enforce it. This needn’t always be in the form of centralised government, and state ownership of the commons or privatisation of the commons subject to market forces; there have been many examples of successfully managed communally owned commons¹²¹³. In the case of a communally owned commons, I think politics works by reducing a tragedy of the commons to a volunteer’s dilemma; where volunteers are needed to design the system, monitor for defectors, report defectors, and enforce punishment of defectors. The effectiveness of this, and direct democracies in general, does depend on the size of the group though. As with most politics, there is rarely a “one size fits all” (or rather a “one fits all sizes”) solution, and sometimes there isn’t a good solution at all.

So far we’ve only considered what I’ll call ’pure group cooperation’ where the benefit is shared equally among the group (which we could model without loss of generality by the ‘generalised public goods game’). But group cooperation in a more general sense of just creating a benefit to each individual that can’t be attained individually, needn’t be like this. If we relax the assumption that all members benefit equally, we can find other examples of ‘group cooperation’ that can be consistent with natural selection. In particular a network of pairwise cooperations can give the illusion of group cooperation, and in contrast to the pure group cooperations we’ve looked at so far can scale much more easily to larger groups. The example I have in mind, which I think is the only example of this kind, is human trade networks… a topic significant enough to deserve it’s own post¹⁴.

In conclusion, the Tragedy of the Commons is such a useful concept to explicitly recognise, both for its abstract properties but also for how it models the limits of group cooperation. We’ve also seen how general group cooperation as modelled by the ‘generalised public goods game’, while sometimes a tragedy of the commons, need not always be, enabling us to much more easily reconcile many examples of group cooperation with the theory of natural selection.