To get cooperation, change the structure
2026-08-15 · Adaptation & Evolution
Every cooperation that holds has a structure behind it that makes defection a losing trade. Find the parameters in that structure and you can dial cooperation up — or wipe it out with a single order, which is exactly what happened on the Western Front in 1918.
The usual explanation for cooperation is moral: good people, decent norms, a community that pulls together. The trouble with that explanation is that it predicts nothing. The same owner runs a restaurant very differently outside a tourist attraction than outside their own housing block. The same army holds an unspoken truce on one stretch of front and fights viciously on the next. The people did not change. Something else did.
This issue is about that something else. It is not a metaphor. It is a handful of quantities you can write down and compute: whether there will be a next time, whether your behaviour is visible to others, and how many people you have to face. Move those three and cooperation grows on its own — or collapses on its own — with nobody's heart getting better or worse.
The awkward part comes after. Once you accept that cooperation is a product of structure, "raise the moral standard" stops being the main intervention and becomes the least efficient one available.
Start with the simplest case. Two people each choose once: cooperate, or defect. Four combinations, each with a result.
Use the classic numbers. Both cooperate: 3 each. Both defect: 1 each. One defects while the other cooperates: the defector takes 5, the cooperator gets 0. As long as those four numbers satisfy one ordering — I defect while they cooperate (5) > both cooperate (3) > both defect (1) > I cooperate while they defect (0) — this is a prisoner's dilemma. The exact values do not matter; the ordering does.
Notice what the picture actually says. Not that people are selfish, but that under this ordering, defecting is better no matter what the other side does. A choice like that is called a dominant strategy. When one exists you do not even need to guess what the other person is thinking — guessing changes nothing.
Which is why "we should just trust each other more" is inert here. Trust addresses "I don't know what they'll do," and in this game I do know, and knowing does not help. Mutual defection is also a Nash equilibrium: standing in that cell, either player who changes their mind alone only makes things worse for themselves. It is stable. It is just stable in a bad place.
To decide whether something is a prisoner's dilemma, don't look at how well the two sides get along — rank the four outcomes by how good they are for you. If "I defect while they cooperate" ranks first and "both defect" ranks third, that's it. If you can't produce that ranking, don't use the term: most conflicts that get called prisoner's dilemmas have a different structure and need different tools.
The last section had one round and two people. The real world has a crowd bumping into each other repeatedly, and most of the time nobody "works out" what to do — people copy whoever nearby seems to be doing well, and bacteria and animals do not think at all.
The standard tool for this is replicator dynamics (Taylor and Jonker, 1978). The rule fits in one line: a strategy's share of the population grows at a rate proportional to its payoff minus the population average. Above average and it spreads, below average and it shrinks, exactly average and it holds still. → replicator dynamics
Here is the easy thing to skip past: a strategy's payoff depends on what everyone else is currently playing. A bullying strategy does spectacularly well in a crowd of pushovers and is suicide in a crowd of hard cases. So "the optimal strategy" is a suspect phrase here — the optimum drifts as the mix drifts.
Run it on the previous section's prisoner's dilemma: defectors out-earn cooperators at every mix, so they are always above average, so the cooperator share falls all the way to zero without stopping. That is the real severity of the problem — not that cooperation is hard to sustain, but that in this structure cooperation cannot exist at all.
Change the payoff structure and the ending changes immediately. The Hawk-Dove game (Maynard Smith and Price, 1973) has two animals contesting a resource: a hawk always fights, a dove bluffs and backs off the moment the other side gets serious. The resource is worth V, an injury costs C. When injury costs more than the prize (C > V), too many hawks means they maim each other, too many doves means hawks take everything for free. The result settles at a fixed mix: hawks at V/C. With V = 2 and C = 5, that is 40% hawks and 60% doves.
That resting mix has a name: an evolutionarily stable strategy, or ESS. The definition is plain — in a population all playing it, any small band of invaders playing something else does worse and gets squeezed out. An ESS is not "the best strategy," it is "the strategy nothing can dislodge." Those two are often not the same thing.
Stop asking "which strategy is best" and ask "at the current mix, which strategy beats the average." The first question frequently has no answer in a system where payoffs drift with the mix. The second always has one, and if you can estimate what share of people are currently doing what, you can compute it.
The first change that actually works: stop playing only one round.
Define w: the probability that, after this round, the two of you meet again. If w is 0 this is a one-shot deal; if w is 0.9 you can expect roughly 10 more rounds (the expected number of rounds is 1 ÷ (1 − w)).
Now try an almost insultingly simple strategy: tit-for-tat, or TFT — cooperate on the first round, then copy whatever the other side did last round. Reach out first, then mirror. Anatol Rapoport submitted it to the strategy tournament Robert Axelrod ran in 1980, and this handful of lines won the first round (14 entries). After Axelrod published the results — including a full account of why it won — he ran a second tournament, and among 62 entries from six countries it won again.
Why? Run the numbers from the last section. Drop one incorrigible defector (call it "always defect") into a population of TFT players:
Two TFT players cooperate every round: 3 + 3w + 3w² + … = 3 ÷ (1 − w).
"Always defect" against TFT takes a free 5 in round one, after which TFT never cooperates again and both take 1 per round: 5 + w ÷ (1 − w).
Require the first to be at least the second and you get w ≥ (5 − 3) ÷ (5 − 1) = 0.5. In other words, once the chance of a next round is better than even — about two more rounds on average — the person who took the free lunch is already behind on the running total.
That threshold deserves a moment. It contains no term for character. Same person, same payoffs: move w from 0.4 to 0.6 and the rational move flips from defect to cooperate. So "this industry has a bad culture" and "this industry has low w" are often descriptions of the same thing — except the second one can be computed, and changed.
A word on TFT's weaknesses, so nobody treats it as a cure-all: it is unforgiving. One misunderstanding between two TFT players (they meant to cooperate, the signal got garbled) and they fall into an endless retaliation loop neither can exit. Win-stay, lose-shift (Nowak and Sigmund, 1993) does better under noise — repeat your last move if you were happy with the outcome, switch if you were not. And Press and Dyson proved in 2012 that the iterated prisoner's dilemma contains a class of extortionate strategies that can force the other side's payoff into a ratio of their choosing. TFT was never the optimum. It only demonstrates one thing: once w is high, even a very stupid rule can hold cooperation in place.
To get someone to behave, first make "there will be a next time" a fact they can verify: break one large contract into several tranches with explicit renewal points, shorten the settlement cycle, write the exit terms out concretely. These change behaviour far more than adding a good-faith clause — the clause does not move w, and the structure does.
The second change is stranger: change nothing at all except "play everyone" into "play the few people next to you."
Nowak and May did exactly this in 1992. Put cooperators and defectors on a square grid; each cell plays the previous section's game against its eight neighbours; then each cell copies the strategy of whichever cell in its neighbourhood (including itself) scored highest. No memory, no retaliation, no recognising anyone — purely "copy whoever nearby is doing best." → cellular automata
In a well-mixed population, we computed the ending last section: cooperators fall to zero, no exceptions. On a lattice, with the same payoffs and the same starting mix, the ending is entirely different.
The mechanism takes one sentence: as soon as cooperators clump, everyone inside the clump is dealing only with cooperators and scoring full marks, while defectors can only nibble at the edge, and once the edge is eaten there is nobody left to eat. Benefits stay local — and so do costs. That is enough. Nowak calls it network reciprocity.
It can even be quantified. Ohtsuki, Hauert, Lieberman and Nowak gave an almost improbably clean approximation in 2006: if cooperating once gives the other person a benefit b and costs you c, and each node in the network has on average k neighbours, then natural selection favours cooperation when b / c > k. The more neighbours, the harder cooperation is to grow.
That rule turns a vague moral topic into a computable engineering problem. You usually cannot change b/c — that is set by the nature of the task. But you can nearly always change k: split a 200-person channel into twenty groups of ten and the threshold drops by an order of magnitude.
To make "lending a hand" normal, reduce the number of people each person faces rather than increasing exhortation and recognition schemes. Splitting into small teams, assigning ownership, fixing pairings, breaking a big channel into small ones — all of these look like mere organisational form, and all of them are moves on k, which is the term that appears in the inequality.
The last two sections were models. Go and look at how humans actually solve these problems and you find something slightly embarrassing for the modellers: they almost never rely on a clever strategy. They rely on rules.
Garrett Hardin's 1968 "Tragedy of the Commons" concluded that a shared pasture must be overgrazed, so there are only two ways out: nationalise it or cut it into private plots. What Elinor Ostrom spent decades doing was going to look at actual common-pool resources — Swiss alpine meadows, Spanish irrigation canals, Philippine water associations, Japanese village commons. Some had indeed collapsed. But a substantial set had run stably for centuries, neither nationalised nor privatised. In 1990 she distilled what those cases had in common into eight design principles; in 2009 she received the Nobel Prize in economics for the work.
One widespread misreading is worth correcting along the way: what Hardin described is an unmanaged open-access resource (anyone may enter, anyone may take), whereas a commons in the historical sense always had boundaries, rules and a membership roll. Conflating the two had consequences — over the centuries a great many functioning common-property institutions were dismantled as things that were doomed anyway.
Three of those eight principles map directly onto this issue's mechanisms. Clear boundaries — who is in the pool and who is not; without them you are not playing a repeated game at all, because you cannot even tell who the opponent is. Monitoring done by the users themselves — defection has to be visible, or you cannot distinguish who is carrying and who is shirking. Graduated sanctions — trivial for the first offence, escalating for repeat offenders; the problem with a severe penalty is not that it is harsh but that it is so harsh nobody is willing to impose it, so it becomes decorative.
The punishment part has hard evidence from the lab. Fehr and Gächter ran a public goods game in 2002: everyone gets a sum, may put some of it into a common pot, the pot is multiplied and split evenly. With no punishment allowed, contributions slide from around two-thirds down to nearly nothing — not because people are bad, but because someone who has been taken advantage of stops volunteering to be taken advantage of. Add one rule, "you may spend your own money to punish others," and contributions climb back up towards the maximum.
Put the three sections together and you get an ordering that runs against common sense: raising the moral standard is the most expensive, slowest and least reliable of the available levers. Drawing boundaries, making behaviour visible, and making punishment cheap can each be done by a small group in a few weeks — and once done, none of them depends on anybody staying virtuous.
Before you introduce penalties, check two things: whether the boundary is clear (who is inside, who is outside, by what criterion) and whether behaviour is visible. Miss either one and penalties will not only fail to work, they will be turned on the people doing the honest work — and as the next section shows, that is not a hypothetical.
All of it shares one soft spot: the whole edifice rests on a payoff matrix, and in the real world you are usually the one who filled that matrix in.
The matrix is invented. Saying "this is a prisoner's dilemma" claims you know what each of the four outcomes is worth to each side. In real conflicts those numbers are rarely measurable, and the two sides may not even share an ordering — you think you are playing a prisoner's dilemma, they are playing Hawk-Dove, or they do not care about winning at all and only care about not appearing to have lost. In that situation the matrix is not an analytical tool, it is a costume put on a conclusion you already held. This is complexity science's most common disease, and the game-theory branch has it worst.
Space does not always help. "Structure promotes cooperation" has become close to a slogan, but Hauert and Doebeli landed a solid counterexample in Nature in 2004: switch to the snowdrift game (two drivers blocked by a snowdrift; shovelling costs you, but one shoveller is enough for both to drive on, so if the other refuses you are still better off shovelling) and spatial structure often lowers the level of cooperation. Those three frames above are not a universal theorem — they are quite fussy about the payoff structure. Do not treat "add some spatial structure" as a general prescription.
Punishment can run backwards. The Fehr and Gächter result is so tidy that it often gets treated as a general law. Herrmann, Thöni and Fehr took the same experiment to sixteen participant pools around the world and published the result in Science in 2008: antisocial punishment is real. In a substantial number of societies, people punish those who contribute more than they do, and cooperation consequently fails to rise. "Give people a channel for punishing free-riders" does not hold in those places, and whether it holds correlates with local rule of law and civic norms — which is no longer something game theory can answer.
b/c > k has preconditions. The rule is beautiful, but the derivation assumes weak selection, a particular update rule, and roughly regular graphs. Change the update rule and the coefficient changes. Use it as an order-of-magnitude intuition; be careful about plugging it into a specific decision as a formula.
Last and most important: this issue is about how cooperation is sustained, not about whether it should be. A price-fixing ring needs exactly the same things internally — high w, high visibility, graduated sanctions. Cartels, bid-rigging pools and the code of silence in a gang run on precisely the structure that neighbourly mutual aid runs on. So the toolkit is neutral: it tells you just as clearly how to dismantle a cooperation you do not want — lower w, scramble the pairings, let defectors stay anonymous and exit safely. That is exactly what Allied high command did in 1918 to the truce in the trenches.
Before using any of this, ask yourself one question: was this payoff matrix measured, or did I invent it? At minimum you should be able to say "if I changed this number to that one, here is how the conclusion would move." If you cannot, you are restating a judgement you already held in game-theoretic vocabulary — and stating the judgement plainly would at least be honest.
One possibility: it compresses a statistic — this person did not take the free lunch in past situations where w was low and taking it was safe. If so, trustworthiness is a measurable quantity with a very specific test: watch only what someone does when there is no next time. Another possibility: people really do internalise norms that do not depend on structure, and those norms are themselves what long-run structural selection produced. Distinguishing the two experimentally is not easy.
w can be raised through contract design, k can be lowered through organisational form, visibility can be supplied by a recording system. The magnitude of b/c is usually fixed by the nature of the task. So when b/c is naturally small — helping is expensive and does not help the other person much — should you give up on engineering cooperation and arrange things some other way entirely?
One candidate account: high contributors raise the reference standard for everyone and therefore threaten free-riders; knocking them down protects your relative position. If that is right, the direction punishment points depends on what people are comparing — absolute payoff or relative rank. Would switching an evaluation system from ranking to absolute standards reduce this kind of punishment?
It is cheap, it offends nobody, it requires changing no one's authority or workflow, and when it fails you can blame the decline of virtue. Drawing boundaries and installing monitoring both require touching specific people and specific permissions. That is itself a game: whoever proposes the structural fix bears the cost alone while the benefit is shared by everyone.
Topic 26 made the point that a model changes the thing it models once it is published. Once the structural conditions for cooperation are widely understood, the first parties to deploy them at scale may well be those most able to change structure — platforms, employers, governments. Does that mean the net effect of this kind of knowledge depends mostly on who learns it first?