Two firms can both keep prices high and share healthy profits, or one can undercut the other and grab the market. If both undercut, both end up worse off than if neither had. This is the prisoner's dilemma, and it describes a surprising amount of life: price wars, arms races, doping in sport, overfishing, and the group project where nobody wants to do the boring part.
The setup
Each player chooses to cooperate or defect. A standard set of payoffs, the one Robert Axelrod used in his famous tournaments, looks like this (your payoff is listed first):
| They cooperate | They defect | |
|---|---|---|
| You cooperate | 3, 3 | 0, 5 |
| You defect | 5, 0 | 1, 1 |
What makes it a dilemma is the ordering. The temptation to defect (5) beats the reward for mutual cooperation (3), which beats the punishment for mutual defection (1), which beats the sucker's payoff (0).
Why defection wins a single round
Whatever the other player does, you score more by defecting: 5 instead of 3 if they cooperate, 1 instead of 0 if they defect. Defection is a dominant strategy, so two rational players both defect and each scores 1, even though both would prefer the 3 they could have had. Individual logic and collective interest point in opposite directions.
Five ways cooperation emerges
Martin Nowak's 2006 paper "Five rules for the evolution of cooperation" sorted the escape routes into five mechanisms:
- Direct reciprocity. If you will meet again, defecting today costs you cooperation tomorrow. With the payoffs above, a strategy of "cooperate until betrayed, then defect forever" keeps both players cooperating as long as each values the next round at least half as much as this one.
- Indirect reciprocity. Reputation lets cooperation travel beyond pairs: I help you because you have a record of helping others. Ratings, references and credit scores are reputation systems.
- Network reciprocity. When cooperators cluster, they mostly meet each other and earn high payoffs, while defectors at the edges meet fewer easy targets.
- Group selection. Groups with more cooperators can outperform and outlast groups of defectors, even if defectors do better within each group.
- Kin selection. Helping relatives helps shared genes. The benefit counts when relatedness times benefit exceeds the cost.
What Axelrod's tournaments found
Around 1980, Robert Axelrod invited researchers to submit computer strategies for a repeated prisoner's dilemma and ran them against each other. The simplest entry won both rounds: tit-for-tat, submitted by Anatol Rapoport. It cooperates on the first move and then copies whatever the opponent did last time.
Axelrod drew four lessons from the winners. Be nice: never defect first. Be retaliatory: punish defection immediately. Be forgiving: return to cooperation as soon as the other side does. Be clear: be easy for others to read.
Tit-for-tat has a weakness when moves are noisy. A single misread move can lock two tit-for-tat players into an endless echo of retaliation. Generous tit-for-tat, which occasionally lets a defection go unpunished, breaks the cycle and does better when mistakes happen.
The commons: many players at once
The tragedy of the commons is the many-player version: each fisher gains by taking one more fish, while the cost of a depleted stock is shared by everyone. The textbook answer was either privatisation or regulation from above.
Elinor Ostrom, who won the 2009 Nobel prize in economics, showed that many communities manage shared resources well with neither. Studying fisheries, forests and irrigation systems that had lasted for generations, she identified eight design principles they had in common:
- Clear boundaries around who may use the resource.
- Rules matched to local conditions.
- The people affected take part in making the rules.
- Monitoring by people accountable to the users.
- Graduated sanctions, starting small.
- Cheap, accessible ways to resolve conflicts.
- Outside authorities recognise the community's right to organise.
- For larger systems, these arrangements are nested in layers.
Designing for cooperation
You can rarely change people, but you can often change the game. That is the idea behind mechanism design:
- Lengthen the shadow of the future. Make interactions repeated and relationships long, for example with multi-year contracts or stable teams.
- Make behaviour visible. Reputation only works when people can see what others did.
- Start small. Cooperation forms more easily in small groups and clusters, then spreads.
- Punish gently, then firmly. Graduated sanctions keep honest mistakes from triggering a spiral.
- Change the payoffs. If defecting stops paying more than cooperating, the dilemma disappears.
To watch strategies compete over many generations, explore the replicator dynamics model, and compare the dilemma with a coordination game, where the hard part is agreeing which good outcome to pick rather than resisting temptation.