The two-player original
The prisoner dilemma comes from a story about two suspects held separately. Each can stay silent or betray the other. The payoffs are arranged so that betraying is the better choice for each, whatever the other does, yet both betraying leaves them worse off than both staying silent. A compact version uses cooperate (C) and defect (D):
| Other cooperates | Other defects | |
|---|---|---|
| You cooperate | (3, 3) | (0, 4) |
| You defect | (4, 0) | (1, 1) |
If the other cooperates, defecting gives you 4 instead of 3. If the other defects, defecting gives you 1 instead of 0. Defecting is a dominant strategy, so both defect and each gets 1, although mutual cooperation would have given 3 each. Every player is following sound individual reasoning, and the group result is poor.
Why more players makes it more common
With more than two players, the dilemma often takes the form of a shared pool or shared risk. Each player can contribute to something that benefits everyone, or hold back and keep the benefit private. The temptation is that you receive a share of what others contribute whether or not you contribute yourself. This is often called free riding.
A four-player example
Four players each have 1 coin. Each secretly chooses to put the coin into a shared pool or keep it. The pool is doubled, and the result is split equally among all four players, whether or not they contributed.
If all four contribute, the pool is 4 coins, doubled to 8, and each player receives 2. Each began with 1 and now holds 2.
Now consider one player’s decision when the other three contribute.
- If you contribute, the pool is 4, doubled to 8, and you receive 2.
- If you keep your coin, the pool is 3, doubled to 6, and you receive 6/4 = 1.5, plus the 1 coin you kept, for 2.5 in total.
Keeping is better by 0.5 coins. This holds whatever the others do. Each coin you contribute returns only 2/4 = 0.5 coins to you, because the doubled value is shared four ways, so contributing always costs you 0.5 net. Keeping is a dominant strategy. If everyone reasons that way, nobody contributes, the pool is empty, and each player holds 1 coin, which is worse than the 2 each from full contribution.
The same structure applies to larger groups with different numbers. As long as each contributed coin returns less than one coin to the contributor, but more than one coin to the group in total, the dilemma is there.
Where it shows up in games
Many game mechanics create this tension:
- Shared defence or shared objectives. In games where players cooperate against the game itself but still score individually, there is a temptation to let others pay the costs while you take the rewards.
- Common resources. When players draw from a shared supply, each benefits from taking more, but heavy use by everyone depletes it. This is the tragedy of the commons in game form.
- Alliances and leader-checking. In multiplayer games with a runaway leader, everyone benefits if someone slows the leader, but each prefers it to be someone else who pays the cost. A coalition against the leader is a contribution problem.
- Negotiated deals. In trading games, honouring a promise that you can no longer enforce on yourself is a defection decision. Settlement-style board games make this concrete through resource trading.
- Online team play. In team matches, a player may prefer personal statistics over team objectives, while the team result depends on enough players doing the group work. The structure appears in multiplayer win chance, where the contribution of each member shapes the group’s odds.
Why cooperation sometimes survives
Real groups often do better than the one-shot theory predicts. Several things help.
Repetition. If the same players meet again and again, defecting today can be punished tomorrow. A simple conditional approach such as cooperating first and then copying the other player’s last move is a famous strategy in repeated games. It is not guaranteed to win, but it shows how future consequences can make cooperation rational. Repetition helps only if the game’s end is not clear. If everyone knows round ten is the last, defecting in round ten is tempting, and by backward reasoning of the kind used in game trees, the unravelling can spread to earlier rounds in theory. In practice people often cooperate for longer than the theory predicts.
Reputation. In groups that play many games together, a player known to defect is likely to be left out of deals. Reputation turns a series of one-shot games into a repeated one.
Communication and agreements. Talking does not change the payoffs, but it can build shared expectations and make cooperation visible. Costly promises, such as handing over something in advance, are more credible than free ones.
Changing the payoffs. Rules that reward contributions, penalise free riding or make contributions visible can reshape the incentives. Game designers use this deliberately, for example by awarding a bonus to whoever helped most, so that defecting is no longer dominant.
Other motives. Many players value fairness, enjoyment or group harmony. Those preferences belong in the payoffs. If they are strong enough, the dilemma disappears, since contributing is no longer a sacrifice in the sense the table assumed.
Is it really a dilemma?
Before concluding that a situation is a prisoner dilemma, check the features that define it:
- Each player does better by defecting, whatever the others do.
- Everyone does better when all cooperate than when all defect.
- There is no way for players to bind themselves to cooperating.
If a game lacks one of these, such as a binding agreement, a different strategy may be right. And if cooperation is better for you in some cases, as in a stag-hunt-style game where you want to join a group effort if enough others do, the equilibrium logic differs. You may then have more than one stable outcome, one of them good.
Practical points
- Identify the temptation. Ask what each player gains by holding back, and what the group loses if everyone does.
- Look for repetition. In long campaigns or regular groups, cooperation is easier to sustain and defection costlier than the single-game numbers show.
- Do not assume bad faith. A player who defects may be responding to incentives, not to character. Fixing the incentive often works better than blaming the player.
- Think about what the others expect. If you believe others will free ride, contributing alone may only lose you coins. A pattern of small, reversible commitments is a cautious way to test trust.
The central lesson is that good individual reasoning does not always add up to a good group result. When it does not, the fix usually lies in the structure of the game, not in asking everyone to try harder.