The dilemma
A move that wins either way
In the matrix, each cell gives your payoff first and the other’s second. Read it one column at a time. If the other cooperates, defecting gives you 5 and cooperating gives you 3. If the other defects, defecting gives you 1 and cooperating gives you 0. A move that is your best reply to anything the other might do is a dominant strategy, and here defecting is one.
| The other cooperates | The other defects | |
|---|---|---|
| You cooperate | 3, 3 | 0, 5 |
| You defect | 5, 0 | 1, 1 |
A Nash equilibrium is a pair of moves in which neither player can do better by changing only their own. The dilemma has one: both defect, at (1, 1). It is inefficient, because both would be better off at (3, 3), and neither can get there alone.
Why taking turns does not help
The payoffs also meet a second condition, 2R > T + S. Per round, it reads 3 > 2.5: cooperating every time pays more than taking turns at defecting, where one player gets 5 and the other 0, round after round. Without it, two players could beat cooperation by alternating. The condition comes from Axelrod and Hamilton (1981).
The repeated dilemma
When two people will meet again, the future weighs on every round: defecting today can cost you the other’s cooperation tomorrow. Axelrod and Hamilton (1981) model it as the chance that the same two meet again. Axelrod invited programs to play the repeated dilemma against one another in a tournament, and the winner was Tit-for-Tat: cooperate first, then copy whatever the other did last. To play the repeated game, the place is The Evolution of Trust (opens in a new tab), by Case (2017).
Cheap talk
In theory, a message that is free and commits no one should not change what anyone does. If defecting pays more, it still pays more after you say you will cooperate, and the other knows it, so they have no reason to believe you. Experiments find otherwise. Vanberg (2008) starts the abstract of his article there: “Numerous psychological and economic experiments have shown that the exchange of promises greatly enhances cooperative behavior in experimental games.” Why that happens is the question the rest of this site follows.