A paradox of rational choice: Reflections on rational non-cooperation in symmetrical games (Q1283284)

In the prisoner's dilemma, two prisoners who committed a joint crime are interrogated separately. If none confesses, each gets a light sentence of \(b\) years. If only one of them confesses, he gets \(a<b\) years and the other gets \(d>b\) years. If both confess, each gets \(c\in (b,d)\) years. In this non-cooperative game, a rational (stable) strategy is to confess. However, if both players do not follow this rational strategy and, e.g., each flips a coin to decide whether to confess or not, the resulting expected outcome can be better than for two rational players. Thus, ``irrational'' behavior can lead to a better result than the rational one -- a seeming paradox. The author analyzes a similar paradox on the example of other games, including general \(n\)-player games which are symmetrical (invariant under arbitrary permutation on players).