We demonstrate that in simple 2 x 2 games (cumulative) prospect theory

preferences can be evolutionarily stable, i.e. a population of players with

prospect theory preferences can not be invaded by more rational players. This

holds also if probability weighting is applied to the probabilities of mixed

strategies. We also show that in a typical game with infinitely many strategies,

the “war of attrition”, probability weighting is evolutionarily stable.

Finally, we generalize to other notions of stability. Our results may help to

explain why probability weighting is generally observed in humans, although

it is not optimal in usual decision problems.