We report the experimental results on a game with an outside option where forward induction contradicts with backward induction based on a focal, risk dominant equilibrium. The latter procedure yields the equilibrium selected by Harsanyi and Selten's (1988) theory, which is hence here in contradiction with strategic stability (Kohlberg and Mertens, 1986). We find the Harsanyi–Selten solution to be in much better agreement with our data. Since fairness and bounded rationality seem to matter we discuss whether recent behavioral theories, in particular fairness theories and learning, might explain our findings. The fairness theories by Bolton and Ockenfels (2000), Charness and Rabin (2002), or Fehr and Schmidt (1999), when calibrated using experimental data on dictator‐ and ultimatum games, indeed predict that forward induction should play no role for our experiment and that the outside option should be chosen by all sufficiently selfish players. However, there is a multiplicity of ‘fairness equilibria’, some of which seem to be rejected because they require too many levels of reasoning. We show that learning theories based on naive priors could alternatively explain our results, but not that of closely related experiments.