An experiment on forward vs. backward induction: how fairness and level k reasoning matter

Abstract

We report the experimental results o n a game with an outside optionwhere forward induction contradicts with backward induction based on a focal, riskdominant equilibrium. The latter procedure yields the equilibrium selected by Harsanyiand 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 bet-ter agreement with our data. Since fairness and bounded rationality seem to matter wediscuss whether recent behavioral theor ies, in particular fairness theories and learning,might explain our findings. The fairness theories by Bolton and Ockenfels (2000), Char-ness and Rabin (2002), or Fehr and Schmidt (1999), when calibrated using experimen-tal data on dictator- and ultimatum games, indeed predict that forward inductionshould play no role for our experiment and that the outside option should be chosen byall 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 ourresults, but not that of closely related experiments.