On the limits to rational learning

This paper summarizes recent work of Foster and Young (2001), which shows that some games are unlearnable in principle by perfectly rational players. That is, under any learning rule - including Bayesian updating of common priors - the players' strategies fail to come close to Nash equilibrium with probability one. Furthermore at least one of them is unable to predict the behavior of the other in an asymptotic sense. This result can be interpreted as an "uncertainty principle" that applies to some kinds of interactive learning problems. (C) 2002 Elsevier Science B.V. All rights reserved.