In addition to Prase's comment on the possibility of an unbounded chain of strategies (and building off of what I think shminux is saying), I'm also wondering (I'm not sure of this) if bounded cognitive strategies are strictly monotonically increasing? i.e.( For all strategies X and Y, X>Y or Y>X). It seems like lateral moves could exist given that we need to use bounded strategies - certain biases can only be corrected to a certain degree using feasible methods, and mediation of biases rests on adopting certain heuristics that are going to be better optimized for some minds than others. Given two strategies A and B that don't result in a Perfect Bayesian, it certainly seems possible to me that EU(Adopt A) = EU(Adopt B) and A and B dominate all other feasible strategies by making a different set of tradeoffs at equal cost (relative to a Perfect Bayesian).