A number of recent papers have highlighted the importance of uncertain
ty about others' information in models of asymmetric information. We i
ntroduce a notion that reflects the depth of knowledge in an informati
on system. We show how the depth of knowledge can be used to bound the
effect of higher order uncertainty in certain problems. We further pr
ovide bounds on the size of bubbles in finite horizon rational expecta
tions models where the bounds depend on the depth of knowledge.