  Stern-judging is one of the best-known assessment rules in indirect
reciprocity. Indirect reciprocity is a fundamental mechanism for the evolution
of cooperation. It relies on mutual monitoring and assessments, i.e.,
individuals judge, following their own assessment rules, whether other
individuals are "good" or "bad" according to information on their past
behaviors. Among many assessment rules, stern-judging is known to provide
stable cooperation in a population, as observed when all members in the
population know all about others' behaviors (public information case) and when
the members never commit an assessment error. In this paper, the effect of
assessment error and private information on stern-judging is investigated. By
analyzing the image matrix, which describes who is good in the eyes of whom in
the population, we analytically show that private information and assessment
error cause the collapse of stern-judging: all individuals assess other
individuals as "good" at random with a probability of 1/2.
