  We introduce a toy probabilistic model to analyze job-matching processes in
recent Japanese labor markets for university graduates by means of statistical
physics. We show that the aggregation probability of each company is rewritten
by means of non-linear map under several conditions. Mathematical treatment of
the map enables us to discuss the condition on which the rankings of arbitrary
two companies are reversed during the dynamics. The so-called `mismatch'
between students and companies is discussed from both empirical and theoretical
viewpoints.
