The results of computer simulations are presented which give evidence for the existence of an interesting symmetry in a many-agent model which demonstrates, in special cases, both Bose-Einstein and Fermi-Dirac statistics. This symmetry is expressed in the close vicinity of the mean values of the degree of ultrametricity and the fraction of isosceles of the sets of agent memories (histories) coded by two different information-loss coding schemes. It is shown that this (in some sense) approximate statistical supersymmetry is probably broken at low temperatures--below some condensation limit. This breaking leads to the appearance of specific coding schemes for boson and fermion histories. The meaning of this specificity is revealed by applying the interpretation of the many-agent model described earlier [A. A. Ezhov and A. Yu. Khrennikov, Phys. Rev. E 71, 016138 (2005)].